Factoring, Finding x-intercepts & Multiplying Binomials

Front

What is factoring in algebra?

Back

Factoring is the process of breaking down an expression into a product of simpler expressions, called factors.

Front

What are x-intercepts?

Back

X-intercepts are the points where a graph crosses the x-axis, which occur when the output (y-value) is zero.

Front

How do you find the x-intercepts of a quadratic equation in factored form?

Back

Set each factor equal to zero and solve for x.

Front

What is the product of (x + a)(x + b)?

Back

The product is x² + (a + b)x + ab.

Front

What is the difference of squares formula?

Back

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

Front

What does it mean to multiply binomials?

Back

Multiplying binomials involves using the distributive property to combine two binomials into a single polynomial.

Front

What is the result of multiplying (x - 3)(x - 3)?

Back

The result is (x - 3)² or x² - 6x + 9.

Front

How do you convert a quadratic expression to factored form?

Back

Look for two numbers that multiply to the constant term and add to the coefficient of the linear term.

Front

What is the standard form of a quadratic equation?

Back

The standard form is ax² + bx + c, where a, b, and c are constants.

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.