Question 1155606
Let {{{ h(x)=4x^4+15x^3-10x+2 }}}. Express h(x) in the form h(x)= q(x)(x+3)+r where q(x) is a polynomial and r is a number. Use the Remainder Theorem to check that you have the correct remainder.
<pre>Using LONG DIVISION of POLYNOMIALS or SYNTHETIC DIVISION, we get: {{{matrix(1,3, q(x), "=", 4x^4 + 3x^3  -  9x + 17)}}}
We then get: {{{highlight_green(system(matrix(1,7, h(x), "=", 4x^4 + 15x^3  -  10x + 2, "====>", h(x), "=", 4x^3 + 3x^2  -  9x + 17 + (- 49)/(x + 3)), or, matrix(1,3, h(x), "=", (4x^3 + 3x^2 - 9x + 17)(x + 3) - 49)))}}}.