Question

Factor the polynomial x^2+5x-14=

Answer 1

Factors the polynomial
`x^2+5x-14` is
`(x+7)(x-2)`

Explanation:

Given:

Polynomial
`x^2+5x-14`

To Find:

Factors of the polynomial=?

Solutions:

Step 1: Factorize 14 as 14 = -7 x 2 or 7 x -2 We have to find a pair, such that its product is equal to -14 and summation is equal to 5. Only one such pair is possible i.e. 7 and -2

7-2=5

7 x (-2)= -14

Step 2: Break middle term in terms of the summation of a pair of numbers such that its product is equal to c i.e. 14 in above case. We will write 5=7-2

`x^2+ (7-2)x -14`

`x^2+ 7x - 2x - 14`

Step 3: Form pairs of terms and factor out GCD of the two pairs separately.

=
`x^2+ 7x - 2x -14`

=
`(x^2+ 7x) -(2x + 14)`

=
`x(x+7)-2(x+7)`

Step 4: Again factor out GCD of remaining sum of products. Follow factorization procedure of binomials as explained earlier. Factor out (x+6) from sum of product,

=x(x+7)-2(x+7) =
`(x+7)(x-2)`