Factor completely: 4m^2 + m - 5
Understand the Problem
The question is asking us to factor the quadratic expression completely, which involves finding two binomials whose product equals the given expression.
Answer
The completely factored form is $(4m + 5)(m - 1)$.
Answer for screen readers
The completely factored form of the expression is $(4m + 5)(m - 1)$.
Steps to Solve
-
Identify coefficients The quadratic expression is in the form $ax^2 + bx + c$.
Here, $a = 4$, $b = 1$, and $c = -5$. -
Find two numbers that multiply and add We need to find two numbers that multiply to $a \cdot c = 4 \cdot (-5) = -20$ and add to $b = 1$.
The numbers are $5$ and $-4$ since $5 \cdot (-4) = -20$ and $5 + (-4) = 1$. -
Rewrite the quadratic expression Use the numbers found to rewrite the expression:
$$4m^2 + 5m - 4m - 5$$ -
Group terms Group the terms:
$$(4m^2 + 5m) + (-4m - 5)$$ -
Factor by grouping Factor out the common factors in each group:
$$m(4m + 5) - 1(4m + 5)$$ -
Factor out the common binomial Now factor out the common binomial $(4m + 5)$:
$$(4m + 5)(m - 1)$$
The completely factored form of the expression is $(4m + 5)(m - 1)$.
More Information
Factoring quadratics is a useful skill in algebra that lets you solve equations and simplify expressions. The method shown here utilizes grouping, which is a common technique for factoring when straightforward methods aren't clear.
Tips
- Forgetting to change the signs when rewriting the middle term can lead to incorrect factors.
- Not checking if the found factors multiply correctly back to the original expression.
AI-generated content may contain errors. Please verify critical information
