Factoring Trinomials 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 when 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.

Front

What is the first step in factoring a trinomial with a leading coefficient greater than 1?

Back

The first step is to multiply 'a' and 'c' (the leading coefficient and the constant term).

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

Factor the trinomial: 4x² - 9

Back

(2x - 3)(2x + 3) - This is a difference of squares.

Front

Factor completely: 6x² + 5x - 6

Back

(3x - 2)(2x + 3) - This involves finding two numbers that multiply to -36 and add to 5.

Front

Factor the trinomial: 2m² + 3m - 9

Back

(m + 3)(2m - 3) - Split the middle term using the numbers 6 and -3.

Front

Factor the trinomial: 3v² - 4v - 7

Back

(3v - 7)(v + 1) - Use the ac method to find suitable factors.