Factorise 45x squared + 36x + 20

Answer 1

To factorize the quadratic expression 45x^2 + 36x + 20, we first need to find the factors of 45 and 20:

Factors of 45: 1, 3, 5, 9, 15, 45
Factors of 20: 1, 2, 4, 5, 10, 20

Now we need to find two numbers that multiply to 45*20=900 and add up to 36. The two numbers are 30 and 30.

Next, we rewrite the middle term (36x) using the two numbers we found:

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

Now, we can group the terms and factor by grouping:

5x(9x + 6) + 4(9x + 6)

Now we can see that we have a common factor of (9x + 6) in both terms:

(5x + 4)(9x + 6)

Therefore, the factorized form of 45x^2 + 36x + 20 is (5x + 4)(9x + 6).