Factor Quadratic Expressions (1)

Front

What is the general form of a quadratic expression?

Back

The general form of a quadratic expression is ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does it mean to factor a quadratic expression?

Back

Factoring a quadratic expression means rewriting it as a product of two binomials.

Front

What is the factored form of the quadratic expression 3x² - 5x - 2?

Back

(3x + 1)(x - 2)

Front

How do you determine the coefficients in a quadratic expression?

Back

The coefficients are the numerical factors in front of the variables: a is the coefficient of x², b is the coefficient of x, and c is the constant term.

Front

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

Back

The leading coefficient (a) determines the direction of the parabola: if a > 0, the parabola opens upwards; if a < 0, it opens downwards.

Front

What is the process for factoring a quadratic expression?

Back

To factor a quadratic expression, find two numbers that multiply to ac (the product of a and c) and add to b, then rewrite the expression using these numbers.

Front

What is the factored form of the quadratic expression 6x² - 7x - 10?

Back

(6x + 5)(x - 2)

Front

What is the role of the discriminant in factoring quadratic expressions?

Back

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

Front

What is the factored form of the quadratic expression 2x² - 7x + 6?

Back

(x - 2)(2x - 3)

Front

How can you check if your factored expression is correct?

Back

You can check by multiplying the binomials back together to see if you obtain the original quadratic expression.