what is the answer of the question?

Question

Degree 4; zeros −5, 0, 1, 6; coefficient of x³ is 4 find the polynomial 

Answer 1

f(x) = (x + 5)(x)(x - 1)(x - 6)

f(x) = (x² + 5x)(x² - 7x + 6)

f(x) = x⁴ - 7x³ + 6x + 5x³ - 35x + 30x

 

Simplify.

Adjust so it contains 4x³ 

Answer 2

Using the given roots, we can write

 

f(x) = A(x + 5)(x - 0)(x - 1)(x - 6) = 0

 

f(x) = A(x + 5)x(x - 1)(x - 6)

 

We will find an A that makes the coefficient of x³ eqaul to 4.

 

f(x) = A(x² + 5x)(x² - 7x + 6)

 

Expand and get

 

f(x) = A(x⁴ - 2x³ - 29x² + 30x)

 

Then -2A = 4 ⇒ A = -2

 

f(x) = -2(x⁴ - 2x³ - 29x² + 30x) = -2x⁴ + 4x³ + 58x² - 60x