Question

Find the value of t for which the polynomial,
$p\left(x\right)=x^3+3x^2+2x+t$ gives 3 as remainder when
divided by $x-1$.

Answer 1

Explain:

Using the remainder theorem, the remainder when $p\left(x\right)$ is divided by $x-1$ is $p\left(1\right)$. The remainder is given to be equal to 3 therefore p(1) = 3.

< Dictate and write,

p(x) = x³ + 3x² + 2x + t

p(1) = $(1{)}^3+3\times (1{)}^2+2\times \left(1\right)+t$

p(1) = 1 + 3 + 2 + t

3 = 6 + t

t = -3