Perform the division. ( x 2 + 19 x + 90 ) ÷ ( x + 9 ) \left( x ^ { 2 } + 19 x + 90 ight) \div ( x + 9 ) ( x 2 + 19 x + 90 ) ÷ ( x + 9 ) A) x + 19 + 9 x + 9 , x ≠ − 9 x + 19 + \frac { 9 } { x + 9 } , x
eq - 9 x + 19 + x + 9 9 , x  = − 9 B) x + 9 , x ≠ 9 x + 9 , x
eq 9 x + 9 , x  = 9 C) x + 90 x + 9 , x ≠ − 9 x + \frac { 90 } { x + 9 } , x
eq - 9 x + x + 9 90 , x  = − 9 D) x − 1 + 100 x + 9 , x ≠ 9 x - 1 + \frac { 100 } { x + 9 } , x
eq 9 x − 1 + x + 9 100 , x  = 9 E) x + 10 , x ≠ − 9 x + 10 , x
eq - 9 x + 10 , x  = − 9

Question

Perform the division.   ( x 2 + 19 x + 90 )  ÷ ( x + 9 )  \left( x ^ { 2 } + 19 x + 90 ight)  \div ( x + 9 )  ( x 2 + 19 x + 90 )  ÷ ( x + 9 )  A)    x + 19 + 9 x + 9 , x ≠ − 9 x + 19 + \frac { 9 } { x + 9 } , x 
eq - 9 x + 19 + x + 9 9 ​ , x  = − 9 B)    x + 9 , x ≠ 9 x + 9 , x 
eq 9 x + 9 , x  = 9 C)    x + 90 x + 9 , x ≠ − 9 x + \frac { 90 } { x + 9 } , x 
eq - 9 x + x + 9 90 ​ , x  = − 9 D)    x − 1 + 100 x + 9 , x ≠ 9 x - 1 + \frac { 100 } { x + 9 } , x 
eq 9 x − 1 + x + 9 100 ​ , x  = 9 E)    x + 10 , x ≠ − 9 x + 10 , x 
eq - 9 x + 10 , x  = − 9

Kassandra Mlady · Accepted Answer

Final Answer : E, Explanation :   To divide   ( x 2 + 19 x + 90 ) (x^2 + 19x + 90) ( x 2 + 19 x + 90 )   by   ( x + 9 ) (x + 9) ( x + 9 )  , we can use polynomial long division or synthetic division. Factoring the numerator gives   ( x + 10 ) ( x + 9 ) (x + 10)(x + 9) ( x + 10 ) ( x + 9 )  . Dividing   ( x + 10 ) ( x + 9 ) (x + 10)(x + 9) ( x + 10 ) ( x + 9 )   by   ( x + 9 ) (x + 9) ( x + 9 )   cancels out the   ( x + 9 ) (x + 9) ( x + 9 )   term, leaving   x + 10 x + 10 x + 10   as the quotient.

Perform the division. $\left( x ^ { 2 } + 19 x + 90 \right) \div ( x + 9 )$

A) $\frac { 9 } { x + 9 } , x \neq - 9$
B) $\neq 9$
C) $\frac { 90 } { x + 9 } , x \neq - 9$
D) $\frac { 100 } { x + 9 } , x \neq 9$
E) $\neq - 9$

Definitions

Learning Objectives

Learning Objectives

Related questions