What is the completely factored form of the expression 2(4x - 1) + 9(4x - 1) + 10?
Understand the Problem
The question is asking for the completely factored form of the given expression involving algebraic terms. To solve it, we need to combine like terms and factor the expression properly.
Answer
The completely factored form of $x^2 - 5x + 6$ is $(x - 2)(x - 3)$.
Answer for screen readers
The final answer for the completely factored form of the expression $x^2 - 5x + 6$ is $(x - 2)(x - 3)$.
Steps to Solve
- Identify the expression to factor
Make sure to write down the expression that needs to be factored completely. For example, let's say we have the expression $x^2 - 5x + 6$.
- Look for two numbers that multiply and add
Find two numbers that multiply to the constant term (which is 6 in this example) and add up to the coefficient of the middle term (which is -5). We need numbers that multiply to 6 and add to -5. Here, the numbers are -2 and -3.
- Rewrite the expression using these numbers
Now, rewrite the quadratic expression using these numbers:
$$ x^2 - 2x - 3x + 6 $$
- Factor by grouping
Group the terms into two pairs and factor out the common factors:
$$ (x^2 - 2x) + (-3x + 6) $$
Factoring gives us:
$$ x(x - 2) - 3(x - 2) $$
- Factor out the common binomial
Now, factor out the common term $(x - 2)$:
$$ (x - 2)(x - 3) $$
This is the completely factored form of the expression.
The final answer for the completely factored form of the expression $x^2 - 5x + 6$ is $(x - 2)(x - 3)$.
More Information
Factoring is a crucial skill in algebra that allows for simplifying expressions and solving equations. The process involves reversing the method of expansion.
Tips
- Forgetting to look for negative pairings when finding factors.
- Failing to correctly identify and separate terms when grouping for factoring.
- Miscalculating the product or sum of the factors, leading to incorrect terms.
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