lucas and erick are factoring the polynomial 12x³ - 6x² + 8x - 4. lucas groups the polynomial (12x³ +…

lucas and erick are factoring the polynomial 12x³ - 6x² + 8x - 4. lucas groups the polynomial (12x³ + 8x)+(-6x² - 4) to factor. erick groups the polynomial (12x³ - 6x²)+(8x - 4) to factor. who correctly grouped the terms to factor? explain.

lucas and erick are factoring the polynomial 12x³ - 6x² + 8x - 4. lucas groups the polynomial (12x³ + 8x)+(-6x² - 4) to factor. erick groups the polynomial (12x³ - 6x²)+(8x - 4) to factor. who correctly grouped the terms to factor? explain.

Answer

Explanation:

Step1: Recall factoring by grouping concept

When factoring by grouping, we group terms to find a common - factor within each group.

Step2: Analyze Lucas's grouping

For Lucas's grouping ((12x^{3}+8x)+(-6x^{2} - 4)), in the first group (12x^{3}+8x = 4x(3x^{2}+2)), and in the second group (-6x^{2}-4=-2(3x^{2} + 2)). After factoring out the common factors from each group, we can then factor out the common binomial ((3x^{2}+2)) further.

Step3: Analyze Erick's grouping

For Erick's grouping ((12x^{3}-6x^{2})+(8x - 4)), in the first group (12x^{3}-6x^{2}=6x^{2}(2x - 1)), and in the second group (8x - 4=4(2x - 1)). After factoring out the common factors from each group, we can then factor out the common binomial ((2x - 1)) further.

Answer:

Both Lucas and Erick correctly grouped the terms to factor. Lucas grouped the terms to factor out a common factor of (4x) and (- 2) respectively from the two groups and then a common binomial ((3x^{2}+2)). Erick grouped the terms to factor out a common factor of (6x^{2}) and (4) respectively from the two groups and then a common binomial ((2x - 1)).