Factoring Trinomials a > 1

Front

What is a trinomial?

Back

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

Front

What does it mean to factor a polynomial?

Back

Factoring a polynomial means expressing it as a product of its factors, which are polynomials of lower degrees.

Front

What is the general form of a quadratic trinomial?

Back

The general form of a quadratic trinomial is ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

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

Back

The leading coefficient (a) determines the direction of the parabola when graphed and affects the factoring process.

Tags

CCSS.HSF-IF.C.7A

Front

How do you factor a trinomial when a > 1?

Back

To factor a trinomial when a > 1, look for two numbers that multiply to ac and add to b, then use these to split the middle term.

Front

What is the process of grouping in factoring?

Back

Grouping is a method used to factor polynomials by rearranging terms and factoring out common factors from groups.

Front

What is the difference of squares?

Back

The difference of squares is a factoring pattern that states a² - b² = (a - b)(a + b).

Tags

CCSS.HSA.APR.C.4

Front

What is the role of the quadratic formula in factoring?

Back

The quadratic formula can be used to find the roots of a quadratic equation, which can help in factoring the trinomial.

Tags

CCSS.HSF-IF.C.7C

Front

What are the steps to factor the trinomial 6x² + 5x - 6?

Back

1. Multiply a and c (6 * -6 = -36). 2. Find two numbers that multiply to -36 and add to 5 (9 and -4). 3. Rewrite the trinomial as 6x² + 9x - 4x - 6. 4. Factor by grouping: (3x - 2)(2x + 3).

Front

What is the factored form of 3x² - 75?

Back

The factored form is 3(x + 5)(x - 5), using the difference of squares.

Tags

CCSS.HSA.APR.C.4