Algebra 1 Unit 6: Polynomials and Factoring

Adding, subtracting and multiplying polynomials, and factoring by common factor, trinomials, special products and grouping. 12 questions. Have a go at each one on paper before you tap "Show me how".

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Question 1

Adding and subtracting polynomialsNo calculator

Simplify $(3x^2-5x+2)-(x^2+4x-7)$.

1. $2x^{2}-9x-5$
2. $4x^{2}-x-5$
3. $2x^{2}-9x+9$
4. $2x^{2}-x-5$

Question 2

Multiplying polynomialsNo calculator

Multiply $(2x-3)(x+5)$.

1. $2x^{2}+13x-15$
2. $2x^{2}-7x-15$
3. $2x^{2}-15$
4. $2x^{2}+7x-15$

Question 3

Multiplying polynomialsNo calculator

Expand $(x-4)^2$.

1. $x^{2}-16$
2. $x^{2}+16$
3. $x^{2}-4x+16$
4. $x^{2}-8x+16$

Question 4

Factoring trinomialsNo calculator

Factor $x^2+2x-24$.

1. $(x+6)(x-4)$
2. $(x-6)(x+4)$
3. $(x-8)(x+3)$
4. $(x+8)(x-3)$

Question 5

Factoring trinomialsNo calculator

Factor $2x^2+7x+3$.

1. $(2x+1)(x+3)$
2. $(x+1)(x+3)$
3. $(2x-1)(x-3)$
4. $(2x+3)(x+1)$

Question 6

Special productsNo calculator

Factor $9x^2-49$.

1. $(3x+7)^{2}$
2. $(3x-7)^{2}$
3. $(3x-7)(3x+7)$
4. $(9x-7)(x+7)$

Question 7

Greatest common factorNo calculator

Factor out the greatest common factor: $6x^3-15x^2$.

1. $3x^{2}(2x-5)$
2. $3x(2x^{2}-5x)$
3. $3x^{2}(2x+5)$
4. $x^{2}(6x-15)$

Question 8

Polynomial vocabularyNo calculator

What are the degree and the leading coefficient of $4x^3-2x^5+x-7$?

1. Degree 5, leading coefficient 2
2. Degree 3, leading coefficient 4
3. Degree 5, leading coefficient -2
4. Degree 4, leading coefficient -7

Question 9

Factoring completelyNo calculator

Factor completely: $2x^2-18$.

1. $2(x-3)^{2}$
2. $(2x-6)(x+3)$
3. $2(x-3)(x+3)$
4. $2(x^{2}-9)$

Question 10

Factoring by groupingNo calculator

Factor completely: $x^3+3x^2-4x-12$.

1. $(x+3)(x-2)(x+2)$
2. $(x+3)(x^{2}-4)$
3. $(x-3)(x-2)(x+2)$
4. $(x+3)(x-4)(x+1)$

Question 11

Multiplying polynomialsNo calculator

A rectangle has length $3x+2$ and width $x-4$. Which expression gives its area?

1. $3x^{2}-14x-8$
2. $4x-2$
3. $8x-4$
4. $3x^{2}-10x-8$

Question 12

Zero product propertyNo calculator

Solve $(2x-5)(x+3)=0$.

1. $x=\frac{2}{5} \text{ or } x=-3$
2. $x=5 \text{ or } x=-3$
3. $x=\frac{5}{2} \text{ or } x=-3$
4. $x=-\frac{5}{2} \text{ or } x=3$