Question

Factor completely

`3x²+20x-7`
Please show all workings

Answer 1

Explanation:-

First Method: (By splitting the middle term)

We have to find p and q such that p+q = 20 and

pq = 3×(-7) = -21

Let us looks for the pair of factors of -21 such that their sum is 20 and product is -21.

20 = 21 - 1 and -21 = 3(-7)

∴ 3x² + 20x - 7 = 3x² + 21x - 1x - 7

= 3x(x + 7) -1(x + 7)

= (x + 7)(3x - 1)

Second method: (Using the factor theorem)

Answer 2

• (x + 7)(3x - 1)

Explanation:

See the steps below:

• 3x² + 20x - 7 =
• 3x² + 21x - x - 7 =
• 3x(x + 7) - (x + 7) =
• (x + 7)(3x - 1)