Example Card: Multiplying a Rational Expression by a Polynomial
Multiply rational expressions by polynomials by factoring first and canceling common factors. Work through Grade 9 algebraic fraction multiplication step by step.
Key Concepts
See how factoring first makes a tricky multiplication problem surprisingly simple. This is a core part of multiplying rational expressions.
Example Problem.
Multiply $\frac{8}{2x 12} \cdot (x^2 3x 18)$ and simplify.
Common Questions
How do you multiply a rational expression by a polynomial?
Write the polynomial as a fraction over 1, factor all expressions completely, cancel common factors between any numerator and denominator, then multiply across.
Why factor before multiplying rational expressions?
Factoring first reveals common factors you can cancel, keeping numbers small. Multiplying first creates larger polynomials that are harder to factor afterward.
What common factors appear in these problems?
Look for binomial factors like (x-3) or (x+5). For 8/(2x-12) times (x^2-3x-18), factor to 8/[2(x-6)] times (x-6)(x+3), then cancel (x-6) to get 4(x+3).