Question

6
the following
1) Divide x? +4x?– 3x – 10 by x +1 to obtain the quotient
and remainder.​

Answer 1

Answer:

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Step-by-step explanation:

x + 1 ⎞⎠ x3 + 4x2 − 3x − 10⎛⎝ x2 + 3x − 6 x3 + x2 0 + 3x2 − 3x + 3x2 + 3x 0 − 6x − 10 − 6x − 6 0 − 4So, quotient = x2 + 3x − 6remainder = −4VERIFICATION BY REMAINDER THEOREM :Let p(x) = x3 + 4x2 − 3x − 10Let g(x) = x + 1Now, zero of g(x) is given by solving the equation, g(x) = 0⇒x + 1 = 0⇒x = −1By remainder theorem, when p(x) is divided by g(x), then required remainder isp(−1).Now,p(−1) = (−1)3 + 4(−1)2 − 3(−1) − 10 = −1 + 4 × 1 + 3 −10 = −1 + 4 + 3 −10 = 6 − 10 = −4So, remainder = p(−1) = −