Question

Factor the GCF out of the following expression and write your answer in factored form: 45x³y7 +33x³y³ +78x²y4

Answer 1

To factor the GCF out of the expression 45x³y7 + 33x³y³ + 78x²y⁴, we find the highest common factor of the coefficients and the variables' exponents. The GCF of the coefficients is 3, and the GCF of the variables' exponents is x³y⁷. The factored expression is 3x³y⁷ (15x⁰ + 11xy⁻⁴ + 26x⁻¹y⁻³).

Step-by-step explanation:

To factor the GCF (Greatest Common Factor) out of the expression 45x³y7 + 33x³y³ + 78x²y⁴, we need to look for the highest common factor of the coefficients and the variables' exponents.

For the coefficients, the highest common factor is 3.

For the variables' exponents, we can see that the highest power of x is x³ and the highest power of y is y⁷. Therefore, the highest common factor of the variables' exponents is x³y⁷.

Combining the highest common factor of the coefficients (3) and the highest common factor of the variables' exponents (x³y⁷), the factored expression is 3x³y⁷ (15x⁰ + 11xy⁻⁴ + 26x⁻¹y⁻³).

Answer 2

The expression 45x³y⁷ + 33x³y³ + 78x²y⁴ is factored by first finding the GCF of the coefficients and variables, which is 3x²y³. Dividing each term by the GCF gives us the factored form: 3x²y³(15xy⁴ + 11x + 26y).

Step-by-step explanation:

To factor the Greatest Common Factor (GCF) out of the expression 45x³y⁷ + 33x³y³ + 78x²y⁴, we first need to identify the GCF of the numerical coefficients and the variables in each term. The numerical coefficients are 45, 33, and 78. The GCF of these numbers is 3. For the variables, we look for the lowest exponent of x which is 2 and the lowest exponent of y which is 3. Therefore, the GCF is 3x²y³.

Factoring out the GCF, we divide each term by 3x²y³:

• (45x³y⁷) / (3x²y³) = 15xy⁴
• (33x³y³) / (3x²y³) = 11x
• (78x²y⁴) / (3x²y³) = 26y

The expression in factored form is:

3x²y³(15xy⁴ + 11x + 26y)