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2 answers:
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<u>Answer:</u>
(x - 2) is not a factor of f(x) = 3x^5 - 7x^3 - 11x^2 + 2
<u>Step-by-step explanation:</u>
According to the Remainder Theorem, when a polynomial f(x) is divided by a term (x - r), then the remainder must be f(r).
So first we will divide f(x) by (x - 2) using long division to get:
(3x^5 - 7x^3 - 11x^2 + 2) / (x - 2)
= 3x^4 + (6x^4 - 7x^3 - 11x^2 + 2) / (x-2)
= 3x^4 + 6x^3 + (5x^3-11x^2+2) / (x - 2)
= 3x^4 + 6x^3 + 5x^2 (-x^2 + 2) / (x - 2)
= 3x^4 + 6x^3 + 5x^2 -x -2 - (2) / (x -2)
=
Therefore the remainder is -2.
Now check x = 2 for 3x^5 - 7x^3 - 11x^2 + 2:
3(2)^5 - 7(2)^3 - 11(2)^2 + 2 = -2
The Remainder Factor theorem also states that if (x - r) is a factor of f(x) then f(r) must be 0.
So we found that f(2) = -2, therfore (x - 2) is not a factor of f(x) .
Answer:
Yes there is enough information to find both triangles DEF and DHG are congruent.
Both the triangles are congruent by SAS theorem of congruence.
Step-by-step explanation:
Lets have a look to both of the triangles.
And mention what are the given information in our question.
We have DEF and
DHG.
Where
- FD
DG
- ED
And we can see that (Vertically opposite angles).
So we have two sides equal and an angle between the two are equal.
Then we can say that through SAS property of congruence DEF and
DHG are congruent
's
Answer:
-5
Step-by-step explanation:
<u>Given that , </u>
- A number is taken away from 40 and the result is 45 .
<u>L</u><u>et </u><u>:</u><u>-</u><u> </u>
- The required number be x .
<u>According</u><u> to</u><u> Question</u><u> </u><u>:</u><u>-</u><u> </u>
40 - x = 45
- x = 45 - 40
- x = 5
x = -5