Question

Without actual division show that p(x) = 4x^3 + 3x^2 - 4x - 3 is exactly divisible by ( x+1)and (4x+3)​

Answer 1

Answer:

It's simple

Step-by-step explanation:

just put the values x=-1,x=-3/4 in the polynomoal

Answer 2

$g(x) = x + 1 \\ g(0) = x + 1 = 0 \\ \: \: \: \: \: \: \: \: = x = - 1. \\ p(x) = 4x {}^{3} + 3x {}^{2} - 4x - 3 \\ p( - 1) = 4( - 1) {}^{3} + 3( - 1) ^{2} - 4 \times - 1 - 3 \\ \: \: \: \: \: \: \: \: \: = - 4 + 3 + 4 - 3 \\ \: \: \: \: \: \: \: \: \: \: \: = 0. \\ g(x) = 4x + 3 \\ g(0) = 4x + 3 = 0 \\ \: \: \: \: \: \: \: = x = - 3/4 \\ p( - 3 /4) = 4 \times ( - 3 /4) {}^{3} + 3 \times ( - 3/4) {}^{2} - 4 \times - 3/4 - 3 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = - 3/16 + 27/16 + 3 - 3 \\ \: \: \: \: \: \: \: \: \: \: \: = 24/16 = 3/2. \\x + 1is \: divisible \: by \: p(x)but \: 4x + 1is \: not \: divisible \: by \: p(x).$