Factors the polynomial [tex]x^2+5x-14[/tex] is [tex](x+7)(x-2)[/tex]
Step-by-step explanation:
Given:
Polynomial [tex]x^2+5x-14[/tex]
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
[tex]x^2+ (7-2)x -14[/tex]
[tex]x^2+ 7x - 2x - 14[/tex]
Step 3: Form pairs of terms and factor out GCD of the two pairs separately.
=[tex]x^2+ 7x - 2x -14[/tex]
= [tex](x^2+ 7x) -(2x + 14)[/tex]
= [tex]x(x+7)-2(x+7)[/tex]
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) = [tex](x+7)(x-2)[/tex]
