Algebra Quiz: Multiplication & Division Of Polynomials

1. What is the product of -3x and -6x?

-18x2

18x

18x2

-18x

The product of -3x and -6x can be found by multiplying the coefficients (-3 and -6) and the variables (x and x). When multiplying the coefficients, we get 18. When multiplying the variables, we get x^2. Therefore, the product is 18x^2.

Explanation

The product of -3x and -6x can be found by multiplying the coefficients (-3 and -6) and the variables (x and x). When multiplying the coefficients, we get 18. When multiplying the variables, we get x^2. Therefore, the product is 18x^2.

2. What is the quotient of 2⁷z⁵ divided by 2⁶z³?

213z8

27/z2

Z/28

2z2

The correct answer is 2z2 because when you divide 27z5 by 26z3, you divide the coefficients (27/26) and subtract the exponents of the variables (5-3). This results in a quotient of 2z2.

Explanation

The correct answer is 2z2 because when you divide 27z5 by 26z3, you divide the coefficients (27/26) and subtract the exponents of the variables (5-3). This results in a quotient of 2z2.

3. If Anna would evaluate this expression, a⁷/a² using the quotient rule, the what is the result?.

A-9

A-5

A5

A9

When evaluating the expression a7/a2 using the quotient rule, we divide the exponent of the numerator (7) by the exponent of the denominator (2). This gives us a result of a5, as the quotient rule states that when dividing variables with the same base, we subtract the exponents. Therefore, the correct answer is a5.

Explanation

When evaluating the expression a7/a2 using the quotient rule, we divide the exponent of the numerator (7) by the exponent of the denominator (2). This gives us a result of a5, as the quotient rule states that when dividing variables with the same base, we subtract the exponents. Therefore, the correct answer is a5.

4. If you divide 10x⁶ + 5x⁴ + 15x³ by 5x³, the result is .

2x3 - x + 3

2x3 + x + 3

2x3 - x – 3

2x3 + x – 3

When dividing 10x6 + 5x4 + 15x3 by 5x3, we can simplify the expression by dividing each term by 5x3. The first term, 10x6, divided by 5x3 is 2x3. The second term, 5x4, divided by 5x3 is x. The third term, 15x3, divided by 5x3 is 3. Therefore, the result of the division is 2x3 + x + 3.

Explanation

When dividing 10x6 + 5x4 + 15x3 by 5x3, we can simplify the expression by dividing each term by 5x3. The first term, 10x6, divided by 5x3 is 2x3. The second term, 5x4, divided by 5x3 is x. The third term, 15x3, divided by 5x3 is 3. Therefore, the result of the division is 2x3 + x + 3.

5. What is the result in multiplying (-2x) to (4x² + 3x - 3)?

8x3 – 6x2 + 6x

-8x3 – 6x2 + 6x

-8x3 + 6x2 - 6x

8x3 + 6x2 – 6x

When multiplying (-2x) to (4x^2 + 3x - 3), we can use the distributive property. We multiply -2x by each term inside the parentheses.

-2x * 4x^2 = -8x^3
-2x * 3x = -6x^2
-2x * -3 = 6x

Combining these terms, we get -8x^3 - 6x^2 + 6x. Therefore, the answer is -8x^3 - 6x^2 + 6x.

Explanation

When multiplying (-2x) to (4x^2 + 3x - 3), we can use the distributive property. We multiply -2x by each term inside the parentheses.

-2x * 4x^2 = -8x^3
-2x * 3x = -6x^2
-2x * -3 = 6x

Combining these terms, we get -8x^3 - 6x^2 + 6x. Therefore, the answer is -8x^3 - 6x^2 + 6x.

6. Find the quotient of x³ + 5x² + 2x – 8 divided by x + 2.

X2 + 3x – 4

X2 – 3x – 4

X2 + 3x + 4

X2 – 3x – 4

The quotient of x3 + 5x2 + 2x – 8 divided by x + 2 is x2 + 3x – 4. This can be determined by performing polynomial long division.

Explanation

The quotient of x3 + 5x2 + 2x – 8 divided by x + 2 is x2 + 3x – 4. This can be determined by performing polynomial long division.

7. Find the product of (2n – 4) and (3n² - 6n + 4).

6n3 – 24n2 + 32n – 16

6n3 + 24n2 – 32n – 16

6n3 – 24n2 – 32n + 16

6n3 + 24n2 + 32n + 16

The given expression is a product of two binomials. To find the product, we can use the distributive property.
(2n - 4) * (3n^2 - 6n + 4) = 2n * (3n^2 - 6n + 4) - 4 * (3n^2 - 6n + 4)
Simplifying further, we get: 6n^3 - 12n^2 + 8n - 12n^2 + 24n - 16
Combining like terms, we have: 6n^3 - 24n^2 + 32n - 16
Therefore, the correct answer is 6n^3 – 24n^2 + 32n – 16.

Explanation

The given expression is a product of two binomials. To find the product, we can use the distributive property.
(2n - 4) * (3n^2 - 6n + 4) = 2n * (3n^2 - 6n + 4) - 4 * (3n^2 - 6n + 4)
Simplifying further, we get: 6n^3 - 12n^2 + 8n - 12n^2 + 24n - 16
Combining like terms, we have: 6n^3 - 24n^2 + 32n - 16
Therefore, the correct answer is 6n^3 – 24n^2 + 32n – 16.

8. The length of the rectangle is 5m + 4 and the width is m - 9. What is the area of the rectangle?

5m2 – 41m – 36

5m2 + 41m – 36

5m2 – 41m + 36

5m2 + 41m + 36

The area of a rectangle is calculated by multiplying its length by its width. In this case, the length of the rectangle is given as 5m + 4 and the width is given as m - 9. Therefore, the area of the rectangle can be found by multiplying (5m + 4) by (m - 9). Simplifying this expression gives us 5m^2 - 41m - 36, which matches the given correct answer.

Explanation

The area of a rectangle is calculated by multiplying its length by its width. In this case, the length of the rectangle is given as 5m + 4 and the width is given as m - 9. Therefore, the area of the rectangle can be found by multiplying (5m + 4) by (m - 9). Simplifying this expression gives us 5m^2 - 41m - 36, which matches the given correct answer.

9. What is the area of a square if its side measures 9x - 4?

81x2 + 72x + 16

81x2 – 72x – 16

81x2 + 72x – 16

81x2 – 72x + 16

The given expression represents the area of the square. The side of the square is given as 9x - 4. To find the area of a square, we square the length of one side. So, we square (9x - 4) which gives us 81x^2 - 72x + 16. Therefore, the correct answer is 81x^2 - 72x + 16.

Explanation

The given expression represents the area of the square. The side of the square is given as 9x - 4. To find the area of a square, we square the length of one side. So, we square (9x - 4) which gives us 81x^2 - 72x + 16. Therefore, the correct answer is 81x^2 - 72x + 16.

10. What is the result if x³ – 5x² + x + 15 will be divided by x – 3?

X2 – 2x + 5

X2 + 2x + 5

X2 – 2x – 5

X2 + 2x – 5

When we divide x^3 - 5x^2 + x + 15 by x - 3 using long division, we get x^2 - 2x - 5 as the quotient. This means that x^2 - 2x - 5 is the result of the division.

Explanation

When we divide x^3 - 5x^2 + x + 15 by x - 3 using long division, we get x^2 - 2x - 5 as the quotient. This means that x^2 - 2x - 5 is the result of the division.