Algebra Presentation on Topic Modulus Function and Polynomials

ALGEBRAAurelya & Michelle Laurencya

MODULUS
FUNCTION POLYNOMIAL01 02

is a function which gives the absolute value of a number or variable. It produces
the magnitude of the number of variable. It is also termed as an absolute value
function. The outcome of this function is always positive, no matter what input
has been given to the function.
In mathematics, the absolute value or modulus of a real number x, denoted
|x|, is the non-negative value of x without regard to its sign. Namely, |x| = x if
x is positive, and |x| = −x if x is negative (in which case −x is positive), and
|0| = 0.
MODULUS FUNCTION

If all x values with −1 ≤ x ≤ 3
satisfy |x+2 | − √(4x + 8) ≤ 0 is
a ≤ x ≤ b, so the value 2a + b is
CASE 1: MODULUS FUNCTION

ANSWER
To solve the absolute value inequality above we try to use √x = | x | and the definition
{x, untuk x ≥ 0
x, untuk x < 0}
We start from the condition for the function √(4x + 8), so that it is real, then 4x + 8 ≥ 0 or x ≥ −2
of the absolute value | x | =
|x + 2| - √(4x + 8) ≤ 0
2
√(x + 2) ≤ √(4x + 8)
22
x + 4x + 4 ≤ 4x + 8
2
x + 4x + 4 - 4x - 8 ≤ 0
2
x - 4 ≤ 0
2
(x-2)(x+2) ≤ 0
−2 ≤ x ≤ 2
The intersection of x ≥ −2 and −2 ≤ x ≤ 2 is −2 ≤ x ≤ 2.

Since the required x value is all x values at −1 ≤ x ≤ 3 so that the required set of solutions is the
intersection of −1≤ x ≤ 3 and −2 ≤ x ≤ 2, that is going to be:
From the illustration in the picture above we get that the slice is −1≤ x ≤ 2 ≡ a ≤ x ≤ b so
that the value 2a + b = −2 + 2 = 0.

is an expression consisting of variables (also
called indeterminates) and coefficients, that
involves only the operations of addition,
subtraction, multiplication, and non-negative
integer exponentiation of variables.
POLYNOMIAL

CASE 2 : Polynomial
A polynomial p(x) is given by
a. Find the remainder and the quotient when p(x) is divided by x + 2x + 5
A different polynomial q(x) is defined as
b. Find the value of the constants a and b so that when q(x) is divided by
x + 2x + 5 there is no reminder
3p(x) = 4x - 2x + x + 52
2
3p(x) = 4x - 2x + ax + b2
2

ANSWERS
a. There are several ways to do the polynomial division, and we’re gonna
do it by Long Division
4x-10
x +2x+5√4x -2x+x+5
4x +8x -20x
-10x +21x+5
-10x - 20x+50
41x - 45
Quotient
Remainder
>
^
2 2
2
2
2
3
3

b. Using inspection as there is no remainder
p(x) = 4x -2x +ax+b = (x +2x-5) (4x+c)
● p(0) = b = -5c
● p(1) = 2+a+b = -2 (4x+c)
● p(-1) = -6+a+b = -6 (4x+c)
-4 + 2b = -2 (4x+c) - 6 (4x+c)
-4 + 2b = -8 - 2c - 24 -6
-4 + 2b = 16 - 8c
-2 + b = 8 - 4c
-2 + (-5c) = 8 - 4c
-10 = c
● b = -5c
b = -5 (-10)
b = 50
● 2+a+b = -8 -2c
2+a+50 = -8 -2(-10)
a+52 = 12
a = -40
3 2 2
Adding all the 2 equations

Algebra Presentation on Topic Modulus Function and Polynomials

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