Math 1 Unit 8: Factoring Quadratics a>1

Front

What is factoring in mathematics?

Back

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

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 does it mean if a quadratic has a leading coefficient greater than 1?

Back

It means that the coefficient of the x² term (a) is greater than 1, which affects how the expression is factored.

Front

Factor the quadratic: 3x² - 17x + 10

Back

(x - 5)(3x - 2)

Front

Factor the quadratic: 2x² - 13x - 70

Back

(2x + 7)(x - 10)

Front

Factor the quadratic: x² + 9x - 36

Back

(x + 12)(x - 3)

Front

What is the first step in factoring a quadratic expression?

Back

The first step is to identify the coefficients a, b, and c in the expression ax² + bx + c.

Front

What is the significance of the discriminant in factoring quadratics?

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.

Front

Factor the quadratic: 3v² - 4v - 7

Back

(3v - 7)(v + 1)

Front

Factor the quadratic: 5x² - 13x + 6

Back

(5x - 3)(x - 2)