Question

What do we get after factorising x^2+6x-27?

(a) (x+9)(x-3)

(b) (x-9)(x+3)

(c) (x-9)(x-3)

(d) (x+9)(x+3)

This question was posed to me in an international level competition.

I would like to ask this question from Factorisation of Polynomials and Algebraic Identities in chapter Polynomials of Mathematics – Class 9

Answer 1

Correct choice is (a) (x+9)(x-3)

To elaborate: To factorise  x^2+6x-27, we have to find two numbers ‘a’ and ‘b’ such that a+b=6 and a*b=27.

For that we have to find factors of -27, which are ±1, ±3, ±9.

Now we have to arrange two numbers from these numbers such that a+b=6 and a*b=27.

By considering this, we get two numbers +9 and -3

9 + (-3) = 6 and 9*-3 = -27

Now after manipulating terms, we get  x^2+9x- 3x-27.

x^2+9x- 3x-27 = x(x+9)-3(x+9)

= (x+9)(x-3).