factor ( x^{3}-7x^{2}-5x + 35 ) by grouping. what is the resulting expression?\n( (x^{2}-7)(x - 5) )\n(…

factor ( x^{3}-7x^{2}-5x + 35 ) by grouping. what is the resulting expression?\n( (x^{2}-7)(x - 5) )\n( (x^{2}-7)(x + 5) )\n( (x^{2}-5)(x - 7) )\n( (x^{2}+5)(x - 7) )

factor ( x^{3}-7x^{2}-5x + 35 ) by grouping. what is the resulting expression?\n( (x^{2}-7)(x - 5) )\n( (x^{2}-7)(x + 5) )\n( (x^{2}-5)(x - 7) )\n( (x^{2}+5)(x - 7) )

Answer

Explanation:

Step1: Group the terms

Group the first two terms and the last two terms: $$(x^{3}-7x^{2})+(-5x + 35)$$

Step2: Factor out the greatest common factor from each group

For the first group (x^{3}-7x^{2}), the GCF is (x^{2}), so (x^{2}(x - 7)). For the second group (-5x + 35), the GCF is (-5), so (-5(x - 7)). The expression becomes (x^{2}(x - 7)-5(x - 7))

Step3: Factor out the common binomial factor

Factor out ((x - 7)) from both terms: ((x^{2}-5)(x - 7))

Answer:

((x^{2}-5)(x - 7)) (Option C)