Gcf and Factoring Trinomials with a > 1

Front

What is the Greatest Common Factor (GCF)?

Back

The GCF is the largest positive integer that divides all the coefficients of a polynomial without leaving a remainder.

Front

How do you factor a trinomial of the form ax² + bx + c?

Back

To factor a trinomial, find two numbers that multiply to ac (the product of a and c) and add to b. Then, rewrite the middle term using these numbers and factor by grouping.

Front

Factor Completely: 2x² + x - 6

Back

(x + 2)(2x - 3)

Front

What is a trinomial?

Back

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

Front

Factor Completely: 3v² - 4v - 7

Back

(3v - 7)(v + 1)

Front

What does it mean to factor a polynomial?

Back

Factoring a polynomial means expressing it as a product of its factors, which can be simpler polynomials.

Front

Factor Completely: 3x² + 7x + 2

Back

(3x + 1)(x + 2)

Front

What is the significance of the leading coefficient in a trinomial?

Back

The leading coefficient (a) affects the shape and direction of the parabola represented by the trinomial when graphed.

Front

Factor Completely: 2m² + 3m - 9

Back

(m + 3)(2m - 3)

Front

What is the difference between factoring and expanding a polynomial?

Back

Factoring breaks a polynomial into simpler components, while expanding multiplies those components to form the original polynomial.