Vocabulary
In the expression
-2x^3+3x^2-4
, what is the
-2
called?
Answer: Leading Coefficient
Rewrite in standard form:
\(4x + x^2 - 9\)
Answer: \(x^2 + 4x - 9\)
Question: (3x + 4) + (2x + 5)
Answer: 5x + 9
Question: (6x + 8) - (2x + 3)
Answer: 4x + 5
A student simplified (x + 3) + (2x + 4) and got
3x^2 + 7.
What did they do wrong?
They added the exponents instead of just adding the coefficients.
Write an expression for the perimeter of a rectangle with side lengths of (3x + 2) and (x - 1).
8x + 2
In the expression
5x^2 - 8x + 12
, what is the
12
called?
Answer: Constant (or Constant Term)
Rewrite in standard form:
\(15 - 3x^3 + 6x\)
Answer:
\(-3x^3 + 6x + 15\)
Question: (x^2 - 5x) + (4x^2 + 8x)
Answer: 5x^2 + 3x
Question: (5x^2 + 7x) - (x^2 + 3x)
Answer: 4x^2 + 4x
A student did (5x + 4) - (2x + 1) and got 3x + 5. What was their mistake?
They forgot to distribute the negative sign to the 1.
Store A makes a profit of
(5x^2 + 40)
dollars and Store B makes
(2x^2 - 15)
dollars. Write the expression for their combined profit.
7x^2 + 25
How many terms are in the polynomial
\(x^4 - 3x^2 + 5x - 7\)?
Answer: 4 terms
Rewrite in standard form:
8x^2 + 2x^4 - x + 5
Answer: 2x^4 + 8x^2 - x + 5
Question: (6x^2 - 3) + (x^2 + 4x - 5)
Answer: 7x^2 + 4x - 8
Question: (3x^2 - 6x + 2) - (x^2 - 4x)
Answer: 2x^2 - 2x + 2
A student rewrote
5 - 2x^2 + x^3
into standard form as
2x^2 + x^3 + 5
. What did they forget?
They lost the negative sign attached to the
2x^2
term.
A business tracks Revenue
(9x^2 + 250x)
and Costs
(4x^2 + 80x + 300)
. Set up the subtraction expression to find Net Profit.
(9x^2 + 250x) - (4x^2 + 80x + 300)
What do you call the regular numbers written directly in front of the variables, like the
\(3\)
and
\(-8\)
in
\(3x^2 - 8x\)
?
Answer: Coefficients
Rewrite in standard form:
7x - 9x^3
Answer: -9x^3 + 7x
Question: (4x^3 - 2x^2 + 7) + (3x^2 - 9)
Answer: 4x^3 + x^2 - 2
Question: (7x^3 - 5) - (2x^3 - 6x + 1)
Answer: 5x^3 + 6x - 6
A student calculated
(x^2 - 4) - (3x^2 - 2)
and got
-2x^2 - 6
. Fix their math.
Distributing the negative makes it -4 + 2, which equals -2.
A metal sheet has an original area of
(12x^2 + 6x)
. A mechanic cuts out a square piece with an area of
(x^2 - 5)
. Write an expression for the remaining area.
(12x^2 + 6x) - (x^2 - 5)
In the polynomial
\(6x - 4x^3 + 2\)
, which number is the leading coefficient?
Answer: \(-4\) (Note: It belongs to the highest exponent term)
Rewrite in standard form:
-2x^2 + x^5 - 4x^3 + 11x
Answer: x^5 - 4x^3 - 2x^2 + 11x
Question: (8x^4 - 3x^2 + 6x) + (2x^4 - 4x^2 - 10x)
Answer: 10x^4 - 7x^2 - 4x
Question: (x^2 - 9) - (4x^2 - 5x + 3)
Answer: -3x^2 + 5x - 12
To find the perimeter of a rectangle with sides (x + 2) and (3x - 1), a student wrote 4x + 1. What step did they miss?
They only added two sides instead of adding all 4 sides of the rectangle.
A warehouse starts with
(4x^2 + 50)
boxes. They receive a shipment of
(2x^2 + 15x)
boxes, and then ship out
(x^2 - 10)
boxes. Set up the expression for final inventory.
(4x^2 + 50) + (2x^2 + 15x) - (x^2 - 10)