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59 Cards in this Set
- Front
- Back
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How would you multiply a monomial by a polynomial?
4x(3x² - 6x - 7) = |
i) use the distributive property of multiplication, ii) when distributing, don't forget the rules of handling exponents
12x³ - 24x² - 28x |
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How would you multiply a binomial by a binomial? (x + a)(x + b)
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x²(first) + bx(outer) + ax (inner) + ab(last)
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What is the FOIL method?
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Process of multiplying binomials. Start with the FIRST terms, OUTER terms, INNER terms and then LAST terms. Then simplify by combining like terms where possible.
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Solve (x + 2)(x + 3)
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x² + 5x + 6
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(x + 2)(2x - 5) =
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2x² - x - 10
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When simplifying equations, how should you deal with exponents that are negative?
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You should try to express them as positive by converting them to reciprocals.
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Simplify
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Divide and combine like terms. As messy as this looks, there is no additional simplification that can be done
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Simplify
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8x² - 5x + 3
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What is an undefined fraction?
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fraction in which you divide by 0 - there is a rule in math which states that you can not divide by 0
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What does it mean to factor a polynomial?
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To __find__ the greatest factor, which divides into each term
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Factor 6x² - 10x³
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2x²(3 - 5x)
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When factoring polynomials, how do you factor the variables?
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Use the variable with the lowest exponent
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How would you convert a monomial with a variable that has a negative exponent? 7x⁻⁴
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i) write out the monomial as a fractional operation, ii) negative power = reciprocal with pos. power, ii) simplify it
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What is special about this expression? How is it factored? x² - 25
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binomial which is a difference of two perfect squares;
a² - b² = (a + b)(a - b) |
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Factor 4x² - 49
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(2x + 7)(2x - 7)
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What is special about this expression? How is it factored?
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Trinomial, addition:
a² + 2ab + b² = (a + b)(a + b) or (a + b)² |
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Factor x² + 8x + 16
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(x + 4)²
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What is special about this expression? How is it factored?
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Trinomial that follows the pattern:
a² - 2ab + b² = (a - b)(a - b) or (a - b)² |
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Factor x² - 8x + 16
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(x - 4)²
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When factoring polynomials, what can you deduce from x² ?
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That binomials must be of the form (x )(x )
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When factoring polynomial that do not fit any known patterns, what is the process?
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start with the first term, the last term, then the middle term.
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When factoring polynomial that do not fit any known patterns, what impacts the last term in the expression?
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What two numbers __multiplied__ will equal the last term.
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When factoring polynomial that do not fit any known patterns, what impacts the middle term in the expression?
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What __sum__ of two terms will equal the middle term.
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Factor: 3x² + 8x + 5
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(3x + 5)(x + 1)
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Factor: x² - 2x - 15
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(x - 5)(x + 3)
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a² - b² =
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(a + b)(a - b)
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a² + 2ab + b² =
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(a + b)(a + b)
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a² - 2ab + b² =
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(a - b)(a - b)
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What does it mean to factor a polynomial completely?
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Keep factoring (pulling out) factors until nothing more can be done
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Factor Completely: x⁴ + 3x³ - 10x²
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x²(x - 2)(x + 5)
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The square root sign is often referred to as a
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radical
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The number under the square root sign is called a
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radicand
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√(a x b) can be written as
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√a x √b
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When you have a square root of a product, it can be rewriten as
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product of the square roots
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A square root of a quotient is
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the quotient of the square roots
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Simplify the radical √48
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4√3
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√(a÷b) =
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√a ÷ √b
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√(25/49)
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5/7
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When operating on a radical, what is the principle root?
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Radicals can simplify to either a positive or negative number. Both are correct, however the principle root is the positive answer.
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7√5 + 6√5 =
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13√5
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How do you add radicals?
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if the radicals are the same, you add their coefficients
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How do you subtract radicals?
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if the radicals are the same, you subtract their coefficients
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How do you multiply radicals?
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multiply the radicands, and then the coefficients
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4√3 · 7√5 =
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28√15
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√60 ÷ √4 =
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√15
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27√60 ÷ 3√4 =
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9√15
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What is a complementary angle?
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Two angles, which complement each other and total 90°
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Two angles, which total 90° are known as
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complementary angles
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Two angles are complementary. One measures 3x + 10. The other measures 7x - 20. What is the value of x? What are the two angles?
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x = 10; 40° and 50°
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How do you divide radicals?
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divide the radicands, and then the coefficients
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What are supplementary angles?
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Two angles, which supplement each other along a straight angle, and total 180°
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Two angles, which total 180° and lie along a straight angle are
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supplementary angles
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Two angles are vertical. They measure 2x + 20 and 4x - 10. What is the measure of each angle?
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x=15; 50°
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Angle C and F are known as
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alternate interior angles; are acute and equal
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Angle D and E are known as
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alternate interior angles; are obtuse and equal
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Angles A and H are known as
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alternate exterior angles and are equal in measure
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Angles A and E are known as
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corresponding angles and are equal in measure
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Angles A and B are also known as
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adjacent angles. they are also supplementary because they lie across a straight angle
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How do you find the sum of interior angles of a polygon?
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(n - 2)180, where n is the number of sides
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