Question

Quadratic Expressions:Question 1

Which is a factor of x²+ 7x + 10?
Select one:
a x-5
bx-1
cx+5
dx+1

Answer 1

Option C. (x + 5)

Explanation:

This quadratic equation can either be solved using the quadratic formula or be factorised using The Double Bubble Method.

Double Bubble Method:

After listing the different pairs of factors 10, the pair (that would add together to give 7) are 2 and 5. These two factors will be used to rewrite +7x:

`x^(2) + 2x + 5x + 10`

Factorization by grouping (i.e factorising each separate group sharing a common factor) will then be applied:

`= x(x + 2) + 5(x + 2)`

The common factor, which is the (x + 2) expression, will be extracted:

`= (x + 2)(x + 5)`

∴
`x^(2) + 7x + 10` can be factorised to
`(x + 2)(x + 5)`

It is observed that a factor of the given quadratic equation is x + 5

∴Option C