Question
Factorise x squared plus 4X + 3 on X squared plus 10x plus 21
Answers
GPT 3.5
To factorise x^2 + 4x + 3, we need to find two numbers that multiply to 3 (coefficient of the constant term) and add up to 4 (coefficient of the middle term). The two numbers are 1 and 3.
Therefore, x^2 + 4x + 3 can be factorised as (x + 1)(x + 3).
Now let's factorise x^2 + 10x + 21 using the same method. The two numbers that multiply to 21 and add up to 10 are 7 and 3.
Therefore, x^2 + 10x + 21 can be factorised as (x + 7)(x + 3).
So, the factorisation of x^2 + 4x + 3 over x^2 + 10x + 21 is:
(x + 1)(x + 3) / (x + 7)(x + 3) = (x + 1)/(x + 7)
Therefore, x^2 + 4x + 3 can be factorised as (x + 1)(x + 3).
Now let's factorise x^2 + 10x + 21 using the same method. The two numbers that multiply to 21 and add up to 10 are 7 and 3.
Therefore, x^2 + 10x + 21 can be factorised as (x + 7)(x + 3).
So, the factorisation of x^2 + 4x + 3 over x^2 + 10x + 21 is:
(x + 1)(x + 3) / (x + 7)(x + 3) = (x + 1)/(x + 7)