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22 Cards in this Set
- Front
- Back
- 3rd side (hint)
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The order of a polynomial is determined by? |
The highest power of x |
Powers |
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The coefficient proceeding the highest power of x is known as? |
The lead coefficient |
Follow the... |
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Any coefficient can take any value save for this exception. |
The lead coefficient can not be 0 |
Lead coefficient |
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A positive or negative lead coefficient corresponds with the polynomial being classified as? |
Positive or negative respectively |
Reread the question |
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How are polynomials added or subtracted? |
By adding or subtracting like terms (same order of x) |
X and x |
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How are polynomials multiplied? |
Each term of the first polynomial is multiplied by each term of the second. The products are then added to combine like terms. |
Think dot product |
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When are two polynomials equal? |
They share the same coefficients and the same orders of x. |
Identity property? |
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The remainder theorem says that |
when f(x) is divided by (x-p) the remainder is given by f(p) |
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The factor theorem says that |
if f(p)=0 then (x-p) is a factor |
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f(x) divided by g(x) can be written using a quotient and a remainder as |
f(x)/g(x) = q(x) + r/g(x) |
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To solve any polynomial you need to |
factorize and set the function equal to zero |
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LISA stands for |
Label, Intercepts, Stationary points, Asymptotes |
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A turning point |
location of a local maximum or minimum |
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The maximum number of turning points of a polynomial is |
one less than the degree |
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A repeated root is means there is less turning points than the maximum number. A repeated root is represented as |
a flattening of the 'vertex' in an even repeated root, a flattening of the 'inflection' point in an odd repeated root. |
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To find the equation of a polynomial from its graph don't forget this at the front of the factored form |
a as the coefficient of the lead term. You would divide zero by this when solving so we must remember that it is there when we go backwards |
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b^2-4ac |
discriminant |
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If discriminant is more than zero |
quadratic function has two real roots |
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If discriminant is equal to zero |
quadratic function has one repeated root |
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If a quadratic function has no real roots, the discriminant is |
negative |
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If a quadratic is positive for all x then the discriminant is |
negative |
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If a quadratic is negative for all x then the discriminant is |
negative |
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