Factoring Quadratics When A Is Not Equal To 1

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 does it mean when A is not equal to 1 in a quadratic equation?

Back

In a quadratic equation of the form Ax^2 + Bx + C, if A is not equal to 1, it means the coefficient of x^2 is greater than or less than 1, which affects the factoring process.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is Ax^2 + Bx + C, where A, B, and C are constants and A is not equal to 0.

Front

How do you factor a quadratic expression when A is not equal to 1?

Back

To factor a quadratic expression when A is not equal to 1, you can use the method of grouping or the AC method, where you multiply A and C, find two numbers that multiply to AC and add to B.

Front

What is the AC method in factoring quadratics?

Back

The AC method involves multiplying the coefficient A by the constant C, then finding two numbers that multiply to this product and add to the coefficient B.

Front

Factor the expression: 7x^2 - 16x + 4

Back

(x - 2)(7x - 2)

Front

Factor the expression: 6x^2 + 19x + 8

Back

(3x + 8)(2x + 1)

Front

Factor the expression: 6x^2 - x - 1

Back

(3x + 1)(2x - 1)

Front

Factor the expression: 9x^2 - 20x + 4

Back

(9x - 2)(x - 2)

Front

What is a quadratic trinomial?

Back

A quadratic trinomial is a polynomial of three terms in the form Ax^2 + Bx + C.