Polynomial Functions

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Mathematics

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10th - 12th Grade

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Erich Myers

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5 Slides • 3 Questions

Polynomial Functions

Reteach on Algebra 2 Topic 3

Polynomial Functions

When you add and subtract polynomial expressions you can only add like terms.
Example:

$\left(2x^2+3x\ -3\right)\ +\ \left(3x^2-5x\ +6\right)$

2x^2+3x^2+3x-5x-3+6

5x^2-2x+3

Polynomial Functions

When you multiply polynomial expressions, you distributed every term in one parenthesis to every term in the second parenthesis.
Example:

\left(2x^2-5x+4\right)\left(x-3\right)

2x^2\left(x\right)+2x^2\left(-3\right)-5x\left(x\right)-5x\left(-3\right)+4\left(x\right)+4\left(-3\right)

2x^3-6x^2-5x^2+15x+4x-12

2x^3-11x^2+19x-12

Multiple Choice

Simplify $\left(3x^3-2x^{2\ }-\ 7\right)+\left(2x^2+6x\ -3\right)$

$3x^3+4x^2+6x\ -10$

$5x^3+4x^2-10$

$3x^3+6x-10$

$3x^3+6x+10$

Multiple Choice

$\left(5x^2+2x-3\right)\left(x-4\right)$

Simplify

$5x^3-18x^2-11x+12$

$5x^3+18x^2+11x+12$

$5x^2-18x^2-11x-12$

$5x^3-18x+11x+12$

Zeros of a Polynomial Function

When we are looking to solve a polynomial function, often times we are looking for the x-value that makes the whole function equal to zero.

Zeros of a Polynomial Function

Find the zeros of the following function:

f\left(x\right)=3x^3-9x^2-12x

Factor\ f\left(x\right)=3x\left(x^2-3x-4\right)

Factor\ trinomial\ f\left(x\right)\ =\left(3x\right)\left(x-4\right)\left(x+1\right)

The\ zreos\ of\ the\ function\ are\ x=0,\ x=4,\ x=-1

Multiple Choice

$f\left(x\right)=x^3-8x^2+16x$

Find the zeros of the following function:

$x=0,\ x=4,\ x=-4$

$x=0,\ x=4$

$x=0,\ x=-4$

$x=0,\ x=8,\ x=-16$

Polynomial Functions

Reteach on Algebra 2 Topic 3

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