Mid Chapter Review
Chapter
Chapter 2
Section
Mid Chapter Review
Solutions 33 Videos

Simplify.

\displaystyle (4a^2-3a + 2)-(-2a^2-3a + 9) 

Q1a

Simplify.

\displaystyle (2x^2 -4xy + y^2)-(4x^2+7xy-2y^2)+(3x^2 + 6y^2) 

Q1b

Simplify.

\displaystyle -(3d^2-2cd + d)+d(2c -5d) -3c(2c + d) 

Q1c

Simplify.

\displaystyle 3x(2x + y)-4x[5-(3x + 2)] 

Q1d

Simplify.

\displaystyle 2a(3a - 5b + 4) - 6(3-2a -b) 

Q1e

Simplify.

\displaystyle 7x(2x62 + 3y -3)-3x (9 -2x + 4y) 

Q1f

Determine whether each pair of functions is equivalent.

\displaystyle g(t) = (t - 2)^5  and \displaystyle h(t) = (2 -t)^5 

Q2a

Determine whether each pair of functions is equivalent.

\displaystyle f(x) = (x^2 -6x)-(x^2 + x - 4)+(2x^2 + 1)  and \displaystyle g(x) = (4x^2-7x -3) - (2x^2 -8) 

Q2b

Determine whether each pair of functions is equivalent.

\displaystyle h(x) = (x -4)(x + 7)(x + 4)  and \displaystyle d(x) = (x + 7)(x^2 -16) 

Q2c

Determine whether each pair of functions is equivalent.

\displaystyle a(t) = (3t + 1)^3  and \displaystyle b(t) = 27t^3 + 27t^2 + 9t -1 

Q2d

If you multiply a linear polynomial by a quadratic one, what is the degree of the product polynomial? Justify your answer.

Q3

The sum of the ages of Pam, Dion, and their three children, in years, is 5x - 99, where x is Dion’s age. Pam is five years younger than Dion. What is the sum of the ages of their children?

Q4

Expand and simplify.

\displaystyle 2(x-5)(3x -4) 

Q5a

Expand and simplify.

\displaystyle (3x -1)^3 

Q5b

Expand and simplify.

\displaystyle 2(x^2 -3x +4)(-x^2+3x -4) 

Q5c

Expand and simplify.

\displaystyle (4x -4)(3x- 5) - (2x -3)^2 

Q5d

Expand and simplify.

\displaystyle 3(2x -5)-9(4x-5) 

Q5e

Expand and simplify.

\displaystyle -(x - y)^3 

Q5f

If the length of the rectangle shown is increased by 2 and the width is decreased by 1, determine the change in

a) the perimeter

b) the area

Q6

Factor

\displaystyle x(x -2) -3(x -2) 

Q7a

Factor

\displaystyle x^2 -11x + 28 

Q7b

Factor

\displaystyle 3a^2 -10a -8 

Q7c

Factor

\displaystyle 30x^2-9x -3 

Q7d

Factor

\displaystyle 16 - 25x^2 

Q7e

Factor

\displaystyle 4(2-a)^2-81 

Q7f

Factor

\displaystyle 2n -6m + 5n^2 -15 mn 

Q8a

Factor

\displaystyle y^2 + 9 -6y -x^2 

Q8b

Factor

\displaystyle y - b - (y -b)^2 

Q8c

Factor

\displaystyle 2x^2-8y^2 + 8x + 8 

Q8d

Factor

\displaystyle w^2 + wb -aw -ab 

Q8e

Factor

\displaystyle ab + b^2 +6a + 6b 

What is the perimeter of the square shown if the Area is given as \displaystyle 25x^2 + 20x + 4 
The expression 3n^2 - 11n + k can be factored into two linear polynomials with integer coefficients. Determine the possible values of k.