Unit 2 Lesson 14

We know these things about a polynomial function,  $f\left(x\right):$  it has exactly one relative maximum and one relative minimum, it has exactly three zeros, and it has a known factor of  $\left(x-4\right).$  Which sketch of a graph represents  $f\left(x\right).$  

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Tags

CCSS.HSA.APR.B.3

Here is the graph of a polynomial function with degree 4. Select all of the statements that are true about the function.

• The leading coefficient is positive.

• The constant term is negative.

• It has 4 linear factors.

• One of the zeros is x =2.

• It has 2 relative maximums.

Mai graphs a polynomial function, $f\left(x\right),$  that has three linear factors  $\left(x+6\right),\ \left(x\ +2\right),$  and  $\left(x-1\right).$  But she makes a mistake. What is her mistake?

What is the degree of $f\left(x\right)=2x^3-3x^5-x^2+1.$  

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Which description matches the function: $f\left(x\right)=2x^3-3x^5-x^2+1?$  

• As $x$   gets larger and larger in the either the positive or the negative direction, $f\left(x\right)$   gets larger and larger in the positive direction.

• As $x$   gets larger and larger in the positive direction, $f\left(x\right)$   gets larger and larger in the positive direction. As $x$   gets larger and larger in the negative direction, $f\left(x\right)$   gets larger and larger in the negative direction.

• As $x$   gets larger and larger in the positive direction, $f\left(x\right)$   gets larger and larger in the negative direction. As $x$   gets larger and larger in the negative direction, $f\left(x\right)$   gets larger and larger in the positive direction.

• As $x$   gets larger and larger in the either the positive or the negative direction, $f\left(x\right)$   gets larger and larger in the negative direction.

Is this the graph of $g\left(x\right)=\left(x-1\right)^2\left(x+2\right)$  or  $h\left(x\right)=\left(x-1\right)\left(x+2\right)^2?$  Explain how you know.

Tags

CCSS.HSA.APR.B.3

Kiran thinks he knows one of the linear factors of $P\left(x\right)=x^3+x^2-17x+15.$  After finding that  $P\left(3\right)=0,$  Kiran suspects that  $x-3$  is a factor of  $P\left(x\right),$  so he sets up a diagram to check. Here is the diagram he made to check his reasoning, but he set it up incorrectly. What went wrong?

Tags

CCSS.HSA.APR.B.2

The polynomial function $B\left(x\right)=x^3+8x^2+5x-14$  has a known factor of  $\left(x+2\right).$   Rewrite  $B\left(x\right)$  as a product of linear factors.

Tags

CCSS.HSA.APR.B.2