GCF- Factoring Polynomials

Factor the polynomial: 7x + 49.

Answer explanation

To factor the polynomial 7x + 49, we can factor out the greatest common factor, which is 7. This gives us 7(x + 7). However, the answer choices do not include this option, making the correct answer 0.

Factor the polynomial: 8m − 6.

• 2(4m - 3)

• 4(2m - 1)

• 8(m - 1)

Answer explanation

To factor 8m - 6, we can take out the greatest common factor, which is 2. This gives us 2(4m - 3). The other options do not correctly factor the polynomial.

Factor the polynomial: 5a² − 15.

• 5(a² - 3)

• 5(a + 3)

• 5(a² + 3)

Answer explanation

To factor 5a² - 15, first factor out the common term 5, giving 5(a² - 3). The expression a² - 3 cannot be factored further over the reals, making 5(a² - 3) the correct choice.

Factor the polynomial: 12c² − 20d².

• 4(3c² - 5d²)

• 2(6c² - 10d²)

• 6(2c² - 3.33d²)

Answer explanation

To factor 12c² − 20d², first factor out the greatest common factor, which is 4. This gives 4(3c² - 5d²), confirming that the correct choice is 4(3c² - 5d²).

Factor the polynomial: 64 − 40ab.

• 8(8 - 5ab)

• 4(16 - 10ab)

• 16(4 - 2.5ab)

Answer explanation

To factor 64 - 40ab, we can take out the common factor of 8. This gives us 8(8 - 5ab). The other options do not correctly factor the polynomial, making 8(8 - 5ab) the correct choice.

Factor the polynomial: 36a² + 24a.

• 12a(3a + 2)

• 18a(2a + 1)

• 3a(12a + 8)

Answer explanation

To factor 36a² + 24a, first factor out the greatest common factor, which is 12a. This gives us 12a(3a + 2). Thus, the correct choice is 12a(3a + 2).

Factor the polynomial: 18x⁴ − 12x².

• 6x²(3x² - 2)

• 3x²(6x² - 4)

• 2x²(9x² - 6)

Answer explanation

To factor 18x⁴ - 12x², first factor out the greatest common factor, which is 6x². This gives us 6x²(3x² - 2). The other options do not correctly factor the polynomial.

Factor the polynomial: 12ab³ + 20b.

• 4b(3ab² + 5)

• 2b(6ab² + 10)

• 6b(2ab² + 3)

Answer explanation

To factor 12ab³ + 20b, first identify the common factor, which is 4b. Factoring it out gives 4b(3ab² + 5). This matches the correct choice, confirming that 4b(3ab² + 5) is the factored form.

Factor the polynomial: 10x² + 5x.

• 5x(2x + 1)

• 2x(5x + 1)

• 10x(x + 0.5)

Answer explanation

To factor 10x² + 5x, first factor out the greatest common factor, which is 5x. This gives us 5x(2x + 1). The other options do not correctly factor the polynomial.

Factor the polynomial: 14x² − 21x.

• 7x(2x - 3)

• 14(x² - 1.5x)

• x(14x - 21)

Answer explanation

To factor 14x² - 21x, first factor out the greatest common factor, which is 7x. This gives us 7x(2x - 3). Thus, the correct choice is 7x(2x - 3).