Rearranging Before Factoring
Rearrange polynomials before factoring in Grade 9 algebra. Reorder terms in descending standard form, factor out GCFs, and set up expressions for factoring by grouping.
Key Concepts
Property Before factoring, arrange the polynomial's terms in descending order of the exponents for one variable. The standard form is $ax^2 + bx + c$. Explanation You can’t solve a jumbled puzzle! Always put your polynomial in order from the highest power to the lowest. This makes it easy to identify your 'a', 'b', and 'c' values and start factoring correctly. Examples To factor $ 17x + 5 + 12x^2$, first rearrange it to $12x^2 17x + 5 = (12x 5)(x 1)$. To factor $ 2 7x + 4x^2$, first rearrange it to $4x^2 7x 2 = (4x+1)(x 2)$.
Common Questions
Why do you sometimes need to rearrange terms before factoring?
Rearranging puts terms in standard descending order, making patterns like difference of squares or grouping easier to recognize and apply correctly.
How do you factor by grouping after rearranging?
Group the first two and last two terms, factor GCF from each group, then factor out the common binomial factor. Example: x³ + x² + 2x + 2 = x²(x+1) + 2(x+1) = (x²+2)(x+1).
What is the first step in any factoring problem?
Always look for a GCF first. Factor it out of all terms before applying grouping, difference of squares, or trinomial factoring methods.