# Thread: solving polynomial word problems

1. ## solving polynomial word problems

if anyone could help with any of these questions, it would really make my day!

question 1. When the polynomial mx^3-3x^2+nx+2 is divided by x+3, the remainder is -1. When it is divided by x-2, the remainder is -4. determine the values of m and n.

question 2. A rectangular prism has dimensions 10cm by 10cm by 5cm. when each dimension is increased by the same amount, the new volume 1008 cm. what are the dimensions of the new prism?

question 3. The distance, d, in kilometers, travelled by a plane after t hours can be represented by d(t)=-4t^3+40t^2+500t, where 0<t<10. how long does the plane take to fly 4088km?

2. Originally Posted by extraordinarymachine
if anyone could help with any of these questions, it would really make my day!

question 1. When the polynomial mx^3-3x^2+nx+2 is divided by x+3, the remainder is -1. When it is divided by x-2, the remainder is -4. determine the values of m and n.
for $\displaystyle f(x) = mx^3-3x^2+nx+2$

then $\displaystyle f(-3)=-1$ and $\displaystyle f(2)=-4$

so for $\displaystyle f(-3)=-1$ we get

$\displaystyle f(-3) = m(-3)^3-3(-3)^2+n(-3)+2$

$\displaystyle -1 = m(-3)^3-3(-3)^2+n(-3)+2$

and for $\displaystyle f(2)=-4$ we get

$\displaystyle f(2) = m(2)^3-3(2)^2+n(2)+2$

$\displaystyle -4 = m(2)^3-3(2)^2+n(2)+2$

simplify these equations and solve them simultaneously

3. Originally Posted by extraordinarymachine
question 2. A rectangular prism has dimensions 10cm by 10cm by 5cm. when each dimension is increased by the same amount, the new volume 1008 cm. what are the dimensions of the new prism?
The new dimensions are increased by the same amount, lets call that 'x'

so the equation becomes $\displaystyle (10+x)(10+x)(5+x)= 1008$

Can you solve it from here?

4. Originally Posted by extraordinarymachine

question 3. The distance, d, in kilometers, travelled by a plane after t hours can be represented by d(t)=-4t^3+40t^2+500t, where 0<t<10. how long does the plane take to fly 4088km?

for this equation $\displaystyle d(t)=-4t^3+40t^2+500t$ you have 2 variables distance and time so as 4088km is a distance put this into the equation replacing d(t).

$\displaystyle 4088=-4t^3+40t^2+500t$

$\displaystyle 4t^3-40t^2-500t+ 4088=0$

you need to solve for t from this point. Take out 4 as a common factor
$\displaystyle t^3-10t^2-125t+ 1022=0$

now use the factor theorem which says

If $\displaystyle f(a)=0$ then $\displaystyle (x-a)$ is a factor