5 5/8 - 3 2/8 is equal to 2 3/8.True or False?
2 answers:
You might be interested in
Answer:
See explanation
Step-by-step explanation:
Let be the coordinates of the point which has to be dilated with the scale factor of
with the center of dilation at point
(the origin).
The dilation with the scale factor and the center of dilation at the origin has the rule
So, you have simply to multiply each coordinate of the point by to get the image's coordinates.
According to the rational root theorem, the possible rational factors, if any, of the given polynomial are the factors of 24/1=24.
Thus possible factors are
(x +/- k) where k=1,2,3,4,6,8,12,24.
Since all terms are positive, (x-k) do not exist as factors (see Descartes rule of signs) for all k.
Of the remainder, we note that the
sum of coefficients of even degree terms=1+35+24=60
sum of coefficients of odd degree terms=10+50=60
This means that (x+1) is a factor.
Divide f(x) by (x+1) =>
g(x)=f(x)/(x+1)=x^3+9x^2+26x+24 (no remainder)
We continue with x+2=0, or put x=-2 into g(x), and get
g(-2)=-8+36-52+24=0 => (x+2) is another rational factor.
Again, divide g(x) by (x+2) to get
h(x)=x^2+7x+12 (remainder=0)
We can readily factor h(x) by inspection as h(x)=(x+3)(x+4)
[from 3+4=7,3*4=12]
Therefore
f(x)=x^4+10*x^3+35*x^2+50*x+24=(x+1)(x+2)(x+3)(x+4)
Thus possible factors are
(x +/- k) where k=1,2,3,4,6,8,12,24.
Since all terms are positive, (x-k) do not exist as factors (see Descartes rule of signs) for all k.
Of the remainder, we note that the
sum of coefficients of even degree terms=1+35+24=60
sum of coefficients of odd degree terms=10+50=60
This means that (x+1) is a factor.
Divide f(x) by (x+1) =>
g(x)=f(x)/(x+1)=x^3+9x^2+26x+24 (no remainder)
We continue with x+2=0, or put x=-2 into g(x), and get
g(-2)=-8+36-52+24=0 => (x+2) is another rational factor.
Again, divide g(x) by (x+2) to get
h(x)=x^2+7x+12 (remainder=0)
We can readily factor h(x) by inspection as h(x)=(x+3)(x+4)
[from 3+4=7,3*4=12]
Therefore
f(x)=x^4+10*x^3+35*x^2+50*x+24=(x+1)(x+2)(x+3)(x+4)