Polynomials
Hong Kong
Stage 4 - Stage 5
Further applications of remainder and factor theorem
Interactive practice questions
The polynomials $4x^2-7x-15$4x2−7x−15 and $5x^2+13x+k$5x2+13x+k have a common factor of $x+p$x+p, where $p$p is an integer.
a
Using the fact that $x+p$x+p is a factor of $4x^2-7x-15$4x2−7x−15, solve for the value of $p$p.
b
Using the fact that $x+p$x+p is a factor of $5x^2+13x+k$5x2+13x+k, solve for $k$k.
Easy
6min
Consider the polynomial $x^{99}+1$x99+1.
Easy
2min
The polynomials $P\left(x\right)=x^3+4x^2-5x+n$P(x)=x3+4x2−5x+n and $Q\left(x\right)=x^3+2x+17$Q(x)=x3+2x+17 leave the same remainder when divided by $x+1$x+1.
Solve for the value of $n$n.
Easy
3min
Consider the sequence: $2^5-2$25−2, $3^5-3$35−3, $4^5-4$45−4, $\text{. . .}$. . ., $x^5-x$x5−x.
Easy
1min
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