Factoring Polynomials, Division, Rational Zeros Thm.

k² -36

• (k+6)(k-6)

• (k-6)²

• (k+6)²

• (k+6)²(k-6)²

Find the root(s) of the function.

• x = 3
• x = {-3, -1, 2}
• x = {-3, 2}
• x = -1

Tags

CCSS.HSA.APR.B.2

CCSS.HSA.APR.B.3

CCSS.HSA.REI.B.4

What are all the possible rational roots of x³ - 4x² + 5x - 12?

• +-1, +-2, +-3, +-4, +-6, +-12
• +-1, +-2, +-3, +-4, +-6
• +-2, +-3, +-4, +-6, +-12
• +-1, +-2, +-4, +-6, +-12

Remember to look at your roots, multiplicity, and end behavior!!

Use your notes!

• y = ^_(x + 2)(x - 1)²

• y = -(x - 2)(x + 1)²

• y = (x - 2)(x + 1)²

• y = -x³

Tags

CCSS.HSA.APR.B.3

In the above graph, which root has a multiplicity of 2?

Remember to look at your roots, multiplicity, and end behavior!!

Use your notes!

• -1

• -3

• -120

• 4

Tags

CCSS.HSA.APR.B.3

            Is (x-2) a factor of             f(x)= x³-8x²+14x-4?

• Yes, (x-2) is a factor. There is a remainder.
• No, (x-2) is  not a factor. The remainder is zero.
• Yes, (x-2) is a factor. The remainder is zero.
• No, (x-2) is  not a factor. There is a remainder. 

Tags

CCSS.HSA.APR.B.2

Which of the following is a COMPLETE  list of all possible Rational Zeros?
f(x) = x³ + 2x² - 6x + 8

• ±1, ±8
• ±1, ±2, ±4, ±8
• ±1, ±2, ±4
• 1, 2, 4, 8

Tags

CCSS.HSA.APR.B.2

Solve by using Rational Root Theorem: 
x³ - 7x - 6 = 0

• 1, 2, 3
• -1, -2, - 3
• -1, -2, 3
• 1,-2,-3

Tags

CCSS.HSA.APR.B.2

State the possible rational zeros for each function.  Then find all rational zeros.

•  $Possibilities:\ \pm1,\ \pm\frac{1}{3}$   $Rational\ zeroes:\ -1\ multiplicity\ 2,\ -\frac{1}{3}$ 

•  $Possibilities:\ \pm1,\pm\frac{1}{3}$   $Rational\ Zeroes:0,\ -1\ multiplicity\ 2$ 

•  $Possibilities:\ \pm1,\ \pm5,\ \pm\frac{1}{2}$   $Rational\ Zeroes:\pm2,\ 5,\ -1$ 

•  $Possibilities:\ \pm1,\pm\frac{1}{3}$   $Rational\ Zeroes:-\frac{1}{5},\ -1\ multiplicity\ 2$ 

Consider that you know (x + 2) is a factor of the polynomial function p(x), find the total factorization of the function:

 $p\left(x\right)=x^3-4x^2-7x+10$  

• (x + 2)(x - 1)(x - 5)

• (x + 2)(x - 1)(x + 5)

• (x - 2)(x - 1)(x + 5)

• (x - 2)(x + 1)(x + 5)