Question

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

2x2 − 3x + 1

2x2 + 3x − 1

2x2 − 3x − 1

2x2 + 3x + 1

Answer 1

Correct answer is 2x2 − 3x + 1

Explanation:

Answer 2

Correct choice is A

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).`