KallenayabAllion
Answered

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

Verified Answer :

nobillionaireNobley

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:

Option 2 is correct.

Step-by-step 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


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