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(m-3)(m^2+3m-4)

2 min read Jun 16, 2024
(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:

  1. 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.

  2. Rewrite the middle term using these numbers: m² + 3m - 4 = m² + 4m - m - 4

  3. Factor by grouping: (m² + 4m) + (-m - 4) = m(m + 4) - 1(m + 4)

  4. 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.

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