Factor and Remainder Theorem

Which binomial is a factor of
f(x)= x³ -6x² +3x +10?

• x + 1
• x + 2
• x + 5
• x + 10

Tags

CCSS.HSA.APR.B.2

What is the remainder when a³ - 4 is divided by a + 2?

• -2

• -6

• -12

• 0

What are the three linear factors for the polynomial given the possible rational roots?
 $x^3-3x^2-4x+12;\ given:\pm2,\pm3$   

• (x-2) (x+2) (x+3) 

• (x-2) (x-2) (x+3)

• (x+2) (x+2) (x+3)

• (x-2) (x+2) (x-3)

If f(x) = 3x² -9x -20, find the value of f(5).

• 0

• 10

• 15

• -7

Find all the real zeros of the function

f(x) = 2x³ - 19x² + 38x + 24 given that x-4 is a factor.

• x = -4, -1/2, 6

• x = 4, -1/2, -6

• x = 4, -1/2, 6

• x = -4, 1/2, -6

Is (x - 2) a factor of $f\left(x\right)=x^3-8x^2+14x-4$  ?

      

• 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. 

One of the zeros of

 $f\left(x\right)=x^3-4x^2-25x+100$  is 5.  Factor $f\left(x\right).$  

•  $\left(x+4\right)\left(x-5\right)\left(x+5\right)$  

•  $\left(x-5\right)\left(x-4\right)\left(x+4\right)$  

•  $x\left(x-4\right)\left(x-5\right)$  

•  $\left(x-4\right)\left(x-5\right)\left(x+5\right)$  

Given $f\left(x\right)=3x^3-2x+k$ , and  $x+2$  is a factor of f(x), what is the value of k? 

• -2

• 20

• 2

• -20