Factor completely: 2u² + 40u - 42
Understand the Problem
The question is asking to factor the quadratic expression completely. We need to find factors of the expression 2u² + 40u - 42.
Answer
$2(u + 21)(u - 1)$
Answer for screen readers
The completely factored form of the expression is $2(u + 21)(u - 1)$.
Steps to Solve
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Identify the common factor First, look for the greatest common factor (GCF) of the coefficients in the expression $2u^2 + 40u - 42$. The GCF is 2.
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Factor out the GCF Factor out the GCF from the expression: $$ 2(u^2 + 20u - 21) $$
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Factor the quadratic expression Now focus on factoring the quadratic expression $u^2 + 20u - 21$. We need two numbers that multiply to -21 (the constant term) and add up to 20 (the coefficient of $u$).
The numbers that meet these criteria are 21 and -1.
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Write the factored form Using the numbers identified, we can write: $$ u^2 + 20u - 21 = (u + 21)(u - 1) $$
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Combine the factors Putting it all together, we have: $$ 2(u + 21)(u - 1) $$
The completely factored form of the expression is $2(u + 21)(u - 1)$.
More Information
Factoring is a crucial skill in algebra, particularly for solving quadratic equations. The process involves breaking down an expression into simpler components that, when multiplied together, give the original expression.
Tips
- Forgetting to factor out the GCF: Always check for a common factor first.
- Incorrect factor pairs: Ensure that the pairs you find multiply to the product of the constant term and add to the middle coefficient.
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