Factoring

Front

What is factoring in algebra?

Back

Factoring is the process of breaking down an expression into a product of simpler expressions, or factors, that when multiplied together give the original expression.

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts of a quadratic function are the points where the graph intersects the x-axis, which occur when the function equals zero.

Front

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

Back

To find the x-intercepts, set the quadratic equation to zero and solve for x using factoring, completing the square, or the quadratic formula.

Front

What is a factor of a polynomial?

Back

A factor of a polynomial is a polynomial of lower degree that divides the original polynomial without leaving a remainder.

Front

What is the relationship between factors and roots of a polynomial?

Back

The roots of a polynomial are the values of x that make the polynomial equal to zero, and these values correspond to the x-intercepts of the graph.

Front

What is the standard form of a quadratic equation?

Back

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

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 difference of squares?

Back

The difference of squares is a special factoring pattern that states 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 a trinomial of the form x² + bx + c?

Back

To factor a trinomial of the form x² + bx + c, find two numbers that multiply to c and add to b, then express it as (x + m)(x + n).