Write a polynomial function h in standard form that has -3 and 5 as zeros of multiplicity of 2.

Question

This is the whole problem.

Answer 1

If x = -3 is a zero, then x + 3 is a factor.

If x = 5 is a zero, then x - 5 is a factor.

Multiplicity of 2 means each of these factors happens twice, or is squared.

h(x) = (x+3)² (x-5)²

Now you have to foil each of these squared terms, then multiply each term in the first by each term in the second. FOIL first:

h(x) = (x²+6x+9)(x²-10x+25)

Start by multiplying the first term (x²) of the first expression, by every term in the second expression:

x⁴ - 10x³ + 25x²

Then multiply the second term (6x) of the first expression, by every term in the second expression:

6x³ - 60x² + 150x

Then multiply the third term (9) of the first expression, by every term in the second expression:

9x² - 90x + 225

Now - combine all the like terms in these last three expressions:

h(x) = x⁴ - 4x³ - 26x² + 60x + 225