Factor Theorem: If 4x^2-4x-3 is factor of 8x^4+px^3+qx^2+x+3

[teddybear67]

ok, im stuck with this question:

Find the values of p and q if 4x^2-4x-3 is a factor of the expression 8x^4 + px^3 + qx^2 + x + 3. Hence, factorise the expression completely

It is based on factor theorem...if u've ever heard of it...

The answer is p= -12, q= -6 and the factors are (x-1)(2x-3)(2x+1)^2
I got the answers from the answer key behind the book

Its due tomorrow so can someone please help meee?

 

[stapel]

Find the values of p and q if 4x^2-4x-3 is a factor of the expression 8x^4 + px^3 + qx^2 + x + 3. Hence, factorise the expression completely

:arrow: What does the Factor Theorem say about the relationship between factors and remainders? If the given polynomial is a factor, then what remainder should you get when you do the long division?

Set the remainder expression you get equal to this value, and solve for p and q. :idea:

If you get stuck, please reply showing all of your work and reasoning. Thank you!

Eliz.