Question

Divide 2x2 + 17x + 35 by x + 5

Answer 1

2 x + 7

Explanation:

Simplify the following:

(2 x^2 + 17 x + 35)/(x + 5)

Factor the quadratic 2 x^2 + 17 x + 35. The coefficient of x^2 is 2 and the constant term is 35. The product of 2 and 35 is 70. The factors of 70 which sum to 17 are 7 and 10. So 2 x^2 + 17 x + 35 = 2 x^2 + 10 x + 7 x + 35 = 5 (2 x + 7) + x (2 x + 7):

(5 (2 x + 7) + x (2 x + 7))/(x + 5)

Factor 2 x + 7 from 5 (2 x + 7) + x (2 x + 7):

((2 x + 7) (x + 5))/(x + 5)

((2 x + 7) (x + 5))/(x + 5) = (x + 5)/(x + 5)×(2 x + 7) = 2 x + 7:

Answer: 2 x + 7

Answer 2

the quotient is
`2x+7` and the remainder is 0

Explanation:

First, multiply
`x+5` by 2x and subtract the result from the polynomial
`2x^2+17x+35` to eliminate the first term in it.

`2x^2+17x+35-2x(x+5)=2x^2+17x+35-2x^2-10x=7x+35.`

Now, multiply
`x+5` by 7 and subtract the result from the polynomial
`7x+35:`

`7x+35-7(x+5)=7x+35-7x-35=0.`

Therefore,

`2x^2+17x+35=(x+5)(2x+7).`