Multiplying and Dividing Rational Expressions Quiz
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Questions and Answers

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?

  • 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?

  • 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?

    <p>The factor 1</p> Signup and view all the answers

    Why is it recommended to replace $7-x$ with $-1(x-7)$ in rational expressions?

    <p>To facilitate cancellation of the factor</p> Signup and view all the answers

    When factoring the trinomial $-2x^{2}+x+3$, what is the recommended first step?

    <p>Factor out $-1$ first, then factor the resulting trinomial</p> Signup and view all the answers

    What should be included if the entire numerator cancels out in a rational expression?

    <p>The factor $1$</p> Signup and view all the answers

    When factoring the denominator $x^{2}-25$, what method should be used?

    <p>Difference of squares</p> Signup and view all the answers

    Why is it recommended to replace $7-x$ with $-1(x-7)$ in rational expressions?

    <p>To facilitate factoring and cancellation</p> Signup and view all the answers

    When multiplying and canceling rational expressions, what should be done first?

    <p>Factor all numerators and denominators completely</p> Signup and view all the answers

    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-x with -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, since x^2 - 25 can 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.

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