The model represents an algebraic expression. Identify the expression and its factors.
The model represents an algebraic expression. Identify the expression and its factors.
Factor
\displaystyle
20x^2 -4x
Factor
\displaystyle
3n^2 -6n + 15
Factor
\displaystyle
-2x^3 + 6x^2 + 4x
Factor
\displaystyle
6a(3- 7a) -5(3 - 7a)
The area of a rectangle is given by the relation
\displaystyle
A = 16x^2 -24
.
Determine the possible dimensions of this rectangle.
a) Write three polynomials whose terms have a greatest common factor of 4x^3 y.
b) Factor each polynomial you wrote in part a)
Identify each expression that is modelled below, and state its factors.
Identify each expression that is modelled below, and state its factors.
Factor fully
\displaystyle
x^2 + 16x + 63
Factor fully
\displaystyle
x^2 - 7x - 60
Factor fully
\displaystyle
x^2 + 6x - 27
Factor fully
\displaystyle
5x^2 - 5x - 100
Examine the relation y = x^2+7x +12.
a) Write the relation in factored form.
b) Determine the coordinates of the x—intercepts.
c) Determine the coordinates of the vertex.
d) State the minimum value of the relation and where the minimum value occurs.
Identify the expression that is modelled below, and state its factors.
Identify the expression that is modelled below, and state its factors.
Factor fully.
\displaystyle
15x^2 -4x -4
Factor fully.
\displaystyle
20x^2+3x-2
Factor fully.
\displaystyle
7x^2-19x -6
Factor fully.
\displaystyle
5a^2+23a+15
Factor fully.
\displaystyle
12x^2-16x+5
Factor fully.
\displaystyle
6n^2 -11ny-10y^2
The profit on the watches they sell is determined by the relation P = -2n^2 + 120n -1000, where n is the number of watches sold and P is the profit in dollars.
a) What are the break-even points?
b) What is the maximum profit?
Identify the expression that is modelled below, and state its factors.
Identify the expression that is modelled below, and state its factors.
Factor fully.
\displaystyle
144x^2 -25
Factor fully.
\displaystyle
36a^2+12a + 1
Factor
\displaystyle
18x^5 - 512xy^2
Factor fully.
\displaystyle
4(x-2)^2-20(x -2) + 25
Factor fully.
\displaystyle
(x + 5)^2-y^2
Factor fully.
\displaystyle
x^2-6x+9-4y^2
Factor fully
\displaystyle
7x^2-26x -8
Factor fully
\displaystyle
64x^6 -25
Factor fully
\displaystyle
18ac - 12a - 15c + 10
Factor fully
\displaystyle
4x^2y - 44xy + 72y
Factor fully
\displaystyle
20x^2+61x + 45
Factor fully
\displaystyle
z^4-13z^2+40
Factor fully
\displaystyle
2s^2+3s-5
Factor fully
\displaystyle
15-2x -x^2
Factor fully
\displaystyle
x^4-4x^2-32
Factor fully
\displaystyle
16x^2-121y^2
Factor fully
\displaystyle
9 - 30a + 25a^2
Factor fully
\displaystyle
x^2 + 16x + 64-25y^2
A box has dimension defined by V =18x^3 -2x + 45x^2 -5.
a) Determine expressions for the possible dimensions of these boxes.
b) Determine the dimensions and volume of a box if x = 2 cm
Determine the coordinates of the vertex of each relation.
\displaystyle
y = x^2 -10x + 24
Determine the coordinates of the vertex of each relation.
\displaystyle
y = 2x^2 -24x + 72
Determine the coordinates of the vertex of each relation.
\displaystyle
y = -5x^2 + 500
Determine the coordinates of the vertex of each relation.
\displaystyle
y = 2x^2-7x -4
Determine the coordinates of the vertex of each relation.
\displaystyle
y = 4x^2 + 16x
Determine the coordinates of the vertex of each relation.
\displaystyle
y = x^2 + 10x + 25