Chapter
Chapter 4
Section
Solutions 25 Videos

Determine the value fo each symbol.

\displaystyle x^2 - \diamond x - 56 = (x + 7)(x - \square) 

Q1a

Determine the value fo each symbol.

\displaystyle 16x^2 - \diamond = ( \square x -3)(\square x + \circ) 

Q1b

Determine the value fo each symbol.

\displaystyle 12x^2 + \circ x + 5 = (4x + \square)(\diamond x + 5) 

Q1c

Determine the value fo each symbol.

\displaystyle 25x^2 + \circ x + 49 = (\square x + \diamond)^2 

Q1d

Identify each trinomial that is modelled below, and state its factors.

Q2a

Identify each trinomial that is modelled below, and state its factors.

Q2b

Factor fully.

\displaystyle 20x^5 -30x^3 

Q3a

Factor fully.

\displaystyle -8yc^3 + 4y^2c - 6yc 

Q3b

Factor fully.

\displaystyle 2a(3b + 5) + 7(3b + 5) 

Q3c

Factor fully.

\displaystyle 2st + 6s + 5t + 15 

Q3d

Factor 25x^2 -30x + 9 using two different strategies.

Q4

Factor fully.

\displaystyle x^2 + 4x - 77 

Q5a

Factor fully.

\displaystyle a^2-3a -10 

Q5b

Factor fully.

\displaystyle 3x^2 -12x + 12 

Q5c

Factor fully.

\displaystyle m^3 + 3m^2-4m 

Q5d

Factor fully.

\displaystyle 6x^2 -x -2 

Q6a

Factor fully.

\displaystyle 8n^2 + 8n - 6 

Q6b

Factor fully.

\displaystyle 9x^2 +12x +4 

Q6c

Factor fully.

\displaystyle 6ax^2+5ax-4a 

Q6d

A graphic arts company creates posters with areas that are given by the equation A = 2x^2 + 11x+12

a) Write expressions for possible dimensions of the posters.

b) Write expressions for the dimensions of a poster whose width is doubled and whose length is increased by 2. Write the new area as a simplified polynomial.

c) Write expressions for possible dimensions of a poster whose area is given by the expression 18x^2 + 99x + 108.

Q7

Factor fully.

\displaystyle 225x^2 -4 

Q8a

Factor fully.

\displaystyle 9a^2 -48a + 64 

Q8b

Factor fully.

\displaystyle x^6 -4y^2 

\displaystyle (3 + n)^2 -10(3 + n) + 25 
A parabola is defined by the equation y = 2x^2 - 11x + 5.