Zeros of polynomials (with factoring

We want to find the zeros of this polynomial:

p (x) = 2x3 + 5x2 - 2x - 5

Plot all the zeros (x-intercepts) of the polynomial in the interactive graph.

x = - 5/2 x=1 x = - 1

Step-by-step explanation:

p (x) = 2x^3 + 5x^2 - 2x - 5

Use factor by grouping

p (x) = 2x^3 + 5x^2 - 2x - 5

Factor x^2 from the first group and - 1 from the second group

x^2 (2x + 5) - 1 (2x+5)

Then factor out 2x+5

p (x) = (2x+5) (x^2-1)

Factor x^2 - 1 as the difference of squares

p (x) = (2x+5) (x-1) (x+1)

Set to zero to find the x intercepts

0 = (2x+5) (x-1) (x+1)

Using the zero product property

2x+5 = 0 x-1 = 0 x+1 = 0

2x = - 5 x=1 x=-1

x = - 5/2 x=1 x = - 1

The zeroes are (-1,0), (1, 0) and (-5/2, 0)

Step-by-step explanation:

We can find the zeroes by factoring:

2x^3 + 5x^2 - 2x - 5 = 0

x^2 (2x + 5) - 1 (2x + 5) = 0

(x^2 - 1) (2x + 5) = 0

(x - 1) (x + 1) (2x + 5) = 0

So x = - 1, 1, - 5/2.