Find the quotient. (6x^2 + 23x + 20) ÷ (5 + 2x)

Question

whpalmer4 · Answer

You can divide polynomials just like you do ordinary long division.  Write both the polynomial to be divided and the divisor in order of the highest order terms first (so the divisor in this case would be $2x + 5$.  Then for the first term, decide what the biggest term you could multiply the first term of the divisor by that would be less than or equal to the first term of the polynomial.  Here, the first term of the polynomial is $6x^2$, and the first term of the divisor is $2x$, so the first term of the quotient will be $6x^2/2x=3x$.  Multiply the divisor by that term ($3x*(2x+5) = 6x^2+15x$) and subtract it from the polynomial (leaving us with $8x + 20$).  Now repeat the process with the remaining terms of the polynomial.