1.5.6 Polynomials and rational expressions

The displacement of a particle $s$ (in meters) from a reference point at time $t$ (in seconds) is modeled by the function:

s(t) = (t - 2)(3t^2 + 10t + k) + 48

where $k\,$ is a constant.

State the remainder when $s (t)$ is divided by $(t - 2)$ .

[2]

Given that the particle is at the reference point ( $s = 0$ ) when $t=23\displaystyle t = \frac{2}{3}$ , show that $k = 28$ .

[4]

ci.

Hence

fully factorise the expression for $s (t)$ ,

[3]

cii.

Hence

find the number of real solutions of the equation $s (t) = 0$ , giving a reason for your answer.

[3]

1.5.6 Polynomials and rational expressions Questions

The displacement of a particle $s$ (in meters) from a reference point at time $t$ (in seconds) is modeled by the function:

s(t) = (t - 2)(3t^2 + 10t + k) + 48

where $k\,$ is a constant.

State the remainder when $s (t)$ is divided by $(t - 2)$ .

[2]

Given that the particle is at the reference point ( $s = 0$ ) when $t=23\displaystyle t = \frac{2}{3}$ , show that $k = 28$ .

[4]

ci.

Hence

fully factorise the expression for $s (t)$ ,

[3]

cii.

Hence

find the number of real solutions of the equation $s (t) = 0$ , giving a reason for your answer.

[3]