Answer:
f(x) = x³+8x²+9x-18
Step-by-step explanation:
Factors are: (x+6)(x+3)(x-1)
= (x+6)(x²+3x-x-3)
= (x+6)(x²+2x-3)
= x³+2x²-3x+6x²+12x-18
f(x) = x³+8x²+9x-18
Answer:
[tex]f(x)=x^3+8x^2+9x-18[/tex]
Step-by-step explanation:
If [tex]c[/tex] is a zero of [tex]f[/tex], then [tex]x-c[/tex] is a factor of [tex]f[/tex].
Since -6,-3, and 1 are zeros, then we have the following factors of [tex]f[/tex]:
[tex](x-(-6))[/tex], [tex](x-(-3))[/tex], and [tex](x-1)[/tex].
Let's put it together.
[tex]f(x)=a(x+6)(x+3)(x-1)[/tex], where [tex]a[/tex] is the leading coefficient and we are given to make it equal to 1, has zeros -6,-3, and 1.
We now need to put the factored form of [tex]f[/tex] into standard form by using multiplication and combining of like terms.
[tex]f(x)=(x+6)(x+3)(x-1)[/tex]
[tex]f(x)=(x^2+6x+3x+18)(x-1)[/tex]
[tex]f(x)=(x^2+9x+18)(x-1)[/tex]
[tex]f(x)=x^3+9x^2+18x-x^2-9x-18[/tex]
[tex]f(x)=x^3+8x^2+9x-18[/tex]
