Factoring Quadratic

Front

What is factoring in mathematics?

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 is a quadratic expression?

Back

A quadratic expression is a polynomial of degree 2, typically in the form ax² + bx + c, where a, b, and c are constants.

Front

What is the difference of squares formula?

Back

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

Front

Factor the expression: x² - 16

Back

(x + 4)(x - 4) - This is an example of the difference of squares.

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 ≠ 0.

Front

How do you factor a quadratic expression of the form x² + bx + c?

Back

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

Front

Factor the expression: x² + 5x + 6

Back

(x + 2)(x + 3) - The numbers 2 and 3 multiply to 6 and add to 5.

Front

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

Back

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

Front

Factor the expression: 2x² + 8x

Back

2x(x + 4) - Factor out the greatest common factor.

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.