Factoring quadratic trinomials
This Grade 6 algebra skill from Yoshiwara Elementary Algebra teaches students to factor quadratic trinomials of the form ax^2 + bx + c. Students learn to find two binomial factors whose product equals the trinomial, using methods such as trial and error, the AC method, or factoring by grouping.
Key Concepts
Property To factor $x^2 + bx + c$, we look for two numbers $p$ and $q$ so that.
$pq = c$ and $p + q = b$.
When we expand the factored form $(x + p)(x + q)$, we get $x^2 + (p + q)x + pq$.
Common Questions
How do you factor a quadratic trinomial?
Find two numbers that multiply to give c and add to give b in x^2 + bx + c. Write the factors as (x + p)(x + q) where p x q = c and p + q = b.
What is the AC method for factoring quadratic trinomials?
For ax^2 + bx + c, multiply a x c. Find two numbers that multiply to ac and add to b. Rewrite the middle term and factor by grouping.
What if a quadratic trinomial cannot be factored over integers?
Not all quadratics factor over integers. If no integer pairs satisfy the required conditions, the polynomial is prime over integers and requires the quadratic formula.
How do you check a factored quadratic?
Multiply the two binomial factors using FOIL and verify you get the original trinomial.
Where is factoring quadratic trinomials taught?
Factoring quadratic trinomials is covered in the Yoshiwara Elementary Algebra textbook for Grade 6.