Divide 2x2 + 17x + 35 by 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

frika frika · Answer 2 · 2019-02-07T21:50:51+01:00

Answer:

the quotient is [tex]2x+7[/tex] and the remainder is 0

Step-by-step explanation:

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

[tex]2x^2+17x+35-2x(x+5)=2x^2+17x+35-2x^2-10x=7x+35.[/tex]

Now, multiply [tex]x+5[/tex] by 7 and subtract the result from the polynomial [tex]7x+35:[/tex]

[tex]7x+35-7(x+5)=7x+35-7x-35=0.[/tex]

Therefore,

[tex]2x^2+17x+35=(x+5)(2x+7).[/tex]