Factoring Trinomials with a > 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 with a > 1?

Back

The general form is ax² + bx + c = (px + q)(rx + s), where p, q, r, and s are constants.

Front

How do you identify the coefficients in a trinomial?

Back

In ax² + bx + c, 'a' is the coefficient of x², 'b' is the coefficient of x, and 'c' is the constant term.

Tags

CCSS.6.EE.A.2B

Front

What is the first step in factoring a trinomial with a > 1?

Back

The first step is to multiply 'a' and 'c' to find the product.

Front

What is the purpose of finding two numbers that multiply to ac and add to b?

Back

These two numbers help in splitting the middle term to facilitate factoring.

Front

What is the significance of the leading coefficient in factoring?

Back

The leading coefficient (a) affects the factors of the trinomial and must be considered when finding the binomials.

Front

What does it mean if a trinomial is not factorable?

Back

If a trinomial is not factorable, it cannot be expressed as a product of two binomials with rational coefficients.

Front

How can you check if your factorization is correct?

Back

You can check by multiplying the binomials back together to see if you obtain the original trinomial.

Front

What is the factored form of 5x² - 15x + 10?

Back

5(x - 2)(x - 1)