Factoring Trinomials (a not 1)

Front

What is a trinomial?

Back

A trinomial is a polynomial with three terms, typically in the form ax² + bx + c.

Front

What does it mean to factor a trinomial?

Back

Factoring a trinomial involves rewriting it as a product of two binomials.

Front

What is the general form of factoring a trinomial of the form ax² + bx + c?

Back

The general form is (px + q)(rx + s) where p*r = a, q*s = c, and p*s + q*r = b.

Front

What is the first step in factoring a trinomial?

Back

Identify the coefficients a, b, and c in the trinomial ax² + bx + c.

Front

How do you find two numbers that multiply to ac and add to b?

Back

List the factors of ac and find a pair that sums to b.

Front

What is the significance of the leading coefficient in factoring?

Back

The leading coefficient (a) affects the way you group terms and find factors.

Front

What is the difference between factoring a trinomial with a leading coefficient of 1 and one that is not?

Back

With a leading coefficient of 1, you directly find two numbers that add to b. If a is not 1, you must consider ac.

Front

Factor the trinomial: 15t² - 27t - 6

Back

3(5t + 1)(t - 2) is the factored form.

Front

Factor the trinomial: 4h² - 17h + 4

Back

(h - 4)(4h - 1) is the factored form.

Front

Factor the trinomial: 6x² + 5x - 6

Back

(3x - 2)(2x + 3) is the factored form.