## kerstie 2 years ago HELP ME PLEASE! Write a polynomial function in standard form with zeros at 5, 2, and 1.

1. mathstudent55

Think of it this way, instead of solving a polynomial equation and getting x=a, x=b, x=c, you have the answer and you're going backwards. If you had a polynomial equation that factored into (x - 3)(x + 5)(x -2)= 0, the next step would be x -3 = 0 or x + 5 = 0 or x - 2 = 0, and the answer would be x = 3 or x = -5 or x = 2

zero means x=0 x=2 or x-2=0 x=5or x-5=0 (x)(x-2)(x-5) The resultant equation is \[x^{3}-7x^{2}+10x\]

3. mathstudent55

Now look at the last line and go backwards. In your problem here, you are given x = 5, x = 2, x = 1 Go 1 step back: x - 5 = 0 or x - 2 = 0 or x - 1 = 0 Go 1 more step back (x - 5)(x - 2)(x - 1) =0 Now multiply these 3 binomials together, collect like terms and write the answer in descending order of the power of x.

4. kerstie

so x^3

5. mathstudent55

Be careful, shahzadjalbani misread the problem and thinks there is a zero at 0. His solution is correct for the problem he solved, but it's not your problem.

6. mathstudent55

Multiply the first two binomials using foil. Then multiply by the third one.

7. mathstudent55

(x - 5)(x - 2)(x - 1) = 0 (x^2 - 2x - 5x + 10)(x - 1) = 0 (x^2 - 7x + 10)(x - 1) = 0 continue...

oh sorry x=1 x-1=0 x=2 x-2=0 x=5 x-5=0 Multiply (x-1)(x-5)(x-2) The result would be x^3-8x^{2}+17x-10

9. kerstie

THANKS ALOT