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Lesson · Grade 10 · Foundations of Mathematics and Pre Calculus

Factoring Out the Greatest Common Factor

  • Grade 10
  • Foundations of Mathematics and Pre Calculus
  • 2 min 12 s
  • British Columbia
  • BC10-MA-31

The video factors 6x² + 9x step by step: it finds the GCF from the factors of 6 and 9 and the shared x, divides each term by 3x to get 3x(2x + 3), and checks the answer by multiplying back. It then shows the common mistake of taking out only the 3, which leaves 3(2x² + 3x) not fully factored, and works a second example, 4a²b − 10ab² = 2ab(2a − 5b), before ending on a one-line recap.

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In one sentence

The question this lesson answers

How do we factor six x squared plus nine x?

It has two terms, six x squared and nine x, joined by a plus sign.

Transcript

What the lesson says

How do we factor six x squared plus nine x?

It has two terms, six x squared and nine x, joined by a plus sign.

To factor it, we write it as a product, a multiplication.

The greatest common factor, or GCF, is the largest factor that divides every term.

The factors of 6 are 1, 2, 3 and 6. The factors of 9 are 1, 3 and 9.

The largest factor they share is 3.

Six x squared is 6 times x times x, and nine x is 9 times x, so both share one x.

So the GCF is three x.

Six x squared divided by three x is two x, and nine x divided by three x is 3.

Write three x outside the brackets and two x plus 3 inside.

Check by multiplying back: three x times two x is six x squared, and three x times 3 is nine x.

A common mistake is taking out only the 3: 3 times, in brackets, two x squared plus three x.

Both terms inside still have an x, so it is not fully factored. Take out all of three x.

One more: four a squared b minus ten a b squared.

The GCF of 4 and 10 is 2, and both terms share an a and a b, so the GCF is two a b.

Dividing each term by two a b leaves two a and negative five b.

So it equals two a b times, in brackets, two a minus five b.

Multiplying back gives four a squared b minus ten a b squared again.

Take out the GCF, put what is left in brackets, and check by multiplying back.

Curriculum

Where this fits

British Columbia, Grade 10

Foundations of Mathematics and Pre Calculus 10, Algebra: polynomial factoringBC10-MA-31

Previous: Squaring a Binomial: Don't Forget the Middle TermNext: Factoring a Trinomial: Multiply to c, Add to b

The outcomes and strands follow the British Columbia curriculum.

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