SOLUTION: What is the expression of lowest degree by which {{{ (2*x^2-3*x-9) }}}{{{ (x^2-8*x+16) }}} must be multiplied to give a perfect square?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: What is the expression of lowest degree by which {{{ (2*x^2-3*x-9) }}}{{{ (x^2-8*x+16) }}} must be multiplied to give a perfect square?      Log On


   

Question 775397: What is the expression of lowest degree by which +%282%2Ax%5E2-3%2Ax-9%29++%28x%5E2-8%2Ax%2B16%29+ must be multiplied to give a perfect square?
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

+%282%2Ax%5E2-3%2Ax-9%29++%28x%5E2-8%2Ax%2B16%29+

It factors as

(x-3)(2x+3)(x-4)(x-4)

To make the entire expression a perfect square it 
needs to have two of each factor, so it needs to 
be multiplied by (x-3)(2x+3)= 

2x²-3x-9,

then it will be

(x-3)²(2x+3)²(x-4)²

Edwin