factor 15x^3 - 5x^2 + 6x - 2 by grouping. what is the resulting expression? (5x^2 + 2)(3x - 1) (5x^2 - 2)(3x…

factor 15x^3 - 5x^2 + 6x - 2 by grouping. what is the resulting expression? (5x^2 + 2)(3x - 1) (5x^2 - 2)(3x + 1) (15x^2 + 2)(x - 1) (15x^2 - 2)(x + 1)

factor 15x^3 - 5x^2 + 6x - 2 by grouping. what is the resulting expression? (5x^2 + 2)(3x - 1) (5x^2 - 2)(3x + 1) (15x^2 + 2)(x - 1) (15x^2 - 2)(x + 1)

Answer

Explanation:

Step1: Group the terms

Group the polynomial (15x^{3}-5x^{2}+6x - 2) into two - groups: ((15x^{3}-5x^{2})+(6x - 2))

Step2: Factor out the GCF from each group

From the first group (15x^{3}-5x^{2}), the GCF is (5x^{2}), so (15x^{3}-5x^{2}=5x^{2}(3x - 1)). From the second group (6x - 2), the GCF is (2), so (6x - 2=2(3x - 1))

Step3: Factor out the common binomial factor

We now have (5x^{2}(3x - 1)+2(3x - 1)). Factoring out the common binomial factor ((3x - 1)), we get ((3x - 1)(5x^{2}+2))

Answer:

((5x^{2}+2)(3x - 1))