Skip to content
Request a demo

Grade 10 · Core Mathematics · Lesson 6 of 14

Factor Pairs and Grouping

A Grade 10 Core Mathematics CBE lesson from the sub-strand Quadratic Expressions and Equations. In it, learners find a factor pair matching product and sum.

Strand Numbers and AlgebraSub-strand Quadratic Expressions and EquationsLesson code 10CM-13-L640 minutes · 2 slides

KICD learning outcome (d)

Factorise quadratic expressions from different situations.

By the end of this lesson, learners should be able to

  1. Find a factor pair matching product and sum.
  2. Split the middle term.
  3. Factor by grouping and verify by expansion.

Key vocabulary

Factor pair
Two numbers whose product equals a stated target.
The pair 29 and 527 multiplies to 15283 and sums to 556.
Grouping
Rearranging terms into groups that share a factor.
Grouping 17z²+29z and 527z+899 reveals 17z+29.

Lesson preview

Slide 1 · Search a product-sum pairOpening · 18 min
A tree diagram displaying the factor pairs of 15283, highlighting the pair 29 and 527 that adds up to the target sum of 556.
Figure 1: A tree diagram displaying the factor pairs of 15283, highlighting the pair 29 and 527 that adds up to the target sum of 556.

For 17z²+556z+899, the first and last coefficients create a target product of 15283. The middle coefficient asks for a pair with sum 556. The pair must satisfy both the target product and target sum. Use Figure 1 to see how to systematically find a pair that meets both targets.

  • Multiply 17 by 899 to get 15283.
  • List integer factor pairs of 15283.
  • Select 29 and 527 because 29+527=556.
  • Keep signs positive for this expression.
Worked example. The target product is 17×899=15283. The useful pair is 29 and 527 because 29×527=15283 and 29+527=556. Rewrite 556z as 29z+527z. Answer: The middle term splits as 29z+527z..

Check question: When factorising the quadratic expression 17z2+556z+899, what target product must the factor pair produce?

  1. 15283
  2. 899
  3. 556
  4. 9452
Show answer

15283. The target product is found by multiplying the leading coefficient by the constant term: 17×899=15283.

Slide 2 · Group and verifyModel · 22 min
A calculation showing how to group terms to extract a common binomial, including an arrow demonstrating how to multiply to verify the result.
Figure 2: A calculation showing how to group terms to extract a common binomial, including an arrow demonstrating how to multiply to verify the result.

Teach the full lesson on the projector

This lesson, and every other Grade 1–10 CBE lesson, comes ready to project with the EAP ClassKit. It runs without electricity or internet.

  • Both slides with diagrams and class activities
  • Teacher notes, SNE adaptations and assessment checks
  • Homework and the other 13 lessons in this sub-strand
See the school projectorWhatsApp us

All 14 lessons in Quadratic Expressions and Equations

  1. 1Building Quadratic Expressions from DimensionsForm quadratic expressions from different situations
  2. 2Four Products on a NoticeboardForm quadratic expressions from different situations
  3. 3Deriving a Square Identity by AreaDerive the quadratic identities from the concept of area
  4. 4Restoring a Difference-Square AreaDerive the quadratic identities from the concept of area
  5. 5Nearby Bases for Mental SquaringApply quadratic identities in numerical cases
  6. 6Factor Pairs and GroupingFactorise quadratic expressions from different situations
  7. 7Forming an Area EquationForm quadratic equations in different situations
  8. 8A Consecutive-Integer EquationForm quadratic equations in different situations
  9. 9Solving by FactorisationSolve quadratic equations by factorisation
  10. 10Exact Roots with Signed FactorsSolve quadratic equations by factorisation
  11. 11A Triangular Sign ModelApply quadratic equations to real life situations
  12. 12Planning a Rectangular TankApply quadratic equations to real life situations
  13. 13Exploring Quadratic Models for a Community MuralExplore the use of quadratic equations in real life situations
  14. 14Exploring a Community Greenhouse FrameExplore the use of quadratic equations in real life situations