Polynomials

Hong Kong

Stage 4 - Stage 5

Christa wants to test whether various linear expressions divide exactly into $P\left(x\right)$`P`(`x`), or whether they leave a remainder. For each linear expression below, state the value of $x$`x` that needs to be substituted into $P\left(x\right)$`P`(`x`) to find the remainder.

a

$x+3$`x`+3

b

$8-x$8−`x`

c

$5+4x$5+4`x`

d

$6-x$6−`x`

Easy

1min

Fill in the gap to make the statement true.

Easy

1min

If $P\left(x\right)=-2x^4+7x^3-3x^2-6x-5$`P`(`x`)=−2`x`4+7`x`3−3`x`2−6`x`−5 and $A\left(x\right)=x+2$`A`(`x`)=`x`+2. Use the remainder theorem to find the remainder when $P\left(x\right)$`P`(`x`) is divided by $A\left(x\right)$`A`(`x`).

Easy

3min

Using the remainder theorem, find the remainder when $P\left(x\right)=-4x^4+6x^3+4x^2-7x+7$`P`(`x`)=−4`x`4+6`x`3+4`x`2−7`x`+7 is divided by $A\left(x\right)=3x-1$`A`(`x`)=3`x`−1.

Easy

5min

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