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23 Cards in this Set
- Front
- Back
The leading term of a polynomial is |
The leading term of a polynomial is the term with the highest power of x |
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The degree of a polynomial is |
The degree of a polynomial is the highest power of x |
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A monic polynomial has |
A monic polynomial has a leading coefficient of 1 |
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A zero of a polymonial is |
A zero of a polymonial is a value of x which makes the polynomial zero |
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The constant term of a polynomial is |
The constant term of a polynomial is the term with no variable (variable has power 0) |
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If P(x) = 0 the values of x which are solutions to this equation are called |
If P(x) = 0 the values of x which are solutions to this equation are called the roots of the polynomial equation. |
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For quadratic polynomial equations the __________ can indicate the number of roots |
For quadratic polynomial equations the discriminant can indicate the number of roots |
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A polynomial P ( x ) can be written as P(x) = A(x). Q(x)+ R(x) A(x) is Q(X) is R(X) is |
A polynomial P ( x ) can be written as P(x) = A(x). Q(x)+ R(x) A(x) is the divisor Q(X) is the quotient R(X) is the remainder |
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The degree of the remainder is |
The degree of the remainder is less than the degree of the divisor |
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Remainder theorem states |
Remainder theorem states that if P(x) is divided by (x - a) then the remainder is P(a) |
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Factor theorem states |
Factor theorem states that if (x - a) is a factor of P(x) then P(a) = 0 |
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If x - a is a factor of polynomial P(x), then a is a factor of |
If x - a is a factor of polynomial P(x), then a is a factor of the constant term |
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To factorise a polynomial |
To factorise a polynomial use the factors of the constant term and the factor theorem to find one (or more) factors and then use division to reduce polynomial to one that can be factorised |
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Solve 2cos³θ - cos²θ -cosθ = 0 |
Substitute x = cosθ, solve for x then find θ |
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When graphing a polynomial, the zeros give |
When graphing a polynomial, the zeros give the x-intercepts |
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When graphing a polynomial, the constant gives |
When graphing a polynomial, the constant gives the y-intercept |
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When graphing a polynomial, once the x-intercepts are plotted |
When graphing a polynomial, once the x-intercepts are plotted use the sign of the leading coefficient to determine whether graph starts above or below x-axis |
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When graphing a polynomial, a double root |
When graphing a polynomial, a double root causes the curve to touch the x-axis at that point |
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When graphing a polynomial, a triple root causes the curve to |
When graphing a polynomial, a triple root causes the curve to have a point of inflexion on the x-axis at that point |
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If x = a is a double root of P(x) =0 then |
If x = a is a double root of P(x) =0 then P(a) = 0 and P'(a) = 0 |
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For ax² + bx + c = 0 |
For ax² + bx + c = 0 ∑α = -b/a ∑αβ = c/a |
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For ax³ + bx² + cx + d = 0 |
For ax³ + bx² + cx + d = 0 ∑α = -b/a ∑αβ = c/a ∑αβγ = -d/a |
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For ax⁴ + bx³ + cx²+ dx + e = 0 |
For ax⁴ + bx³ + cx²+ dx + e = 0 ∑α = -b/a product of roots one at a time ∑αβ = c/a product of roots two at a time ∑αβγ = -d/a product of roots three at a time ∑αβγδ = e/a product of roots four at a time |