Question

How do you factor `2x^2 + 21x + 10`?

Answer 1

`(2x+1)(x+10)`

Explanation:

To factorise `2x^2+21x+10` we need to find two integers `p` and `q` such that:

`(2x+p)(x+q) -= 2x^2+21x+10`

`2x^2+(p+2q)x +pq -= 2x^2+21x+10`

`:. pxxq = 10` and `2q+p=21`

Considering factors of 10: `1xx10, 2xx5`

By inspection we see that `p=1` and `q=10` satisfy the conditions.

Hence: `2x^2+21x+10 = (2x+1)(x+10)`

Please note: After some practice, for simple quadratic functions that can be expressed as two linear factors, as in this example, you should be able to factorise the the function by inspection - without the need to express the logic above in written form. However, you will still perform the equivalent logic mentally.