Question Type 2: For small polynomials, given a remainder or factor, finding a parameter's value Bootcamps

Find the value of $b$ if the polynomial $3x^2 + bx + 10$ gives a remainder of $3$ when $x = 2$.

Find $k$ if the polynomial $2x^3 + kx^2 -5x +1$ is exactly divisible by $x - 1$.

Given $P(x)=x^3 + ax^2 - x +2$ leaves remainder $5$ at $x=1$, find $a$.

Determine $r$ such that $x^4 + r x^2 - x +4$ has remainder $0$ when divided by $x - 1$.

The polynomial $4x^3 + a x^2 -7x +1$ has factor $x - 1$. Find $a$.

If $5x^3 - m x^2 +2x +1$ gives a remainder of $-3$ when $x = -1$, find $m$.

The polynomial $h(x)=3x^3 - p x +4$ has factor $x + 2$. Determine $p$.

Find $k$ such that $Q(x)=x^4 -4x^2 + kx +5$ gives remainder $13$ when $x=2$.

Find $k$ such that $x^5 + kx^3 - x +2$ is divisible by $x + 1$.

Determine $b$ if $P(x)=2x^4 -3x^2 + b x -6$ gives a remainder of $5$ when $x=2$.

Given $g(x)=6x^4 + d x^3 - x +5$ leaves a remainder of $7$ when $x=1$, find $d$.

Find $c$ if $f(x)=x^3 + c x^2 -4x +3$ is exactly divisible by $x - 3$.