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Lesson · Grade 11 · Pre Calculus

Factoring Trinomials by Decomposition

  • Grade 11
  • Pre Calculus
  • 2 min 1 s
  • British Columbia
  • BC11-MA-68

The video factors 12x² + 14x − 6 step by step: it takes out the greatest common factor 2, uses a × c = −18 to find 9 and −2, splits the middle term and factors by grouping to reach 2(3x − 1)(2x + 3). It warns against dropping the common factor of 2, checks the answer by expanding back to the original trinomial, and ends on a one-line recap of the three steps.

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In one sentence

The question this lesson answers

Let us factor the trinomial 12 x squared plus 14 x minus 6. A trinomial has three terms. To factor it is to write it as a product.

Step 1: take out the greatest common factor. The largest number that divides 12, 14 and 6 is 2.

Transcript

What the lesson says

Let us factor the trinomial 12 x squared plus 14 x minus 6. A trinomial has three terms. To factor it is to write it as a product.

Step 1: take out the greatest common factor. The largest number that divides 12, 14 and 6 is 2.

That leaves 2 times 6 x squared plus 7 x minus 3.

Compare the bracket with a x squared plus b x plus c: a is 6, b is 7 and c is negative 3.

Step 2: multiply a by c. 6 times negative 3 is negative 18.

Now find two numbers that multiply to negative 18 and add to 7.

9 and negative 2 work: their product is negative 18 and their sum is 7.

Step 3: decompose, or split, the middle term: 7 x becomes 9 x minus 2 x.

Step 4: factor by grouping. Take 3 x out of the first pair and negative 1 out of the second.

Both parts share the bracket 2 x plus 3. Take it out: 3 x minus 1 times 2 x plus 3.

Keep the 2 from step 1. Dropping it is a common mistake. The answer is 2 times 3 x minus 1 times 2 x plus 3.

Check by expanding: multiply out the brackets to get 6 x squared plus 9 x minus 2 x minus 3.

That is 6 x squared plus 7 x minus 3, and 2 times that is the trinomial we started with.

To recap: take out the greatest common factor, split the middle term using a times c, then factor by grouping.

Curriculum

Where this fits

British Columbia, Grade 11

Pre Calculus 11, Algebra: polynomial factoringBC11-MA-68

Next: Simplifying Rational Expressions and Their Non-Permissible Values

The outcomes and strands follow the British Columbia curriculum.

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