Question

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

Answer 1

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

Answer 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 \[x^{3}-7x^{2}+10x\]

Answer 3

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.

Answer 4

so x^3

Answer 5

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.

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

THANKS ALOT

Answer 10

Good Luck @kerstie