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Mathematics: Allen Joy P. Bago 10-Diamond

The document contains two mathematics problems, the first involving finding the total distance an object falls using an arithmetic sequence, where the distance increases by 32 feet each second, and the second involving using long division, synthetic division, and the remainder theorem to divide the polynomial 3x^3 + x^2 - 2x - 2 by (x - 1). Both problems show the steps and solutions.

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Al Vincent
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71 views6 pages

Mathematics: Allen Joy P. Bago 10-Diamond

The document contains two mathematics problems, the first involving finding the total distance an object falls using an arithmetic sequence, where the distance increases by 32 feet each second, and the second involving using long division, synthetic division, and the remainder theorem to divide the polynomial 3x^3 + x^2 - 2x - 2 by (x - 1). Both problems show the steps and solutions.

Uploaded by

Al Vincent
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as DOCX, PDF, TXT or read online on Scribd
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MATHEMATICS

Allen Joy P. Bago


10- Diamond
Problem: (Arithmetic
Sequence)

Mr. Revilla and family visits


Mt. Canlaon in Negros
Occidental to have a long
weekend vacation. At the
peak of the mountain his
child drop a piece of paper
clip. The distance the paper
clip will fall is 18 feet in the
first seconds, 50 feet in the
next seconds and 82 feet in
the third seconds and so
on. What is the total
distance the object will fall
in the next eight seconds?
ANSWER:
Finding the common difference (d):
d = a 3 - a5 Arithmetic
sequence: 18 50 82 ?
1
1st 2nd 3rd 8th
d = 82 - 50 Formula:
1 a n = a1 + (n-
1) d
d = 32 a 8 = 18+ (8-
1) 32
1 a 8 = 18 = (7)
32
d = 32 a 8 = 18 + 224
a 8 = 242
The 8th term is 242
Find the sum:
Sn = n (a 1+
an)
2
S8 = 8
(18+242)
2
S 8 = 8 (260)
2
S 8 = 1040 feet -
the distance of the
Paper
clip in the 8th seconds.

PROBLEM: (Polynomial
Equation)

Maria, student from


TMCNHS has an
assignment about
polynomial. Her
teacher told her to
solve 3x +x -2x-2
3 2
divided by x-1 using
long division
method, synthetic
division and
remainder theorem.
Answers:
LONG DIVISION REMAINDER
THEOREM
(3x3+x2-2x-2) by (x-1) (3x3+x2-2x-2)
by (x-1)

x-1 3x3+x2-2x-2 P(x)=


3x3+x2-2x-2
3x3-3x2 P(1)=
3(1)3+(1)2-2(1)-2
+4x2-2x P(1)=
3+1-2-2
4x2-4x P(1)= 4-4
2x-2 P(1)= 0
2x-2
0

SYNTHETIC DIVISION
(3x3+x2-2x-2) by (x-1)

-1 3 1 -2 -2
3 4 2
3 4 2 0

3x2+4x+2=0

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