Find what k equals

Question

If for all x not equal to -1, 3x^2+kx+7 over x+1=3x+7

Answer 1

[ 3x²+kx+7 ] / [ x+1] = 3x+7      multiply both sides by (x+1)

3x²+kx+7 = (3x+7)(x+1)     expand the left by distributing both terms of 1st binomial to both terms of 2nd binomial

3x² + kx + 7 = 3x² + 3x + 7x +7     combine like terms on left

3x² + kx + 7 = 3x² + 10x + 7  subtract 3x² and 7 from both sides

kx = 10x

 

k=10