Factor Quadratics

Front

What is the standard form of a quadratic equation?

Back

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

Front

What does it mean to factor a quadratic expression?

Back

Factoring a quadratic expression means rewriting it as a product of its linear factors.

Front

What is the factored form of the expression a² - 10a + 25?

Back

The factored form is (a - 5)².

Front

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

Back

To factor, find two numbers that multiply to ac and add to b, then rewrite the expression using these numbers.

Front

What is the difference of squares?

Back

The difference of squares is a² - b² = (a - b)(a + b).

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

How do you factor the expression 15t² - 27t - 6?

Back

To factor, first find the GCF, then use the method of grouping or trial and error to find the factors: 3(5t + 1)(t - 2).

Front

What is the significance of the leading coefficient in a quadratic equation?

Back

The leading coefficient (a) determines the direction of the parabola: if a > 0, it opens upwards; if a < 0, it opens downwards.

Front

What are the roots of a quadratic equation?

Back

The roots are the values of x that make the quadratic equation equal to zero.

Front

What is completing the square?

Back

Completing the square is a method used to convert a quadratic equation into a perfect square trinomial.