Factorize the following to answer the code below. Letters may be used more than once. Q3. Find remainder if x 3 – 3x 2 + 4x – 14 is divisible by x + 2.
Q4. Factorize x 3 – x 2 – 22x + 40

3.-42

Step-by-step explanation:

3.

x+2=0,x=-2

f(-2)=(-2)³-3(-2)²+4(-2)-14=-8-12-8-14=-42

4.

x³-x²-22x+40

put x=2

2³-2²-22(2)+40

=8-4-44+40

=48-48

=0

x=2

so x-2 is one factor.

by synthetic division.

2 |  1  -1  -22   40

  |       2    2  -40

     1   1   -20  | 0

x²+x-20=0

x²+5x-4x-20

=x(x+5)-4(x+5)

=(x+5)(x-4)

x³-x²-22x+40=(x+5)(x-2)(x-4)

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

b, i believe, but not sure.