Question

How do you factor the trinomial `2x^2 + 7x + 3`?

Answer 1

The answer is `2x^2+7x+3=(2x+1)(x+3)`

Explanation:

We notice that `x^2` has 2 in front, so we, therefore, want an expression of the form
`(2x+a)(x+b)`
If we multiply, we get `2x^2+(a+2b)x+ab`

The two should be equal term for term, i.e.
`a+2b=7`
`ab=3`

Now if `ab=3` and both are to be whole numbers (no fraqtions), then `a=1, b=3` or `a=3, b=1`
`a=1, b=3` gives `a+2b=1+2*3=7`, which fits
`a=3, b=1` gives `a+2b=3+2*1=5`, which doesn't fit.

Therefore
`2x^2+7x+3=(2x+1)(x+3)`