Factoring Cubics

Front

What is the formula for factoring a difference of cubes?

Back

The formula for factoring a difference of cubes is: a^3 - b^3 = (a - b)(a^2 + ab + b^2).

Front

Factor the expression: 27x^3 - 1

Back

(3x - 1)(9x^2 + 3x + 1)

Front

What is the formula for factoring a sum of cubes?

Back

The formula for factoring a sum of cubes is: a^3 + b^3 = (a + b)(a^2 - ab + b^2).

Front

Factor the expression: 8x^3 - 27

Back

(2x - 3)(4x^2 + 6x + 9)

Front

What is the first step in factoring a cubic polynomial?

Back

The first step is to look for a common factor in all terms.

Front

Factor the expression: x^2 + 5x + 4

Back

(x + 1)(x + 4)

Front

What is the significance of the discriminant in factoring quadratics?

Back

The discriminant (b^2 - 4ac) determines the nature of the roots: if positive, two distinct real roots; if zero, one real root; if negative, no real roots.

Front

Factor the expression: x^3 - 27

Back

(x - 3)(x^2 + 3x + 9)

Front

What is the relationship between the roots and the factors of a polynomial?

Back

The roots of a polynomial are the values of x that make the polynomial equal to zero, and each root corresponds to a factor of the form (x - root).

Front

Factor completely: 4w^2 + 16w + 15

Back

(2w + 5)(2w + 3)