The expression 3x² - 33x - 180 can be factored into the form a(x + b)(x + c), where a, b, and c are constants, to reveal the zeros of the function defined by the expression. What are the zeros of the function defined by 3x² - 33x - 180?

A.) -15 B.) -10 C.) -6 D.) -4 E.) 4 F.) 6 G.) 10 H.) 15

A.) -15 B.) -10 C.) -6 D.) -4 E.) 4 F.) 6 G.) 10 H.) 15

Zeros of a quadratic trinomial are the values for x, when y is set equal to zero. Zeros of a quadratic function are also known as "x-intercepts", "roots", or "solutions". When a graph hits the x-axis,

at the x-intercept, the value of y is zero.

3x² - 33x - 180 = 0 {set the expression equal to 0, to find the zeros of the function}

3(x² - 11x - 60) {factored out the greatest common factor, 3}

3(x - 15)(x + 4) = 0 {factored the quadratic trinomial into two binomials}

x - 15 = 0 or x + 4 = 0 {set each factor equal to 0, of course excluding the 3}

x = 15 or x = -4 {solved each equation for x}

the zeros are D.) -4 and H.) 15

at the x-intercept, the value of y is zero.

3x² - 33x - 180 = 0 {set the expression equal to 0, to find the zeros of the function}

3(x² - 11x - 60) {factored out the greatest common factor, 3}

3(x - 15)(x + 4) = 0 {factored the quadratic trinomial into two binomials}

x - 15 = 0 or x + 4 = 0 {set each factor equal to 0, of course excluding the 3}

x = 15 or x = -4 {solved each equation for x}

the zeros are D.) -4 and H.) 15

*- Algebra House*