Factorise factorise 45x squared + 36x + 20

Answer 1

To factorise the quadratic expression 45x^2 + 36x + 20, we first need to find two numbers that multiply to 45*20=900 (the product of the coefficients of the x^2 and constant terms) and add up to 36 (the coefficient of the x term).

The two numbers that fit these criteria are 30 and 30. So, we rewrite the middle term 36x as 30x + 6x.

45x^2 + 30x + 6x + 20

Next, we group the terms and factor by grouping:

(45x^2 + 30x) + (6x + 20)

Factor out the greatest common factor from each grouping:

15x(3x + 2) + 2(3x + 2)

Now, we factor out the common binomial factor:

(15x + 2)(3x + 2)

Therefore, the factorisation of 45x^2 + 36x + 20 is (15x + 2)(3x + 2).