Question

What numbers go in the gaps to
factorise the expression?
t² +9t + 14 = (t +_) (t+_)

Answer 1

(t + 7) (t + 2)

Step-by-step Step-by-step explanation:

To factorise a quadratic expression, we need to find two numbers that add up to the coefficient of the t term and multiply to the constant term.

In this case, the coefficient of the t term is 9 and the constant term is 14. The two numbers that add up to 9 and multiply to 14 are 2 and 7.

Therefore, we can factorise the expression as follows:

t² + 9t + 14

Doing middle term factorization:

t² + (7+2)t + 14

t² + 7t + 2t + 14

Take common from each two terms:

t(t+7)+2(t+7)

Take common and keep remaining in brackets.

(t + 7) (t + 2)

Therefore, the answer is 2 and 7.