3. Polynomials

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

Approx 2 minutes

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Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x â€“ a is p(a), so p= 0 if and only if (x â€“ is a factor of p(x).