Question

What is the completely factored form of the quadratic expression 3x^2 - 30x - 72?

a) 3(x - 4)(x + 6)
b) 3(x - 6)(x + 4)
c) 3(x + 4)(x - 6)
d) 3(x + 6)(x - 4)

Answer 1

The completely factored form of the quadratic expression 3x^2 - 30x - 72 is 3(x - 4)(x + 6).

Step-by-step explanation:

The completely factored form of the quadratic expression 3x^2 - 30x - 72 is: 3(x - 4)(x + 6) (option a). To factor a quadratic expression, we look for two binomials that multiply to give the original expression. In this case, the factors are (x - 4) and (x + 6). Multiplying these two binomials by the leading coefficient 3 gives us the completely factored form. For example: 3(x - 4)(x + 6) = 3x(x) + 3x(6) - 4(3x) - 4(6) = 3x^2 + 18x - 12x - 24 = 3x^2 + 6x - 24 = 3x^2 - 30x - 72