Question B.4.2: Factoring four-term polynomials by grouping Factor each poly...

a. Factor the common factor x^{2} out of the first two terms and the common factor 3 out of the last two terms:

x^{3}+x^{2}+3 x+3=x^{2}(x+1)+3(x+1)             Factor out common factors.

=(x+1)\left(x^{2}+3\right)              Factor out the common factor (x + 1).

b. We must first arrange the polynomial so that the first group of two terms has a common factor and the last group of two terms also has a common factor.

aw + bc – bw – ac = aw – bw – ac + bc           Rearrange.

= w(a – b) – c(a – b)            Factor out common factors.

= (w – c)(a – b)                   Factor out a – b.