How many distinct x-intercepts does the graph of y = (x-5)(x^2+5x+6) have?

Question

 It is about graphing quadratics.

Answer 1

The graph has three distinct x-intercepts.

 

We can use the zero product principle. A polynomial in factored form is a zero when any of the factors is zero. One of the zeros (x-intercepts) is x=5.

 

For the other two, you can factor the quadratic trinomial in the parenthesis (do it for practice).

 

The x-intercepts (zeros) are x=-2 and x=-3.