Question

factor each polynomial by grouping.

1. 12a³ - 9a² + 4a - 3
2. 9xz - 15x - 21xu + 35u
3. 35xy - 5x - 56y + 8
4. 5n³ - 10n² + 3n - 6
5. 3n³ - 4n² + 9n - 12

Explanation:

Problem 1: \(12a^3 - 9a^2 + 4a - 3\)

Step1: Group the terms

Group the first two terms and the last two terms: \((12a^3 - 9a^2) + (4a - 3)\)

Step2: Factor out GCF from each group

Factor out \(3a^2\) from the first group and \(1\) from the second group: \(3a^2(4a - 3) + 1(4a - 3)\)

Step3: Factor out the common binomial

Factor out \((4a - 3)\): \((3a^2 + 1)(4a - 3)\)

Step1: Group the terms

Group the first two terms and the last two terms: \((35xy - 5x) + (-56y + 8)\)

Step2: Factor out GCF from each group

Factor out \(5x\) from the first group and \(-8\) from the second group: \(5x(7y - 1) - 8(7y - 1)\)

Step3: Factor out the common binomial

Factor out \((7y - 1)\): \((5x - 8)(7y - 1)\)

Step1: Group the terms

Group the first two terms and the last two terms: \((3n^3 - 4n^2) + (9n - 12)\)

Step2: Factor out GCF from each group

Factor out \(n^2\) from the first group and \(3\) from the second group: \(n^2(3n - 4) + 3(3n - 4)\)

Step3: Factor out the common binomial

Factor out \((3n - 4)\): \((n^2 + 3)(3n - 4)\)

Answer:

\((3a^2 + 1)(4a - 3)\)

Problem 2: \(35xy - 5x - 56y + 8\)