4.1 Polynomials practice 1

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Question 1 of 11

1. Question

Consider a polynomial [math](x^4+2x^3+3x^2+4x+5)-(5x^4+4x^3+3x^2+2x+1)[/math]. If the degree, the number of terms, and the leading coefficient of this polynomial are [math]a, b[/math], and [math]c[/math] respectively, what are [math]a, b[/math], and [math]c[/math]?

[math]a=[/math]BLANK 1 of 3 [math]b=[/math]BLANK 2 of 3 [math]c=[/math]BLANK 3 of 3
[math]a=[/math]Fill in the blank 1 of 3

[math]b=[/math]Fill in the blank 2 of 3

[math]c=[/math]Fill in the blank 3 of 3

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Question 2 of 11

2. Question

Simplify the following polynomials.

(a) [math]2(3x-5)+3(1-7x)[/math]

(b) [math](2x^2-4x-7)(6x+1)[/math]

(a) BLANK 1 of 6[math]x+[/math]BLANK 2 of 6 (b) BLANK 3 of 6[math]x^3+[/math]BLANK 4 of 6[math]x^2+[/math]BLANK 5 of 6[math]x+[/math]BLANK 6 of 6
(a) Fill in the blank 1 of 6 [math]x+[/math]Fill in the blank 2 of 6

(b) Fill in the blank 3 of 6 [math]x^3+[/math]Fill in the blank 4 of 6 [math]x^2+[/math]Fill in the blank 5 of 6 [math]x+[/math]Fill in the blank 6 of 6

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Question 3 of 11

3. Question

Find the number of terms of the following polynomials:

(a) [math](x-3y^2)^2+6xy(x-y)[/math]

(b) [math](x^3+1)(x^3+5x+1)[/math]

(a) BLANK 1 of 2 (b) BLANK 2 of 2
(a) Fill in the blank 1 of 2

(b) Fill in the blank 2 of 2

Correct

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Question 4 of 11

4. Question

Let [math]f(x)[/math] be a four-degree polynomial. If [math]f(x)[/math] has no constant term, which of the following equations could be [math]f(x)[/math]?

[math]y=(x^2+1)^2[/math]

Correct Incorrect Correct answer

[math]y=(x^2+x+3)^2[/math]

Correct Incorrect Correct answer

[math]y=x(x+1)(x+2)^2[/math]

Correct Incorrect Correct answer

[math]y=(x^3+1)(x+1)^2[/math]

Correct Incorrect Correct answer

None of the above.

Correct Incorrect Correct answer

Correct

Incorrect
Question 5 of 11

5. Question

Which of the following polynomials has the largest degree?

[math]x^4+x^3y^2[/math]

Correct Incorrect Correct answer

[math]x^4+x^3+y^2[/math]

Correct Incorrect Correct answer

[math]x^3+y^4[/math]

Correct Incorrect Correct answer

[math]x^3+x^4y^2[/math]

Correct Incorrect Correct answer

Correct

Incorrect
Question 6 of 11

6. Question

Simplify [math](x-2)^2-(x+2)^2[/math].

BLANK 1 of 3[math]x^2+[/math]BLANK 2 of 3[math]x+[/math]BLANK 3 of 3
Fill in the blank 1 of 3 [math]x^2+[/math]Fill in the blank 2 of 3 [math]x+[/math]Fill in the blank 3 of 3

Correct

Incorrect
Question 7 of 11

7. Question

How many terms does [math]xy(x^2+xy+y^2)-(xy)^2[/math] have?

BLANK 1 of 1
Fill in the blank 1 of 1

Correct

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Question 8 of 11

8. Question

Simplify the following polynomials.

(a) [math](x^2-1)(x-2)+(x^2+1)(2-x)[/math]

(b) [math]4x^3-7x+6x-(4x^3-8x^2-10)+8x^2[/math]

(a) BLANK 1 of 8[math]x^3+[/math]BLANK 2 of 8[math]x^2+[/math]BLANK 3 of 8[math]x+[/math]BLANK 4 of 8 (b) BLANK 5 of 8[math]x^3+[/math]BLANK 6 of 8[math]x^2+[/math]BLANK 7 of 8[math]x+[/math]BLANK 8 of 8
(a) Fill in the blank 1 of 8 [math]x^3+[/math]Fill in the blank 2 of 8 [math]x^2+[/math]Fill in the blank 3 of 8 [math]x+[/math]Fill in the blank 4 of 8

(b) Fill in the blank 5 of 8 [math]x^3+[/math]Fill in the blank 6 of 8 [math]x^2+[/math]Fill in the blank 7 of 8 [math]x+[/math]Fill in the blank 8 of 8

Correct

Incorrect
Question 9 of 11

9. Question

Simplify the following polynomials.

(a) [math](x-1)(x-2)(x+1)(x+2)[/math]

(b) [math]2(3x^2+5x+7)-6(x^2+x-4)[/math]

(a) BLANK 1 of 8[math]x^4+[/math]BLANK 2 of 8[math]x^3+[/math]BLANK 3 of 8[math]x^2+[/math]BLANK 4 of 8[math]x+[/math]BLANK 5 of 8 (b) BLANK 6 of 8[math]x^2+[/math]BLANK 7 of 8[math]x+[/math]BLANK 8 of 8
(a) Fill in the blank 1 of 8 [math]x^4+[/math]Fill in the blank 2 of 8 [math]x^3+[/math]Fill in the blank 3 of 8 [math]x^2+[/math]Fill in the blank 4 of 8 [math]x+[/math]Fill in the blank 5 of 8

(b) Fill in the blank 6 of 8 [math]x^2+[/math]Fill in the blank 7 of 8 [math]x+[/math]Fill in the blank 8 of 8

Correct

Incorrect
Question 10 of 11

10. Question

Which of the following expression is equivalent to [math](a-b)^3+(b-a)^3[/math]?

[math]0[/math]

Correct Incorrect Correct answer

[math]2(a-b)^3[/math]

Correct Incorrect Correct answer

[math]2a^3[/math]

Correct Incorrect Correct answer

[math]-2b^3[/math]

Correct Incorrect Correct answer

[math]2a^3-2b^3[/math]

Correct Incorrect Correct answer

Correct

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Question 11 of 11

11. Question

Which of the following expression is equivalent to [math](x+y)^3[/math]?

[math]x^3+y^3[/math]

Correct Incorrect Correct answer

[math]x^3+3x^2y+3xy^2+y^3[/math]

Correct Incorrect Correct answer

[math](x+y)(x^2+xy+y^2)[/math]

Correct Incorrect Correct answer

[math]x^3+2xy+y^3[/math]

Correct Incorrect Correct answer

None of the above

Correct Incorrect Correct answer

Correct

Incorrect

4.1 Polynomials practice 1

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