CheerMath

Grade 10 Polynomials Practice

Multiply & Factor Polynomial Expressions

Now the products get bigger and you start working backwards. You'll multiply trinomials, spot the special products, then pull out a GCF and factor differences of squares, trinomials and perfect squares.

Also known as Class 10 maths — the same topics, whether your school calls it grade, class or year.

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Sample questions

A few samples from this topic — try one, then show the answer.

  1. Factor Trinomials with Leading Coefficient 1

    Which of the following is the correct factoring of x2  +  x^2 \; + \;10x   +  x\, \; + \;21?
    • (x  −  3)(x  +  7)(x \; - \; 3)(x \; + \; 7)
    • (x  −  7)(x  +  3)(x \; - \; 7)(x \; + \; 3)
    • (x  −  7)(x  −  3)(x \; - \; 7)(x \; - \; 3)
    • (x  +  3)(x  +  7)(x \; + \; 3)(x \; + \; 7)
    Show answer
    Answer:
    (x  +  3)(x  +  7)(x \; + \; 3)(x \; + \; 7)

  2. Multiply More Complex Polynomials

    Multiply: (x + 3)(x + 1).
    • x2+3x^{2} + 3
    • x2+3x+4x^{2} + 3x + 4
    • x2+4x+3x^{2} + 4x + 3
    • x2+4x+4x^{2} + 4x + 4
    Show answer
    Answer:
    x2+4x+3x^{2} + 4x + 3

  3. Factor a Difference of Squares

    Factor: n2  −  25n^{2} \; - \; 25.e.g., type (x + 3)(x - 3)\quad {\scriptsize\color{gray}{\textrm{e.g., type (x + 3)(x - 3)}}}
    Show answer
    Answer:
    (n + 5)(n - 5)

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A worked example

Which of the following is the correct factoring of x2  +  x^2 \; + \;10x   +  x\, \; + \;21?
  1. To factor x2  +  x^2 \; + \;10x   +  x\, \; + \;21, we need two numbers that multiply to 21 and add to 10.\\For each option, extract the two numbers from the binomials and check both conditions.
  2. Check each option:(x  +  3)(x  +  7)\\ (x \; + \; 3)(x \; + \; 7): 3  ×  \; \times \;7  =  \; = \;21  ✓\;\checkmark, 3  +  \; + \;7  =  \; = \;10  ✓→\;\checkmark \tocorrect(x  −  3)(x  +  7)\\ (x \; - \; 3)(x \; + \; 7): -3  ×  \; \times \;7  =  \; = \;-21  \;✘, -3  +  \; + \;7  =  \; = \;4  \;✘→\towrong product and wrong sum(x  −  7)(x  +  3)\\ (x \; - \; 7)(x \; + \; 3): -7  ×  \; \times \;3  =  \; = \;-21  \;✘, -7  +  \; + \;3  =  \; = \;-4  \;✘→\towrong product and wrong sum(x  −  7)(x  −  3)\\ (x \; - \; 7)(x \; - \; 3): -7  ×  \; \times \;-3  =  \; = \;21  ✓\;\checkmark, -7  +  \; + \;-3  =  \; = \;-10  \;✘→\tosum should be 10
  3. Only 3 and 7 pass both checks:∙  \\ \bullet\;Product: 3  ×  \; \times \;7  =  \; = \;21  ✓∙  \;\checkmark \\ \bullet\;Sum: 3  +  \; + \;7  =  \; = \;10  ✓\;\checkmark
  4. So x2  +  x^2 \; + \;10x   +  x\, \; + \;21  =  (x  +  \; = \; (x \; + \;3)(x  +  )(x \; + \;7)

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