Factoring Quadratics

Front

What is factoring in mathematics?

Back

Factoring is the process of breaking down an expression into simpler components, 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 standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

Front

What are the factors of x² - 81?

Back

(x - 9)(x + 9) - This is a difference of squares.

Front

What is the factored form of x² - 10x + 24?

Back

(x - 4)(x - 6) - This can be found by identifying two numbers that multiply to 24 and add to -10.

Front

How do you factor a quadratic expression?

Back

To factor a quadratic expression, find two numbers that multiply to the constant term and add to the coefficient of the linear term.

Front

What is the factored form of 4x² - 16x - 9?

Back

(2x - 9)(2x + 1) - This involves finding factors of the quadratic.

Front

What are the factors of x² - 8x - 48?

Back

(x - 12)(x + 4) - This can be factored by finding two numbers that multiply to -48 and add to -8.

Front

What is the factored form of x² + 16x + 15?

Back

(x + 1)(x + 15) - This involves finding two numbers that multiply to 15 and add to 16.

Front

What is the difference of squares?

Back

The difference of squares is a special factoring case where a² - b² = (a - b)(a + b).