Question

Write an equation for the cubic polynomial function whose graph has zeroes at 2, 3, and 5.

Write the polynomial function for the graph.

f(x) = (x – 2)(x – 3)(x – 5)

Simplify the right side. What is the equation?




f(x) = x3 + 31x – 30


f(x) = x3 – 10x2 + 31x – 30


f(x) = x3 – 10x2 + 19x – 30


f(x) = x3 + 19x – 30

Answer 1

f(x) = (x - 2)(x - 3)(x - 5) = x[x(x - 5) - 3(x - 5)] - 2[x(x - 5) - 3(x - 5)] = x[x^2 - 5x - 3x + 15] - 2[x^2 - 5x - 3x + 15] = x[x^2 - 8x + 15] - 2[x^2 - 8x + 15] = x^3 - 8x^2 + 15x - 2x^2 + 16x - 30 = x^3 - 10x^2 + 31x - 30

Answer 2

Option 2 is correct.

Explanation:

Whenever we are given zeroes of a polynomial we multiply the factors so, as to create a cubic polynomial

`f(x)=(x-2)(x-3)(x-5)`

when we will multiply the above factors we get

`f(x)=(x-2)(x^2-5x-3x+15)`

After further multiplication we get

`(x-2)(x^2-8x+15)`

After simplification we get

`x^3-8x^2+15x-2x^2+16x-30`

After further simplification we get

`x^3-10x^2+31x-30`

Option 2 is correct