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Factoring Polynomials: How to Factor 20x^4 + 45x^5
Published on March 31, 2026
Algebra
Learn how to factor the expression 20x^4 + 45x^5 by identifying and extracting the greatest common factor of 5x^4, resulting in the expression 5x^4(4 + 9x).
Question
Factor the expression completely. 20, x, to the power 4 , plus, 45, x, to the power 5 20x 4 +45x 5
Answer
To factor the expression
Step 1: Identify the greatest common factor (GCF) of the numerical coefficients.
The coefficients are
The coefficients are
- The factors of
are . - The factors of
are .
The greatest common factor ofand is .
Step 2: Identify the greatest common factor of the variable terms.
The variable terms are
The GCF of
The variable terms are
The GCF of
Step 3: Combine the GCF of the coefficients and the variables.
The overall GCF of the expression
The overall GCF of the expression
Step 4: Factor out the GCF.
Divide each term in the original expression by
Divide each term in the original expression by
Write the expression as the product of the GCF and the remaining polynomial:
The expression is now factored completely.