factor -7x^3 + 21x^2 + 3x - 9 by grouping. what is the resulting expression? (3 - 7x)(x^2 - 3) (7x - 3)(3 +…

factor -7x^3 + 21x^2 + 3x - 9 by grouping. what is the resulting expression? (3 - 7x)(x^2 - 3) (7x - 3)(3 + x^2) (3 - 7x^2)(x - 3) (7x^2 - 3)(3 + x)

factor -7x^3 + 21x^2 + 3x - 9 by grouping. what is the resulting expression? (3 - 7x)(x^2 - 3) (7x - 3)(3 + x^2) (3 - 7x^2)(x - 3) (7x^2 - 3)(3 + x)

Answer

Explanation:

Step1: Group the terms

Group the given expression (-7x^{3}+21x^{2}+3x - 9) into two - groups: ((-7x^{3}+21x^{2})+(3x - 9)).

Step2: Factor out the greatest common factor from each group

From the first group (-7x^{3}+21x^{2}), the GCF is (-7x^{2}), so (-7x^{3}+21x^{2}=-7x^{2}(x - 3)). From the second group (3x - 9), the GCF is 3, so (3x - 9 = 3(x - 3)). The expression becomes (-7x^{2}(x - 3)+3(x - 3)).

Step3: Factor out the common binomial factor

Factor out the common binomial factor ((x - 3)): ((x - 3)(-7x^{2}+3)=(3 - 7x^{2})(x - 3)).

Answer:

C. ((3 - 7x^{2})(x - 3))