#3 Factoring Quadratics

Front

What is factoring in algebra?

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 are the factors of the quadratic expression 4x² - 16x - 9?

Back

(2x-9)(2x+1)

Front

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

Back

(x-4)(x-6)

Front

How do you factor the expression 3v² - 4v - 7?

Back

(3v-7)(v+1)

Front

What is the factored form of 3a² + 4a + 1?

Back

(3a+1)(a+1)

Front

What are the factors of the quadratic expression 3x² - 17x + 10?

Back

(x-5)(3x-2)

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

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

Back

The leading coefficient (the coefficient of x²) determines the direction of the parabola's opening: if positive, it opens upwards; if negative, it opens downwards.

Front

What is the process of completing the square?

Back

Completing the square is a method used to convert a quadratic expression into a perfect square trinomial, making it easier to factor or solve.