SAT preparation test help!

Question

Consider the function y = x³ + 11x² + 25x + 15

which of the following statement is false?

a.) The graph is increasing from quadrant 3 to quadrant 1

b.) The graph has no y-intercept

c.) The graph has two turning points

d.) The graph has three x- intercepts

PS. Online course is hard thanks for helping me ;)

Answer 1

y = x³ + 11x² + 25x + 15

By plugging in -1 for x, we see that -1 is a root (x-intercept), so x + 1 is a factor.

Divide by x + 1 to get y = (x + 1)(x² + 10x + 15)

Setting x² + 10x + 15 equal to zero, we get x = (-10 ± √40) / 2, which are also x-intercepts.

Since the function is of degree 3, there can't be more than 3 x-intercepts.

So, there are exactly 3 x-intercepts.