Polynomial Function

Question

Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1 and zeros at 

x= 1, 2, 5

Answer 1

If a polynomial function has a zero at 1, one of its factors is (x-1), since when

x-1=0

we know x=1.

So there are three factors of this polynomial. Write them beside each other to write the function in factored form: y = (x-1)(x-2)(x-5).

And start multiplying!

y = (x²-3x+2)(x-5)

Then keep multiplying:

y = x³-3x²+2x-5x²+15x-10

And combine like terms to get the final answer:

y=x³-8x²+17x-10

Note: the leading coefficient is already 1. If you wanted a different coefficient, you would just multiply each term by that number.

I hope this helps!

Have fun!