SOLUTION: What polynomial of lowest degree must be multiplied to 2x^3-5x^2-4x+12 to make it a perfect square?

Question 702288: What polynomial of lowest degree must be multiplied to 2x^3-5x^2-4x+12 to make it a perfect square?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
It is a factoring and division of polynomials problem

--> --> -->
That means that is divisible by
Dividing, we find that

Then, it turns out that ,
so ,
and -->
The answer is .

How could you factor ?
If you are good at factoring, you would have no problem.
Otherwise, you could find that the value of for is ,
and dividing by again, would get the factoring.
Another way to do it, would be solving to find that and are the roots of .
RELATED QUESTIONS
what polynomial of lowest degree must be mutiplied to 2x^3-5x^2-4x+12 to make it a... (answered by Edwin McCravy)

What polynomial of lowest degree must be multiplied to the polynomial 8x³-29x²-16x+48... (answered by ikleyn)

what binomial of lowest degree must be multiplied to x3-3x2-9x-5 to make it a polynomial... (answered by KMST)

What is the expression of lowest degree by which {{{ (2*x^2-3*x-9) }}}{{{ (x^2-8*x+16)... (answered by Edwin McCravy)

What is the expression of lowest degree by which (X^2+3X-10)(X^2-X-2) must be multiplied... (answered by venugopalramana)

what must be multiplied to the expression 60x^3y^5 to make it a perfect... (answered by ikleyn,Alan3354)

What must be multiplied to the expression 120x^5y to make it a perfect... (answered by greenestamps,Alan3354)

what expression with the smallest numerical coefficient and smallest degree must be... (answered by Alan3354)

What expression with the smallest numerical coefficient and smallest degree must be... (answered by solver91311)