Hello thisishard

Welcome to Math Help Forum!Have you tried Googling 'synthetic substitution'? I found this very clear explanation very easily: http://hanlonmath.com/pdfFiles/29.Sy...bstitution.pdf

And I Googled 'synthetic division' and came up with: Synthetic Divisiongiven a polynomial and one of its factors, find the remaining factors of the polynomial. some factors may not be binomials.

2x^3 + 15x^2 - 14x -48 ; x - 2

x^3 + 6x^2 - x - 30 ; x + 5

Use the remainder theorem. In the first of these , and in the second . So work out what each of these expressions is in terms of , and then solve each equation to find .Find values of k so that each remainder is 5

(2x^2 - 8x + k) / (x - 7)

(x^4 + kx^3 - 7x^2 + 8x + 25) / (x - 2)

Grandad