Rearranging Terms before Factoring
Rearrange polynomial terms into standard form before factoring to avoid errors. Organize trinomials in descending powers for Grade 9 algebra success.
Key Concepts
Property Always write trinomials in standard form, $x^2 + bx + c$, with descending powers of the variable before you begin factoring. Explanation It’s like organizing your game pieces before you play! A messy trinomial with terms all over the place is confusing. Always line them up in standard form first: the $x^2$ term, then the $x$ term, then the constant. This neat setup makes finding $b$ and $c$ a piece of cake and ensures you don't make a silly mistake when you start factoring. Examples To factor $3x 18 + x^2$, first rearrange it to $x^2 + 3x 18$. The factors of 18 that sum to 3 are 6 and 3, so the result is $(x+6)(x 3)$. To factor $ 30 + 7x + x^2$, first rearrange it to $x^2 + 7x 30$. The factors of 30 that sum to 7 are 10 and 3, so the result is $(x+10)(x 3)$.
Common Questions
Why do you rearrange terms before factoring a trinomial?
Standard form x^2+bx+c with descending powers makes factoring patterns clear and prevents errors. Disorganized terms hide the structure needed to factor correctly.
What is standard form for a trinomial?
Standard form is ax^2+bx+c, with the highest degree term first, followed by lower degrees in descending order. This organization is required before factoring.
How do you rearrange a trinomial into standard form?
Identify each term's degree, then reorder from highest to lowest: x^2 term first, x term second, constant last. Combine like terms after rearranging.