Factor. x^3 - 2x^2 - 5x + 6 ......?

Question

I'm willing to give a best answer to the first person with the correct answer and who has explained how they did. I have already worked out the problem and I have the correct answer, but I feel like giving a best answer. I'd jump all over this; I appreciate math ^_^

Answer 1

to find the roots, plug in the factors of the leading coefficient or the factors of the constant

the leading coefficient is 1
the constant is 6

6 has the factor of +/-1, +/-2, +/-3 +/-6

try 1
1^3 - 2(1)^2 - 5(1) + 6
1 - 2 - 5 + 6
-1 - 5 + 6
-6 + 6
0

1 is the root so (x - 1) is one of the factor

use sythetic long division.

x - 1 is in the form of x - k, thus, k = 1

1 l 1 ... -2 ... -5 ... 6
...l ........ 1 .... -1 .. -6
----------------------------
.... 1 .... -1 ... -6 .. 0

so you have

(x - 1) (x^2 - 1x - 6)

factor the rest

(x - 1) (x + 2) (x - 3)

Answer 2

Hello,

Do you know synthetic substitution??

We can see that if you put 3 in for x that we have a value of 0 for the polynomial. So (x-3) is a factor. I cannot set up synthetic substitution here as the number never line up, but bring down the first coefficient which is 1then

you put in 3 and multiply each coefficient by it and we have 3*1 = 3 and add it the the second one which is -2 giving us 1 which when multiplied by 3 gives us 3 and added to -5 gives us -2 and when multiplied by 3 gives us -6 and added to 6 gives us 0.

So the coefficients of the quotient when we divide by (x-3) which is one of the factors is given by the above numbers or 1x^2 +1x - 2 and this factors into (x+2)(x-1) and our (x-3)

I hope this is somewhat clear.

Answer 3

x^3-2x^2-5x+6
If x is substituted by 1,the value of the polynomial becomes zero therefore x-1 is a factor of the polynomial.
given expression
=x^2(x-1)-x(x-1)-6(x-1)
=(x-1)(x^2-x-6)
=(x-1)(x^2+2x-3x-6)
=(x-1){x(x+2)-3(x+2)}
=(x-1)(x+2)(x-3)

Answer 4

(x+2)(x-1)(x-3) by synthetic division

use a graphing calculator to establish zeros or use the Rational Roots Theorem p/q