factor the polynomial (4x^{4}-20x^{2}-3x^{2}+15) by grouping. what is the resulting expression?\n(…

factor the polynomial (4x^{4}-20x^{2}-3x^{2}+15) by grouping. what is the resulting expression?\n( (4x^{2}+3)(x^{2}-5) )\n( (4x^{2}-3)(x^{2}-5) )\n( (4x^{2}-5)(x^{2}+3) )\n( (4x^{2}+5)(x^{2}-3) )

factor the polynomial (4x^{4}-20x^{2}-3x^{2}+15) by grouping. what is the resulting expression?\n( (4x^{2}+3)(x^{2}-5) )\n( (4x^{2}-3)(x^{2}-5) )\n( (4x^{2}-5)(x^{2}+3) )\n( (4x^{2}+5)(x^{2}-3) )

Answer

Explanation:

Step1: Group the terms

Group the polynomial (4x^{4}-20x^{2}-3x^{2}+15) as ((4x^{4}-20x^{2})+(-3x^{2}+15))

Step2: Factor out the GCF from each group

For the first group (4x^{4}-20x^{2}), the GCF is (4x^{2}), so (4x^{2}(x^{2} - 5)). For the second group (-3x^{2}+15), the GCF is (-3), so (-3(x^{2}-5))

Step3: Factor out the common binomial factor

The polynomial becomes ((x^{2}-5)(4x^{2}-3))

Answer:

((4x^{2}-3)(x^{2}-5)) (the second option)