SOLUTION: FIND THE GREATES COMMON FACTOR OF P AND Q. THEN DIVIDE THE COMMON FACTOR SO THAT THE LEADING COEFFICIENT IS P(X)=X4+2X^3+6X^2+8X+8 Q(X)=X^4+2X^3+8X^2+8X+16 THE GREATEST COMMON FA

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: FIND THE GREATES COMMON FACTOR OF P AND Q. THEN DIVIDE THE COMMON FACTOR SO THAT THE LEADING COEFFICIENT IS P(X)=X4+2X^3+6X^2+8X+8 Q(X)=X^4+2X^3+8X^2+8X+16 THE GREATEST COMMON FA      Log On


   

Question 18515: FIND THE GREATES COMMON FACTOR OF P AND Q. THEN DIVIDE THE COMMON FACTOR SO THAT THE LEADING COEFFICIENT IS P(X)=X4+2X^3+6X^2+8X+8 Q(X)=X^4+2X^3+8X^2+8X+16 THE GREATEST COMMON FACTOR IS ____ (P(X))/(Q(X))=(____)/(____)
Answer by khwang(438) About Me  (Show Source):
You can put this solution on YOUR website!
Factor
+P%28X%29=X%5E4%2B2X%5E3%2B6X%5E2%2B8X%2B8+
= X%5E4+%2B+4X%5E2%2B+2X%5E3+%2B+2x%5E2+%2B+8x+%2B+8
= X%5E2%28X%5E2+%2B+4%29+%2B+2x%5E2%28x%2B1%29+%2B+8%28x%2B1%29
= X%5E2%28X%5E2+%2B+4%29+%2B+2%28x%2B1%29+%28x%5E2%2B4%29
= %28X%5E2+%2B+4%29%28X%5E2+%2B+2X+%2B2%29+
Similarly,
+Q%28X%29=X%5E4%2B2X%5E3%2B8X%5E2%2B8X%2B16+
= X%5E4+%2B+4X%5E2%2B+2X%5E3+%2B+4x%5E2+%2B+8x+%2B+16
= X%5E2%28X%5E2+%2B+4%29+%2B+2x%5E2%28x%2B2%29+%2B+8%28x%2B2%29
= X%5E2%28X%5E2+%2B+4%29+%2B+2%28x%2B2%29+%28x%5E2%2B4%29
= %28X%5E2+%2B+4%29%28X%5E2+%2B+2X+%2B+4%29+
so
THE GREATEST COMMON FACTOR IS +X%5E2+%2B+4

(P(X))/(Q(X))= (____)/(____) ...for you

Kenny