Questions and Answers
When factoring the trinomial $-2x^{2}+x+3$, what is the recommended first step?
Factor out a $-1$
When multiplying and canceling rational expressions, what should be done first?
Factor all numerators and denominators completely
When factoring the denominator $x^{2}-25$, what method should be used?
Difference of squares
What should be included if the entire numerator cancels out in a rational expression?
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Why is it recommended to replace $7-x$ with $-1(x-7)$ in rational expressions?
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When factoring the trinomial $-2x^{2}+x+3$, what is the recommended first step?
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What should be included if the entire numerator cancels out in a rational expression?
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When factoring the denominator $x^{2}-25$, what method should be used?
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Why is it recommended to replace $7-x$ with $-1(x-7)$ in rational expressions?
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When multiplying and canceling rational expressions, what should be done first?
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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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