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 8x² + 31x - 4?

Back

(8x - 1)(x + 4)

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 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 distinct real roots; if zero, one real root; if negative, no real roots.

Front

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

Back

(6x + 5)(x - 2)

Front

What method can be used to factor quadratics when a ≠ 1?

Back

The method of grouping or trial and error can be used to factor quadratics when a ≠ 1.

Front

What is the factored form of the quadratic expression x² + 13x - 48?

Back

(x + 16)(x - 3)

Front

What is the role of the leading coefficient in factoring quadratics?

Back

The leading coefficient (a) affects the shape of the parabola and can influence the methods used for factoring.

Front

What is the factored form of the quadratic expression 8x² + 7x - 4?

Back

(2x - 3)(2x - 5)