IB Mathematics Analysis and Approaches Question Type 3: Finding Several Parameter Values Given Remainder And/or Factors Exercises

For what value of $k$ is the quadratic $k{x}^2-7x+2$ divisible by $x-1$?

The cubic polynomial $P(x)=a{x}^3-2x^2+cx+18$ has a factor $(x-2)$. When $P(x)$ is divided by $(x-4)$, the remainder is 14. Find the values of $a$ and $c$.

Determine $k$ such that the cubic $k{x}^3-x^2+x-k$ is exactly divisible by $x-1$.

Find $k$ if the remainder when $2x^2+kx-8$ is divided by $x-3$ is 10.

Find $b$ and $c$ if the quadratic $x^2+bx+c$ has factors $x+1$ and $x-2$.

Find $p$ and $q$ for the polynomial $p{x}^3+q{x}^2+5x-2$ if it is divisible by $x-1$ and leaves a remainder of 4 when divided by $x-2$.

Determine $k$ such that $x^2+kx-12$ is exactly divisible by $x+4$.

For the quartic $x^4+a{x}^3+b{x}^2+3x+4$ the remainders when divided by $x-1$ and $x+1$ are 5 and 7 respectively. Find $a$ and $b$.

Find $a$ and $b$ if the quartic $$x^4-2x^3+a{x}^2+bx+5$$ has factors $x-1$ and $x+2$.

Find the value of $k$ if the polynomial $k{x}^2+5x+2$ leaves a remainder of 3 when divided by $x-1$.

The cubic polynomial $x^3+a{x}^2+bx+6$ has factors $x-1$ and $x+2$. Find $a$ and $b$.