Year 10 (A1) Mathematics
Polynomial Function (II)
(b) The remainder when $x^{4}+a x+b$ is divided by $(x-2)(x+1)$ is $x+2$. Find the values of and $b$.

Answer

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Answer

\boxed{a = -4, b = -4}

Steps

Step 1 ：Find the remainders when the polynomial is divided by (x-2) and (x+1) using the Remainder Theorem: $f(2) = 2^4 + 2a + b$ and $f(-1) = (-1)^4 - a + b$

Step 2 ：Equate the remainders to the given remainder x+2: $2^4 + 2a + b = 4$ and $(-1)^4 - a + b = 1$

Step 3 ：Solve the system of linear equations to find the values of a and b: $a = -4$ and $b = -4$

Step 4 ：\boxed{a = -4, b = -4}

Year 10 (A1) MathematicsPolynomial Function (II)(b) The remainder when $x^{4}+a x+b$ is divided by $(x-2)(x+1)$ is $x+2$. Find the values of and $b$.

Answer

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Year 10 (A1) Mathematics
Polynomial Function (II)
(b) The remainder when $x^{4}+a x+b$ is divided by $(x-2)(x+1)$ is $x+2$. Find the values of and $b$.