For the polynomial below, 3 and -2 are zeros.

Question

g(x) = x⁴ + 5x - 6x² - 42x - 36

Express g(x) as a product of linear factors.

Answer 1

(x-3)(x+2) = x^2 -x -6 divide into x^4 +5x^3 -5x^2 -41x -42

to get a quadratic (x^2 +6x+7)

(x-3)(x+2(x^2+6x +7)

coefficients changed slightly to get division to work without a remainder

possibly the problem was miscopied

2 real rational zeroes, -2 and 3

x^2 +6x +7

x = -6/2 +/-.5sqr(36-28)= -3 +/-.5sqr8

x = -3 +2.5sqr2 or -3-2.5sqr2

two irrational zeros, they always come in conjugate pairs

using decartes' rule of signs, 1 maximum positive real and 3 maximum negative real zeros