How do you factor y=2x^4+21x^3+49x^2 ?

2 Answers
Apr 12, 2016

y = x^2(2x+7)(x+7)

Explanation:

First identify the factor common to all the terms which is x^2.
Thus
y = x^2(2x^2+21x+49)

The bracketed term can then be factored as
y = x^2(2x+7)(x+7)

Apr 12, 2016

y = x^2(2x + 7)(x + 7)

Explanation:

y = x^2f(x) = x^2(2x^2 + 21x + 49)
Factor f(x) by the systematic new AC Method (Socratic Search)
f(x) = 2x^2 + 21x + 49 = 2(x + p)(x + q)
Converted trinomial: f'(x) = x^2 + 21x + 98 = (x + p')(x + q')
p' and q' have same sign because ac > 0.
Factor pairs of (ac = 98) --> (2, 49)(7, 14). This sum is 21 = b.
Then, p' = 7 and q' = 14.
Back to f(x) --> 3p = (p')/a = 7/2 and q = (q')/a = 14/2 = 7. Factored form: f(x) = 2(x + 7/2)(x + 7) = (2x + 7)(x + 7). Therefor: y = x^2f(x) = x^2(2x + 7)(x + 7)#