How do you write a polynomial function in standard form

segnverd3a

segnverd3a

Answered question

2022-01-29

How do you write a polynomial function in standard form with the zeroes x=3, -2, 1?

Answer & Explanation

Jude Carpenter

Jude Carpenter

Beginner2022-01-30Added 9 answers

f(x)=(x-3)(x+2)(x-1)
=(x2x6)(x1)
=(x2x6)x(x2x6)
=x32x25x+6
sjkuzy5

sjkuzy5

Beginner2022-01-31Added 11 answers

First, we should establish what it means to be a zero. If the function is "zero" at those values, that means that y= 0 at those specific values of x.
Think about what a factored function looks like. It usually is something like
f(x) = (x+2)(x-3) or something like that.
The zeros for the previous function are where (x - 2) = 0 or where (x + 3) = 0. Now we use this general idea with your given zeros.
f(x)=(x+2)(x-3)(x-1)
To make this function in standard form, we need to multiply it all out. I prefer to work with the two left parts first. FOIL them out to get:
f(x)=(x23x2x6)(x1)
Now multiply those together to get
f(x)=x3x2x2x+6x+6
Combining like terms again and we find the polynomial in standard form:
f(x)=x32x25x+6

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