What must be added or subtracted to p(x) 8x^4+14x^3-2x^2+8x-12 so that 4x^2+3x-2 is a factor of p(x)

What must be added or subtracted to p(x) 8x^4+14x^3-2x^2+8x-12 so that

1.	What must be added or subtracted to p(x) 8x^4+14x^3-2x^2+8x-12 so that 4x^2+3x-2 is a factor of p(x)
Answer» Let f(x) = 8x4 + 14x3 - 2x2 +7x - 8 and g(x) = 4x2 + 3x - 2We know that Dividend = Quotient {tex}\\times{/tex}\xa0Divisor + Remainderf(x) = g(x) {tex}\\times{/tex}\xa0q(x) + r(x){tex}\\Rightarrow{/tex}\xa0f(x) - r(x) = g(x) {tex}\\times{/tex}\xa0q(x){tex}\\Rightarrow{/tex} Dividend - Remainder = Quotient {tex}\\times{/tex}\xa0DivisorClearly, RHS of the above result is divisible by the divisor. Therefore, LHS is also divisible by the divisor. Thus, if we subtract remainder from the dividend, then it will be exactly divisible by the divisor.By\xa0long division method.Quotient = 2x2 + 2x - 1 and Remainder = 14x - 10Thus, if we subtract the remainder 14x - 10 from 8x4 + 14x3 - 2x2 + 7x - 8, it will be exactly divisible by 4x2 + 3x - 2.