Chapter Review
Chapter
Chapter 2
Section
Chapter Review
Solutions 51 Videos

Expand and simplify

\displaystyle\begin{array}{c}3 x(2 x-3)+9(x-1)-x(-x-11)\end{array}

Q1a

Expand and simplify

\displaystyle\begin{array}{c}-9(4 a-5)(4 a+5)\end{array}

Q1b

Expand and simplify

\displaystyle\begin{array}{c}2\left(x^{2}-5\right)-7 x(8 x-9)\end{array}

Q1c

Expand and simplify

\displaystyle\begin{array}{c}-5(2 n-5)^{2}\end{array}

Q1d Q2

Determine the missing factor.

\displaystyle 7 x^{2}-14 x=7 x(?)

Q3a

Determine the missing factor.

\displaystyle 3 a^{2}+15 a-9=(?)\left(a^{2}+5 a-3\right)

Q3b

Determine the missing factor.

\displaystyle 10 b^{4}-20 b^{2}=10 b^{2}(?)

Q3c

Factor

\displaystyle 3 a(5-7 a)-2(7 a-5)

Q4d

A rectangle has an area of \displaystyle 6 x^{2}-8 .  a) Determine the dimensions of the rectangle. b) Is there more than one possibility? Explain.

Q5

a) Give three examples of polynomials that have a greatest common factor of \displaystyle 7 x . b) Factor each polynomial from part (a).

Q6

What are the factors of each polynomial being modelled?

\displaystyle \begin{array}{|l|l|}\hline x & x \\ \hline x & x \\ \hline x & x \\ \hline -x^{2} & -x^{2} \mid \\ \hline \\ \hline\end{array}

Q7a

What are the factors of each polynomial being modelled? Q7b

Determine the missing factor.

\displaystyle x^{2}+9 x+14=(x+2)(?)

Q8a

Determine the missing factor.

\displaystyle a^{2}+3 a-28=(?)(a+7)

Q8b

Determine the missing factor.

\displaystyle b^{2}-b-20=(b-5)(?)

Q8c

Determine the missing factor.

\displaystyle -8 x+x^{2}+15=(?)(x-3)

Q8d

Factor.

\displaystyle\begin{array}{c}x^{2}+7 x+10\end{array}

Q9a

Factor.

\displaystyle\begin{array}{c}x^{2}-12 x+27\end{array}

Q9b

Factor.

\displaystyle\begin{array}{c}x^{2}+x-42\end{array}

Q9c

Factor.

\displaystyle\begin{array}{c}x^{2}-x-90\end{array}

Q9d

Determine consecutive integers \displaystyle b  and \displaystyle c , and also \displaystyle m  and \displaystyle n , such that \displaystyle x^{2}+b x+c=(x+m)(x+n)

Q10

How would you decompose the x—term to factor each polynomial?

\displaystyle 6 x^{2}+x-1 

Q11a

How would you decompose the x—term to factor each polynomial?

\displaystyle 12 x^{2}+9 x-30 

Q11b

How would you decompose the x—term to factor each polynomial?

\displaystyle 7 x^{2}-50 x-48 

Q11c

How would you decompose the x—term to factor each polynomial?

\displaystyle 30 x^{2}-9 x-3 

Q11d

Determine the missing factor.

\displaystyle 2 x^{2}+7 x+5=(x+1)(?)

Q12a

Determine the missing factor.

\displaystyle 3 a^{2}+10 a-8=(?)(3 a-2)

Q12b

Determine the missing factor.

\displaystyle 4 b^{2}-4 b-15=(2 b-5)(?)

Q12c

Determine the missing factor.

\displaystyle 20+27 x+9 x^{2}=(?)(3 x+5)

Q12d

Factor.

\displaystyle 6 x^{2}-19 x+10

Q13a

Factor.

\displaystyle 10 a^{2}-11 a-6

Q13b

Factor.

\displaystyle 20 x^{2}+9 x-18

Q13c

Factor.

\displaystyle 6 n^{2}+13 n+7

Q13d

Each diagram represents a polynomial. Identify the polynomial and its factors.

\displaystyle \begin{array}{|c|c|c|c|c|}\hline x & x & x & 1 & 1 \\ \hline x & x & x & 1 & 1 \\ \hline x^{2} & x^{2} & x^{2} & x & x \\ \hline x^{2} & x^{2} & x^{2} & x & x \\ \hline x^{2} & x^{2} & x^{2} & x & x \\ \hline\end{array}

Q14a

Each diagram represents a polynomial. Identify the polynomial and its factors.

\displaystyle \begin{array}{|c|c|c|c|c|}\hline x^{2} & x^{2} & x^{2} & x & x \\ \hline x^{2} & x^{2} & x^{2} & x & x \\ \hline x^{2} & x^{2} & x^{2} & x & x \\ \hline -x & -x & -x & -1 & -1 \\ \hline -x & -x & -x & -1 & -1 \\ \hline \\ \hline\end{array}

Q14b

Determine the missing factor.

\displaystyle x^{2}-25=(x+5)(?)

Q15a

Determine the missing factor.

\displaystyle 9 a^{2}+6 a+1=(?)(3 a+1)

Q15b

Determine the missing factor.

\displaystyle 4 b^{2}-20 b+25=(2 b-5)(?)

Q15c

Determine the missing factor.

\displaystyle 9 x^{2}-64=(?)(3 x+8)

Q15d

Factor.

\displaystyle\begin{array}{c}4 x^{2}-9\end{array}

Q16a

Factor.

\displaystyle 16 a^{2}-24 a+9

Q16b

Factor.

\displaystyle x^{8}-256

Q16c

Factor.

\displaystyle (x-2)^{2}+6(x-2)+9

Q16d

The polynomial \displaystyle x^{2}-1  can be factored.

Can the polynomial \displaystyle x^{2}+1  be factored? Explain.

Q17

Factor each expression. Remember to divide out all common factors first.

\displaystyle x^{2}+2 x-15

Q18a

Factor each expression. Remember to divide out all common factors first.

\displaystyle 5 m^{2}+15 m-20

Q18b

Factor each expression. Remember to divide out all common factors first.

\displaystyle 2 x^{2}-18

Q18c

Factor each expression. Remember to divide out all common factors first.

\displaystyle 18 x^{2}+15 x-3 

Q18d

Factor each expression. Remember to divide out all common factors first.

\displaystyle 36 x^{2}+48 x+16

\displaystyle 15 c^{3}+25 c^{2}