Question

If a polynomial p(x) =x²-5x-14 os divided by another polynomial q(x) we get x-7/x+2,find q(x)

Answer 1

Question :- If a polynomial p(x) = x²- 5x - 14 os divided by another polynomial q(x) we get x-7/x+2,find q(x) ?

Solution :-

Given that, when p(x) is divided by q(x) , we get (x-7/x+2)

So,

→ p(x) / q(x) = (x - 7) / (x + 2)

→ p(x) /{(x - 7) / (x + 2)} = q(x)

→ q(x) = (x + 2) * p(x) / (x - 7) ---------- Equation (1).

Now, Solving p(x) :-

→ p(x) = x² - 5x - 14

→ p(x) = x² - 7x + 2x - 14

→ p(x) = x(x - 7) + 2(x - 7)

→ p(x) = (x - 7)(x + 2)

Putting value of p(x) in Equation (1) Now,

→ q(x) = {(x + 2) * (x - 7) * (x + 2)} / (x - 7)

(x - 7) will be cancel from both numerator and denominator,

→ q(x) = (x + 2)(x - 2)

using (a + b)(a - b) = a² - b² Now,

→ q(x) = (x² - 4) (Ans.)

Hence, value of q(x) will be (x² - 4).

Answer 2

Answer:

value of q(x) will be x^2-4