Podcast
Questions and Answers
When factoring the trinomial $-2x^{2}+x+3$, what is the recommended first step?
When factoring the trinomial $-2x^{2}+x+3$, what is the recommended first step?
- Factor out a $-1$ (correct)
- Factor out a $-2$
- Factor out a $x$
- Factor out a $2$
When multiplying and canceling rational expressions, what should be done first?
When multiplying and canceling rational expressions, what should be done first?
- Expand all the terms in the numerators and denominators
- Look for common factors to cancel first
- Factor all numerators and denominators completely (correct)
- Multiply the numerators and denominators directly
When factoring the denominator $x^{2}-25$, what method should be used?
When factoring the denominator $x^{2}-25$, what method should be used?
- Difference of cubes
- Perfect square trinomial
- Sum of cubes
- Difference of squares (correct)
What should be included if the entire numerator cancels out in a rational expression?
What should be included if the entire numerator cancels out in a rational expression?
Why is it recommended to replace $7-x$ with $-1(x-7)$ in rational expressions?
Why is it recommended to replace $7-x$ with $-1(x-7)$ in rational expressions?
When factoring the trinomial $-2x^{2}+x+3$, what is the recommended first step?
When factoring the trinomial $-2x^{2}+x+3$, what is the recommended first step?
What should be included if the entire numerator cancels out in a rational expression?
What should be included if the entire numerator cancels out in a rational expression?
When factoring the denominator $x^{2}-25$, what method should be used?
When factoring the denominator $x^{2}-25$, what method should be used?
Why is it recommended to replace $7-x$ with $-1(x-7)$ in rational expressions?
Why is it recommended to replace $7-x$ with $-1(x-7)$ in rational expressions?
When multiplying and canceling rational expressions, what should be done first?
When multiplying and canceling rational expressions, what should be done first?
Study Notes
Factoring Trinomials
- When factoring the trinomial
-2x^2 + x + 3, the recommended first step is to factor out the greatest common factor (GCF) if it exists, then look for two binomials that multiply to the last term and add up to the middle term.
Rational Expressions
- When multiplying and canceling rational expressions, the first step is to factor the numerator and denominator completely.
- If the entire numerator cancels out, the fraction should be written as 0.
- Replacing
7-xwith-1(x-7)is recommended in rational expressions to make it easier to factor and cancel out terms.
Factoring Denominators
- When factoring the denominator
x^2 - 25, the method that should be used is difference of squares, sincex^2 - 25can be written as(x + 5)(x - 5).
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Description
Test your understanding of multiplying and dividing rational expressions with this quiz. Practice factoring and canceling common factors to simplify complex trinomials.
