How to factor this trinomial?

Question

2x^2+13x+15

Answer 1

The trinomial 2x² + 13x + 15

Multiply first term 2x² and last term 15 = 30x²

The correct pair of the terms 10x and 3x multiply to 30x² and add to 13x.

Replace the middle term 13x with 10x + 3x.

= 2x² + 10x + 3x + 15

Group the terms into two pairs.

= (2x² + 10x) + (3x + 15)

Factor out 2x from the first group  and factor out 3 from the second group.

= 2x(x + 5) + 3(x + 5)

Factor out common term x + 5.

= (x + 5)(2x + 3)

Factoring of 2x² + 13x + 15 = (x + 5)(2x + 3).

Answer 2

The trinomial is 2x² + 13x + 15.

Compare the equation 2x² + 13x + 15 with ax² + bx + c.

a = 2, b = 13 and c = 15.

We need to find two numbers with a sum of  13 (b = 13) and a product of 2 · 15 or 30 (a = 2 and c = 15). Make an organised list of the factors of 30 and look for the pair of factors with the sum of 13.

Factors of 30 | Sum of Factors

      1, 30           |          31

      2, 15           |          17

      3, 10           |          13

The correct factors are m = 3 and n = 10.

The pattern form of 2x² + 13x + 15

= 2x² + mx + nx + 15

= 2x² + 3x + 10x + 15          (Substitute m = 3 and n = 10)

= (2x² + 3x) + (10x + 15)     (Group terms with common factors)

= x(2x + 3) + 5(2x + 3)         (Factor the GCF from each grouping)

= (2x + 3)(x + 5)                    (2x + 3 is the common factor)

The factor form of 2x² + 13x + 15 = (2x + 3)(x + 5).