x=3,-2,1 write a polynomial function in standard form with the given zeros

Question

anonymous · Answer

But this is almost like the previous question, just that the numbers have changed! :(

campbell_st · Answer

well is x = 3 is a zero then (x - 3) is a binomial factor of the polynomial. 

just find the other binomial factors... 

then 

P(x) = a(x -3)(binomial factor 2)(binomial factor 3)

a is a constant... based on your question I'd use a = 1

anonymous · Answer

i know but i got to (x^2-x-6)(x-1) n idk wat to do now

campbell_st · Answer

well its simply 

$$P(x) = x(x^2 -x -6) -1(x^2 -x -6)$$

distribute and collect like terms to simplify

anonymous · Answer

how do u do it

campbell_st · Answer

well the 1st part is

 $$x^2 \times x -x \times x - 6 \times x$$

and a similar process for the 2nd part.

anonymous · Answer

huh can u put the numbers tho

campbell_st · Answer

well what do you get 

$$x^2 \times x = $$

anonymous · Answer

i got (x-3)(x+2)(x-1)
(x^2+2x-3x-6)(x-1)
(x^2-1x-6)(x-1)
wat do i do after that

campbell_st · Answer

yep thats correct.. 

and the polynomial is degree 3

so you need to distribute 

$$P(x) = (x^2 -x -6) \times(x -1)$$

which can be done by splitting the binomial and multiplying

$$P(x) = x \times (x^2 -x -6) -1\times(x^2 - x -6)$$

you just need to simplify this.

campbell_st · Answer

once its multiplied out... collect the like terms.