Question

given that (x-3) is a factor of x^4-x^3-8x^2+ax+12 show that (x+a) is a factor of x^2-2x+4​

Answer 1

$(x - 3) \\ x - 3 = 0 \\ x = 0 + 3 \\ x = 3 \\ \\ {x}^{4} - {x}^{3} - 8 {x}^{2} + ax + 12 = 0 \\ {3}^{4 } - {3}^{3} - 8 \times {3}^{2} + a \times 3 + 12 = 0 \\ 81 - 27 - 72 + 3a + 12 = 0 \\ - 30 + 3a = 0 \\ 3a = 0 + 30 \\ a = \frac{30}{3} \\ a = 10 \\ \\ {x}^{2} - 2x + 4 \: \: \: \: \: \: \: \: \: (x + a = 0) \\ {( - a)}^{2} - 2 \times ( - a) + 4 \\ { ( - 10)}^{2} - 2 \times ( - 10) + 4 \\ 100 + 20 + 4 \\ = 124$