Factoring a>1

Front

What is the factored form of a quadratic expression?

Back

The factored form of a quadratic expression is expressed as the product of two binomials, typically in the form (ax + b)(cx + d).

Front

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

Back

To factor a quadratic expression of the form ax² + bx + c, look for two numbers that multiply to ac (the product of a and c) and add to b. Use these numbers to split the middle term and factor by grouping.

Front

What is the first step in factoring the expression 16x² - 16x - 12?

Back

The first step is to factor out the greatest common factor (GCF) from all terms, which in this case is 4, resulting in 4(4x² - 4x - 3).

Front

What is the significance of the discriminant in factoring quadratics?

Back

The discriminant (b² - 4ac) determines the nature of the roots of a quadratic equation. If it is positive, there are two distinct real roots; if zero, one real root; and if negative, no real roots.

Tags

CCSS.HSA-REI.B.4B

Front

What does it mean to factor completely?

Back

To factor completely means to break down an expression into its simplest form, where no further factoring is possible.

Front

How can you check if your factored expression is correct?

Back

You can check if your factored expression is correct by multiplying the factors back together to see if you obtain the original expression.

Front

What is the factored form of 6x² + 7x - 3?

Back

The factored form is (2x + 3)(3x - 1).

Front

What is the process of factoring by grouping?

Back

Factoring by grouping involves rearranging and grouping terms in a polynomial to factor out common factors from each group.

Front

What is the factored form of 3x² + 5x - 12?

Back

The factored form is (3x - 4)(x + 3).

Front

What is the role of the leading coefficient in factoring quadratics?

Back

The leading coefficient (the coefficient of x²) affects the methods used for factoring, especially when it is not equal to 1.