Question

eli uses the factor theorem to determine whether x−2 is a factor of 6x5−22x2 11x−126.how does he proceed to the correct answer?

Answer 1

Hello,

Explanation:

`P(x)=6x^5-22x^2+11x-126\\\\P(2)= 6*2^5-22*2^2+11*2-126=0\\\\x-2\ is\ well\ a \ factor\ of\ P(x).\\\\\begin{array}c&x^5&x^4&x^3&x^2&x&1\\---&---&---&---&---&---&---\\&6&0&0&-22&11&-126\\x=2&&12&24&48&52&126\\---&---&---&---&---&---&---\\&6&12&24&26&63&0\end {array}\\\\P(x)=6x^5-22x^2+11x-126=(x-2)*(6x^4+12x^3+24x^2-26x+63)\\`