Question

What is the quotient (2x3 − 13x2 + 16x − 5) ÷ (x − 5)?

Answer 1

Answer:

Correct choice is A

Step-by-step explanation:

1 step. Multiply $x-5$ by $2x^2$ to get $2x^3-10x^2$ and subtract this polynomial from the polynomial $2x^3-13x^2+16x-5:$

$2x^3-13x^2+16x-5-(2x^3-10x^2)=2x^2-13x^2+16x-5-2x^3+10x^2=-3x^2+16x-5.$

2 step. Multiply $x-5$ by $-3x$ to get $-3x^2+15x$ and subtract this polynomial from the polynomial $-3x^2+16x-5:$

$-3x^2+16x-5-(-3x^2+15x)=-3x^2+16x-5+3x^2-15x=x-5.$

3 step.  Multiply $x-5$ by $1$ to get $1$ and subtract this polynomial from the polynomial $x-5:$

$x-5-(x-5)=x-5-x+5=0.$

Then

$2x^3-13x^2+16x-5=(x-5)(2x^2-3x+1).$