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Some Basic Definitions:
Algebraic Expressions:
An algebraic expression is a mathematical phrase that can
contain ordinary numbers, variables (like x or y) and operators
(like add, subtract, multiply, and divide).
Here are some algebraic expressions:
a) a + 1
b) a - b
c) 3x
d) x - a / b
Def. of polynomial:
A polynomial is an expression consisting of variables and
Coefficients which only employs the operations of addition,
Subtraction, multiplication, and non-negative integer exponents.
An example of a polynomial in a single variable x is x2 − 4x + 7.
An example of polynomials in three variables is x3 + 2xyz2 − yz + 1.
Factors (either integers / Polynomials):
When an integer is written as a product of integers, each of the
integers in the product is a factor of the original number.
When a polynomial is written as a product of polynomials, each of
the polynomials in the product is a factor of the original polynomial.
Factoring:
Factoring a polynomial means expressing it as a product of other
polynomials.
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Greatest Common Factor:
Largest quantity that is a factor of all the integers or polynomials
involved.
Monomial:
An algebraic expressions consisting of one term.
Binomial:
An algebraic expression of the sum or the difference of two terms.
Trinomials:
An algebraic expressions consisting of three term.
Vocabulary:
Variable:
A symbol for a number we don't know yet. It is usually a letter like x
or y.
Operator:
An Operator is a symbol (such as +, −, ×, etc.) that shows an
operation.
Coefficients:
A number that is used to multiply with a variable.
Exponents:
The exponents of a number says how many times to use that number
in a multiplication.
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Integers:
A number with no fractional part. It can be zero, positive or negative.
Product:
The answer when two or more numbers multiplied together.
Prime Factors:
A factor that is a prime number.
Quotient:
A result obtained by dividing one quantity by another.
GCF:
Greatest common factor
Q: The greatest common factor of 6x2y3 _ 12x3y2 _ 18x4y.
Q: Solve the Word problems by using factoring.
1. The area of a square is numerically equal to twice its perimeter.
Find the length of aside of the square.
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2. The square of a number equals nine times that number. Find the
number.
3. Suppose that four times the square of a number equals 20 times
that number. What is the number?
4. The combined area of two squares is 20 square centimeters. Each
side of one square is twice as long as a side of the other square.
Find the lengths of the sides of each square.
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5. The sum of the areas of two squares is 234 square inches. Each
side of the larger square is five times the length of aside of the
smaller square. Find the length of a side of each square.
Real Word Problems:
Q 1: A ball is thrown straight up, from 3 m above the ground, with a
velocity of 14 m/s. When does it hit the ground?
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Q 2: A Company is going to make frames as part of a new product they
are launching.
The frame will be cut out of a piece of steel, and to keep the weight
down, the final area should be 28 cm2
The inside of the frame has to be 11 cm by 6 cm
What should the width x of the metal be?
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Q 3: Two resistors are in parallel, like in this diagram:
The total resistance has been
measured at 2 Ohms, and one of the
resistors is known to be 3 ohms
more than the other.
What are the values of the two resistors?
The formula to work out total resistance "RT" is:
1/RT = 1/R1 + 1/R2
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Q 4: An object is thrown downward with an initial velocity of 19 feet
per second. The distance, d it travels in an amount of time, t is given by
the equation d=19t +15𝑡2
. How long does it take the object to fall 50
feet?
Q 5: A 3 hour river cruise goes 15 km upstream and then back again.
The river has a current of 2 km an hour. What is the boat's speed and
how long was the upstream journey?
