Grade 12 Advance Functions Polynomials

Hey can anyone help me with this question? "Show that x+a is a factor of the polynomial P(x)=(x+a)4+(x+c)4-(a-c)4

Answers
Hi Lipi! You know from the factor theorem that if (x+a) is a factor of P(x), then P(-a) = 0. Since P(X) = (x+a)^4+(x+c)^4-(a-c)^4, P(-a) = (c-a)^4-(a-c)^4 = (c-a)^4 - [(-1)^4 * (c-a)^4] = (c-a)^4-(c-a)^4 = 0You have shown P(-a) = 0, therefore (x+a) is a factor of P(x)
mathematician99
07 July 2017
ok thanks
lipi
07 July 2017
Solution_Part_1_Factor_Question.jpg
ajmal_r
29 September 2017
Solution_Part_2_Factor_Question.jpg
ajmal_r
29 September 2017
Add an answer Cancel reply