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Bot GPT 3.5 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).