Question

Factor f(x) into linear factors given that k is a zero of f(x). f(x) = x4 + 3x3 - 42x2 - 172x - 168; k=-2 (multiplicity 2) In completely factored form, f(x) = (Factor completely.)

Answer 1

Factor Theorem For factor any polinomial function f(x), ark is of the polinomial iff f(K) = 0 f(x) = 24+ 3x3_42x2_172x-168 k=-2 is a zero of f(n) We can say that (x+2) is a factor of f(x) Here since then Now at at-442-84 a 4+373-4222_172a-168 x + 2 4 +223 x3-4222_1722-168 +2x2 -442-1722-168 74402 882 - 84 x-168 784a7168 Х (x+2) (x²+x²-440-84) There fore , f(x) =

rt 2 x² - 42 a3 tar_440-84 x3 + 2x^ -ar - 4 4x-84 2x + - 420-84 +420 784 Х f(x) = (x+2)(x+2) Car-x-42) (+2)(2+2) (a²-7x+64-42) (x+2)(x+2) -7) (3+6)