Unit 2 Lesson 12

The polynomial function  $p\left(x\right)=x^3-3x^2-10x+24$  has a known factor of  $\left(x-4\right).$  Rewrite  $p\left(x\right)$  as the product of linear factors.

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.SSE.A.2

Tyler thinks he knows one of the linear factors of $P\left(x\right)=x^3-9x^2+23x-15.$  After finding that  $P\left(1\right)=0,$  he suspects that  $x-1$  is a factor of  $P\left(x\right).$  Here is the diagram he made to check if he's right, but he set it up incorrectly. What went wrong?

Tags

CCSS.HSA.APR.B.2

CCSS.HSA.APR.B.3

The polynomial function $q\left(x\right)=2x^4-9x^3-12x^2+29x+30$  has known factors  $\left(x-2\right)$  and  $\left(x+1\right).$  Which expression represents $q\left(x\right)$  as the product of linear factors?

•  $\left(2x-5\right)\left(x+3\right)\left(x-2\right)\left(x+1\right)$  

•  $\left(2x+3\right)\left(x-5\right)\left(x-2\right)\left(x+1\right)$  

•  $\left(2x+15\right)\left(x-1\right)\left(x-2\right)\left(x+1\right)$  

•  $\left(2x-15\right)\left(x+1\right)\left(x-2\right)\left(x+1\right)$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.SSE.A.2

Each year a certain amount of money is deposited in an account which pays an annual interest rate of $r$  so that at the end of each year the balance in the account is multiplied by a growth factor of  $x=1+r.$  $1,000 is deposited at the start of the first year, an additional $300 is deposited at the start of the next year, and $500 at the start of the following year. Which expression represents the value of the account at the end of three years in terms of the growth factor  $x.$  

•  $1,000x^3+300x^2+500x$  

•  $300x^3+500x^2+1,000x$  

•  $1,000x^3+500x^2+300x$  

•  $1,000x^2+300x+500$  

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.SSE.A.1

Each year a certain amount of money is deposited in an account which pays an annual interest rate of  $r$  so that at the end of each year the balance in the account is multiplied by a growth factor of  $x=1+r.$  $1,000 is deposited at the start of the first year, an additional $300 is deposited at the start of the next year, and $500 at the start of the following year. Determine (to the nearest cent) the amount in the account at the end of three years if the interest rate is 4%.
 

• $1,966.34

• $1,967.34

• $1,968.34

• $1,969.34

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.SSE.A.1

CCSS.HSF.BF.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

State the degree of $f\left(x\right)=5+7x-9x^2+4x^3.$  

• 1

• 2

• 3

• 4

Tags

CCSS.HSA.APR.A.1

What is the end behavior of $f\left(x\right)=5+7x-9x^2+4x^3.$  

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

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10

What is the end behavior of $f\left(x\right)=1+7x+9x^3+6x^4-2x^5.$  

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

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10

What are the points of intersection between the graphs of the functions $f\left(x\right)=\left(x+3\right)\left(x-1\right)$  and  $g\left(x\right)=\left(x+1\right)\left(x-3\right)?$  

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11