Question

Factor the trinomial 5x2+21x+18

Answer 1

(x+3)(5x+6)

Explanation:

To factor the trinomial
`\sf 5x^2 + 21x + 18`, we can use the following steps:

1. Find two numbers that add up to 21 and multiply to 90.
2. Split the middle term of the trinomial into these two numbers.
3. Factor the trinomial as (x + a)(x + b).

The two numbers 15 and 6 satisfy both conditions:

15+ 6 = 21

15 × 6 = 90

Therefore, we can split the middle term of the trinomial as follows:

`\sf 5x^2 + 15x + 6x + 18`

We can now factor the trinomial as follows:

`\sf (5x^2 + 15x) + (6x + 18)`

`\sf = 5x(x + 3) + 6(x + 3)`

`\sf = (x+3)(5x+6)`

Therefore, the factored form of the trinomial is (x+3)(5x+6).