taiwan-gsat 2024 Q14

taiwan-gsat · Other · gsat__math-a 5 marks Factor & Remainder Theorem Remainder by Quadratic or Higher Divisor
It is known that $f(x), g(x), h(x)$ are all real-coefficient cubic polynomials, and their remainders when divided by $x^{2} - 2x + 3$ are $x + 1$, $x - 3$, and $-2$ respectively. If $xf(x) + ag(x) + bh(x)$ is divisible by $x^{2} - 2x + 3$, where $a, b$ are real numbers, then $a =$ (14-1)(14-2), $b =$ (14-3).
It is known that $f(x), g(x), h(x)$ are all real-coefficient cubic polynomials, and their remainders when divided by $x^{2} - 2x + 3$ are $x + 1$, $x - 3$, and $-2$ respectively. If $xf(x) + ag(x) + bh(x)$ is divisible by $x^{2} - 2x + 3$, where $a, b$ are real numbers, then $a =$ (14-1)(14-2), $b =$ (14-3).