Question

When the function f(x) is divided by x + 2, the quotient is x2 – 7x – 9 and the

remainder is 6. Find the function f(x) and write the result in standard form.

Answer 1

f(x)= x^3-5x^2-23x-12

Explanation:

Given:

function f(x) divided by x + 2, the quotient is x2 – 7x – 9 and the

remainder is 6

When a polynomial f(x) is divided by any another polynomial d(x) and there is q(x) and r then it can be written as:

f(x)= d(x)q(x) + r

Now putting values of d(x)= x+2, q(x)= x2 – 7x – 9 and r=6, we get

f(x)= (x+2)(x^2-7x-9)+6

f(x)= x^3 -7x^2-9x+2x^2-14x-18+6

= x^3-5x^2-23x-12 !