Factor the expression completely: -40 + 28x³.
Understand the Problem
The question is asking for the complete factorization of the given expression, which is −40 + 28x³. To solve this, we will first look for the greatest common factor (GCF) and then factor the expression.
Answer
The completely factored expression is \( 4(7x^3 - 10) \).
Answer for screen readers
The completely factored expression is ( 4(7x^3 - 10) ).
Steps to Solve
- Identify the Greatest Common Factor (GCF)
First, we need to find the GCF of the coefficients of the terms in the expression, which are -40 and 28. The factors of -40 are 1, 2, 4, 5, 8, 10, 20, and 40, while the factors of 28 are 1, 2, 4, 7, 14, and 28. The greatest common factor is 4.
- Factor out the GCF
Now, we can factor out the GCF of 4 from the expression. We rewrite the expression as:
$$ -40 + 28x^3 = 4(-10 + 7x^3) $$
- Rearranging Terms
It's often more conventional to write the expression with the highest power term first. We may rearrange to get:
$$ 4(7x^3 - 10) $$
- Conclude with the factored form
The completely factored form of the expression is:
$$ 4(7x^3 - 10) $$
The completely factored expression is ( 4(7x^3 - 10) ).
More Information
Factoring expressions helps in simplifying them and is essential in solving polynomial equations. The GCF method is a fundamental technique used in algebra to break down expressions efficiently.
Tips
- Forgetting to check for negative signs when determining the GCF.
- Not rearranging the terms to follow the conventional order of polynomial expressions.
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