Synthetic Substitution and Division

State if the given binomial is a factor of the given polynomial.

 $8x^4-23x^3+5x^2+18\ ;\ x-2$  

• Yes

• No

State if the given binomial is a factor of the given polynomial.

 $p^5+4p^4-17p^3+18p^2-64p+40\ ;\ p+7$  

• Yes

• No

State if the given binomial is a factor of the given polynomial.

 $x^5+16x^4+58x^3-28x^2+50x+7\ ;\ x+7$  

• Yes

• No

State if the given binomial is a factor of the given polynomial.

 $m^3+4m^{2\ }-44m-3\ ;\ m-5$  

• Yes

• No

State if the given binomial is a factor of the given polynomial.

 $2n^3+13n^2+29n+36\ ;\ n+4$  

• Yes

• No

Use synthetic substitution to evaluate the given value and determine the remainder.

 $f\left(x\right)=\ -5x^5-x^4+x^3-6x^2-1\ at\ x=-1$  

Use synthetic substitution to evaluate the given value and determine the remainder.

 $f\left(x\right)=x^4+5x^3-9x^2-18x-5\ at\ x=-6$  

• -10

• -7

• -5

• 11

Use synthetic substitution to evaluate the given value and determine the remainder.

 $f\left(x\right)=x^3+7x^2-12x-1\ at\ x=-5$  

Use synthetic substitution to evaluate the given value and determine the remainder.

 $f\left(x\right)=-4x^4+9x^3+8x^2+9x-13\ at\ x=3$  

• -11

• 10

• 11

• 5

Divide the polynomial

 $a^5+3a^4-4a^3-6a^2+3a-19$  by  $a+2$  

•  $a^4+a^3-6a^2+6a-9-\frac{1}{a+2}$  

•  $a^4+a^3-6a^2+6a-7+\frac{2}{a+2}$  

•  $a^4+a^3-6a^2+6a-12-\frac{5}{a+2}$  

•  $a^4+a^3-6a^2+6a-12-\frac{3}{a+2}$