Factoring and Solving Quadratics

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 is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants.

Front

What does it mean to solve a quadratic equation by factoring?

Back

To solve a quadratic equation by factoring means to express the equation in the form (px + q)(rx + s) = 0 and then set each factor equal to zero to find the values of x.

Front

What is the zero-product property?

Back

The zero-product property states that if the product of two factors is zero, then at least one of the factors must be zero.

Front

How do you factor the expression 8r³ + 16r²?

Back

8r²(r + 2) is the factored form of the expression.

Front

What are the steps to solve the quadratic equation 2x² + 7x + 6 = 0 by factoring?

Back

1. Factor the quadratic: (2x + 3)(x + 2) = 0. 2. Set each factor to zero: 2x + 3 = 0 or x + 2 = 0. 3. Solve for x: x = -3/2 or x = -2.

Front

What is the factored form of n² + 5n - 6?

Back

(n - 1)(n + 6) is the factored form of the expression.

Front

How do you solve the equation 4x² + 12x - 280 = 0?

Back

1. Factor the quadratic: 4(x + 10)(x - 7) = 0. 2. Set each factor to zero: x + 10 = 0 or x - 7 = 0. 3. Solve for x: x = -10 or x = 7.

Front

What is the first step in factoring the expression 2b² + 14b - 16?

Back

The first step is to factor out the greatest common factor (GCF), which is 2, giving 2(b² + 7b - 8).

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots of the quadratic equation: if it's positive, there are two real roots; if zero, one real root; if negative, no real roots.