Question

How to find three consecutive odd numbers whose product is 2145? How do you turn that in to a polynomial

Answer 1

Given

The product of three consecutive odd numbers is 2145.

To find the numbers.

Explanation:

Let be an odd number.

That implies, the three consecutive odd numbers are,

$(x-2),x,(x+2)$

Since their product is 2145.

Then,

$(x-2)\cdot x\cdot(x+2)=2145$

Since the prime factorization of 2145 is,

That implies,

$\begin{gathered} (x-2)\cdot x\cdot(x+2)=5\times3\times13\times11 \\ =15\times13\times11 \\ =11\cdot13\cdot15 \end{gathered}$

Hence, the three consecutive odd numbers is 11, 13, 15.

And,

$\begin{gathered} (x-2)\cdot x\cdot(x+2)=2145 \\ x(x^2-4)=2145 \\ x^3-4x-2145=0 \end{gathered}$

Therefore, the polynomial is,

$f(x)=x^3-4x-2145$