(m%5E2%2B3m-4).jpeg "(m-3)(m^2+3m-4)")
Factoring the Expression (m-3)(m^2+3m-4)
This expression is already in a factored form, but we can simplify it further by factoring the quadratic expression within the parentheses.
Factoring the Quadratic
The quadratic expression m² + 3m - 4 can be factored into two binomials. Here's how:
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Find two numbers that multiply to -4 and add up to 3. The numbers 4 and -1 satisfy these conditions: 4 * -1 = -4 and 4 + (-1) = 3.
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Rewrite the middle term using these numbers: m² + 3m - 4 = m² + 4m - m - 4
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Factor by grouping: (m² + 4m) + (-m - 4) = m(m + 4) - 1(m + 4)
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Factor out the common binomial: (m + 4)(m - 1)
The Fully Factored Expression
Now, we can substitute the factored quadratic back into the original expression:
(m - 3)(m² + 3m - 4) = (m - 3)(m + 4)(m - 1)
This is the completely factored form of the expression.