How do you factor $50 + 5 a - a^{2}$ $50+5a - a^2$ ?

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Answer 1 · 2015-05-15T22:05:44

First notice that $a = 10$ $a=10$ is a zero of this polynomial, since if $a = 10$ $a=10$ we have

$50 + 5 a - a^{2} = 50 + 5 \cdot 10 - 10^{2} = 50 + 50 - 100 = 0$ $50+5a-a^2 = 50+5*10-10^2 = 50+50-100 = 0$

So $(10 - a)$ $(10-a)$ is one factor.

Comparing coefficients, the other is $(5 + a)$ $(5+a)$ , with $- 5$ $-5$ being another zero of the polynomial.

$(10 - a) (5 + a) = 50 - 5 a + 10 a - a^{2} = 50 + 5 a - a^{2}$ $(10-a)(5+a) = 50-5a+10a-a^2 = 50+5a-a^2$

How do you factor 50+5a−a250+5a - a^2?