Question

Hey, I need help understanding how to get to the answer of the following problem:

3x^4 + x^3 + 4x - 33 divided by x^2 + 4

I already have the answer key..need help in how to solve it!

Answer 1

\[3x^{4} + x^{3} + 4x - 33 \div x^{2} + 4\]First you take a look at which x has the higher power, in this case: \[3x^{4}\]so, to find the first term you devide: \[3x^{4} \div x^{2} = 3x^{2}\] multiply the devider by the term to obtain the first subtraction:\[(3x^{2})(x^{2}+4) = 3x^{4} + 12x^{2}\]hence, \[(3x^{4} + x^{3} + 4x - 33) - (3x^{4} + 12x^{2}) = x^{3} - 12x^{2} + 4x - 33 \] now we have the x with highest power to be \[x^{3}\]therefore:\[(x^{3}) \div x^{2} = x\]multiply this new term by the devidor term to find the second subtraction:\[(x)*(x^{2} + 4) = x^{3} + 4x\]hence,\[(x^{3} - 12x^{2} + 4x - 33) - ( x^{3} + 4x) = -12x^{2} -33\] now, for last we have \[(-12x^{2}) \div (x^{2}) = -12 * (x^{2} +4) = -12x^{2} - 48\]hence,\[( -12x^{2} -33) - (-12x^{2} - 48) = 15\]

did yu understand?