Algebra Presentation on Topic Modulus Function and PolynomialsCreated by : [Dona, Brian]Performance Task Binus School Bekasi

1. Algebra
DONA BRIAN

2. Polynomials
sample question and explanation

3. List the things your students need to get ready
before class. It can be a particular textbook,
the accomplished homework due for the day,
or any specific materials for the topic you're
about to discuss. You can also match it with
corresponding photos or icons.
Prepare these before
we start class:
Suppose f(x) is a polynomial of third degree
whose roots form an arithmetic sequence
with
the value of the third term being three
times the value of the first term; and the
number of roots equal to 12. Then the
remainder of the division of f(x + 6) by x^2
+1 is...

4. Arithmetic sequence:
a, a + b, a + 2b.
U3 = 3a
a + 2b = 3a
2b = 2a
b = a
The sum of the roots = 12
a + a + b + a + 2b = 12
a + a + a + a + 2a = 12
6a = 12
a = 2
Roots of f(x) are 2, 4, 6, thus:
f(x) = (x - 2) (x - 4) (x - 6)
f(x + 6) = (x + 6 - 2) (x + 6 - 4) (x + 6 - 6)
= (x + 4) (x + 2) (x)
= (x^2 + 6x + 8) (x)
= x^3 + 6x^2 + 8x
Explanation

5. f(x + 6) = x^3 + 6x^2 + 8x is
divided by x^2 + 1
x^2 = -1
f(x + 6) = x^3 + 6x^2 + 8x
= (x^2) (x) + 6x^2 +8x
= (-1) (x) + 6 (-1) + 8x
= - x - 6 + 8x
= 7x - 6
Hence, the remainder of the division of f(x +6) = x^3
+ 6x^2 +8x by x^2 + 1 is 7x - 6
Explanation

6. Modulus
Function

7. Question
If all the values of X in −1≤x≤3 which fulfils
|x+2|−√4x+8≤0 is a≤x≤b, so than the value of
2a+b is....

8. answer
|x+2|−√4x+8≤0
(x+2)2≤(√4x+8)2
x2+4x+4≤4x+8
x2+4x+4−4x−8≤0
x2−4≤0
(x−2)(x+2)≤0
−2≤x≤2
so that intersect with −1≤x≤3 is −1≤x≤2
we can conclude that a=-1 and b=2 so -2+2=0

9. Thank You!