Factoring Polynomials by Grouping
Practice factoring polynomials by grouping in Grade 9 math — Explanation Think of a four-term polynomial as a fun team-building exercise! Part of Quadratic Functions and Equations for Grade 9.
Key Concepts
Property When a polynomial has four terms, make two groups and factor out the greatest common factor from each group. Explanation Think of a four term polynomial as a fun team building exercise! First, split them into two pairs. Find what's common in the first pair and factor it out. Do the same for the second pair. If you did it right, both pairs will now share a common binomial expression, which you can factor out for the grand finale! Examples $3x^2 + 6xy + 5x + 10y = (3x^2 + 6xy) + (5x + 10y) = 3x(x + 2y) + 5(x + 2y) = (x + 2y)(3x + 5)$ $a^3 4a^2 + 3a 12 = (a^3 4a^2) + (3a 12) = a^2(a 4) + 3(a 4) = (a 4)(a^2 + 3)$.
Common Questions
What is 'Factoring Polynomials by Grouping' in Grade 9 math?
Explanation Think of a four-term polynomial as a fun team-building exercise! Find what's common in the first pair and factor it out.
How do you solve problems involving 'Factoring Polynomials by Grouping'?
Find what's common in the first pair and factor it out. If you did it right, both pairs will now share a common binomial expression, which you can factor out for the grand finale!.
Why is 'Factoring Polynomials by Grouping' an important Grade 9 math skill?
When you pull a negative GCF out of a group like $(-4x - 12)$, remember to flip the signs of both terms inside the parentheses.. Factoring out $-4$ gives you $-4(x + 3)$, not $-4(x - 3)$.