Example Card: Factoring a Trinomial by Grouping
Master Factoring a Trinomial by Grouping with step-by-step worked examples for Grade 9 math students. Practice identifying key patterns and apply techniques to solve problems accurately.
Key Concepts
Let's turn this three term problem into a four term puzzle we already know how to solve. We will factor a trinomial by grouping, a powerful application of our main concept.
Example Problem Factor the trinomial $x^2 5x 36$ by grouping.
Step by Step 1. First, identify the coefficients $a, b,$ and $c$ in $ax^2 + bx + c$. Here, $a=1, b= 5,$ and $c= 36$. 2. Find the product of $ac$. $$ ac = 1 imes ( 36) = 36 $$ 3. Find two factors of $ac$ that have a sum equal to $b$. The factors of $ 36$ that sum to $ 5$ are $ 9$ and $4$. $$ 9 imes 4 = 36 ext{ and } 9 + 4 = 5 $$ 4. Rewrite the middle term, $ 5x$, using these factors as $ 9x + 4x$. $$ x^2 9x + 4x 36 $$ 5. Now, group the four terms into two binomials and factor out the GCF from each. $$ (x^2 9x) + (4x 36) = x(x 9) + 4(x 9) $$ 6. Factor out the common binomial factor, $(x 9)$. $$ (x 9)(x + 4) $$.
Common Questions
What is Factoring a Trinomial by Grouping in Grade 9 math?
Factoring a Trinomial by Grouping is a key algebra concept where students learn to apply mathematical rules and properties to solve problems. Understanding this topic builds skills needed for higher-level math.
How do you solve problems involving Factoring a Trinomial by Grouping?
Identify the given information, apply the relevant property or formula, simplify step by step, and check your answer. Practice with varied examples to build fluency.
Where is Factoring a Trinomial by Grouping used in real life?
Factoring a Trinomial by Grouping appears in fields like science, engineering, finance, and technology. Understanding this concept helps solve real-world problems that involve mathematical relationships.