Question

Factor x3 – 4x2 – 3x + 18 = 0, given that 3 is a zero.

Answer 1

well, 3 is a zero, or a solution, means that
x = 3
x-3 = 0

that is, (x-3) is a factor of it
so, if you were to divide \(\bf (x^3-4x^2-3x+18) \quad \div \quad (x-3)\)

it will yield you a remainder of 0, and thus, another factor, in this case, likelly a quadratic one
then you can just factor out the quadratic one :)

Answer 2

hint: you can divide them either by synthetic or long division

Answer 3

ok

Answer 4

i did the syntetic and got 1,-1,-6, (0)

Answer 5

well then that means that, those are the coefficients for the other factor :)
recall, you drop by one exponent value, thus
1 -1 and -6 from a cubic polynomial means
\(\bf 1x^2-1x-6\)

Answer 6

ok whats next?

Answer 7

next is, factor \(\large x^2-x-6\) :)

Answer 8

anyhow, that will facot to (x-3)(x+2)

so that means that
\(\bf (x^3-4x^2-3x+18) \implies (x-3)(x-3)(x+2)\implies (x-3)^2(x+2)\)

Answer 9

facot? shoot typos, factor =)

Answer 10

oh ok thank you so much

Answer 11

yw