GCF- Factoring Polynomials

Front

Factor the polynomial: 7x + 49.

Back

7(x + 7)

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.

Front

Factor the polynomial: 8m − 6.

Back

2(4m - 3)

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.

Front

Factor the polynomial: 5a² − 15.

Back

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.

Front

Factor the polynomial: 12c² − 20d².

Back

4(3c² - 5d²)

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).

Front

Factor the polynomial: 64 − 40ab.

Back

8(8 - 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.

Front

Factor the polynomial: 36a² + 24a.

Back

12a(3a + 2)

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).

Front

Factor the polynomial: 18x⁴ − 12x².

Back

6x²(3x² - 2)

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.

Front

Factor the polynomial: 12ab³ + 20b.

Back

4b(3ab² + 5)

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.

Front

Factor the polynomial: 10x² + 5x.

Back

5x(2x + 1)

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.

Front

Factor the polynomial: 14x² − 21x.

Back

7x(2x - 3)

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).