MAT 136 MODULE 6 PROBLEM SET SNH 2026
FULL MATH WORKED SOLUTIONS AND
ANSWERS VERIFIED GRADED A+
◉ Function. Answer: A given input, sent through the function,
produces a given output. f(x) = y
a -> f -> b
Multiple inputs can ONLY produce ONE output
◉ Perfect Square. Answer: In a polynomial expression, two numbers
that add to equal the ax term and multiply to equal the b term.
x(squared) + ax + b
◉ Completing the Square. Answer: In x (squared) + ax + b, where b
is unknown, find b by taking half of a and squaring that answer. Add
b to the opposite side of the equation so that it stays equivalent.
◉ Alternative to Completing the Square. Answer: In x(squared) + ax
= y, move y over to the left hand side: x(squared) + ax + y = 0. Then
complete the square.
, ◉ x ^ -y = 1/x^y. Answer: A base raised to a negative exponent
equals 1 divided by the base raised to the positive exponent.
◉ x^a * x^b = x^[a+b]. Answer: When multiplying numbers WITH
THE SAME BASE raised to a power, just add the powers together.
◉ x^a * y^a = (xy)^a. Answer: When multiplying different numbers
but are raised to the SAME POWER, then just multiply the bases
together.
◉ Root Indicator. Answer: If there is a number on the outside of a
square root symbol, that represents how many numbers should be
multiplied to equal the number under the square root symbol.
◉ Fractional Exponents. Answer: The denominator becomes the
value to which you take the root, and the numerator becomes the
exponent to which you take the number under the root sign.
◉ Remainders. Answer: Now we also know that, when positive
consecutive integers are divided by any number, the remainders
increase by 1 until they hit their highest remainder possible. When
that happens, the next integer remainder resets to 0. This is because
our smaller number has gone into the larger number an even
number of times (which means there is no remainder).
FULL MATH WORKED SOLUTIONS AND
ANSWERS VERIFIED GRADED A+
◉ Function. Answer: A given input, sent through the function,
produces a given output. f(x) = y
a -> f -> b
Multiple inputs can ONLY produce ONE output
◉ Perfect Square. Answer: In a polynomial expression, two numbers
that add to equal the ax term and multiply to equal the b term.
x(squared) + ax + b
◉ Completing the Square. Answer: In x (squared) + ax + b, where b
is unknown, find b by taking half of a and squaring that answer. Add
b to the opposite side of the equation so that it stays equivalent.
◉ Alternative to Completing the Square. Answer: In x(squared) + ax
= y, move y over to the left hand side: x(squared) + ax + y = 0. Then
complete the square.
, ◉ x ^ -y = 1/x^y. Answer: A base raised to a negative exponent
equals 1 divided by the base raised to the positive exponent.
◉ x^a * x^b = x^[a+b]. Answer: When multiplying numbers WITH
THE SAME BASE raised to a power, just add the powers together.
◉ x^a * y^a = (xy)^a. Answer: When multiplying different numbers
but are raised to the SAME POWER, then just multiply the bases
together.
◉ Root Indicator. Answer: If there is a number on the outside of a
square root symbol, that represents how many numbers should be
multiplied to equal the number under the square root symbol.
◉ Fractional Exponents. Answer: The denominator becomes the
value to which you take the root, and the numerator becomes the
exponent to which you take the number under the root sign.
◉ Remainders. Answer: Now we also know that, when positive
consecutive integers are divided by any number, the remainders
increase by 1 until they hit their highest remainder possible. When
that happens, the next integer remainder resets to 0. This is because
our smaller number has gone into the larger number an even
number of times (which means there is no remainder).
