Ultimate Quiz On Factoring Polynomial

1. What is the greatest common factor of the polynomial 8x+14x–32?

2x

2

4

8

The greatest common factor (GCF) of a polynomial is the largest expression that can divide evenly into all the terms of the polynomial. In this case, the terms of the polynomial are 8x, 14x, and -32. The GCF of these terms is 2, because 2 can divide evenly into 8x, 14x, and -32. Therefore, the GCF of the polynomial 8x+14x-32 is 2.

Explanation

The greatest common factor (GCF) of a polynomial is the largest expression that can divide evenly into all the terms of the polynomial. In this case, the terms of the polynomial are 8x, 14x, and -32. The GCF of these terms is 2, because 2 can divide evenly into 8x, 14x, and -32. Therefore, the GCF of the polynomial 8x+14x-32 is 2.

2. Name the greatest common factor of the terms of the binomial –24x²–18x

–6x

–8x

2x

6

The greatest common factor (GCF) of the terms of the binomial –24x^2–18x is the largest expression that can divide evenly into both terms. In this case, the GCF is –6x because it can be factored out of both terms, resulting in –6x(4x+3). This means that –6x is a common factor of both –24x^2 and –18x.

Explanation

The greatest common factor (GCF) of the terms of the binomial –24x^2–18x is the largest expression that can divide evenly into both terms. In this case, the GCF is –6x because it can be factored out of both terms, resulting in –6x(4x+3). This means that –6x is a common factor of both –24x^2 and –18x.

3. A square has an area of 25x² +30x+ 9. What is the measure of one side of the square?

X+3

5x+1

5x+3

5x+9

The given expression represents the area of the square. To find the measure of one side of the square, we need to find the square root of the area. Taking the square root of 25x^2 + 30x + 9 gives us (5x + 3). Therefore, the measure of one side of the square is 5x + 3.

Explanation

The given expression represents the area of the square. To find the measure of one side of the square, we need to find the square root of the area. Taking the square root of 25x^2 + 30x + 9 gives us (5x + 3). Therefore, the measure of one side of the square is 5x + 3.

4.

Kevin is designing a label for a can. The height of the label is 5cm. If the area of the label is 10n²+20n–5, how long is the label?

2n^2+4n–1

N^2+2n–1

2n^2–4n+1

2n^2+5n–1

The area of the label is given by 10n^2 + 20n - 5. To find the length of the label, we need to find the height. The height is given as 5cm. Therefore, the length of the label can be determined by dividing the area by the height. Dividing 10n^2 + 20n - 5 by 5, we get 2n^2 + 4n - 1. Hence, the correct answer is 2n^2 + 4n - 1.

Explanation

The area of the label is given by 10n^2 + 20n - 5. To find the length of the label, we need to find the height. The height is given as 5cm. Therefore, the length of the label can be determined by dividing the area by the height. Dividing 10n^2 + 20n - 5 by 5, we get 2n^2 + 4n - 1. Hence, the correct answer is 2n^2 + 4n - 1.

5. Which shows the polynomial fully factored? 35x² – 14x

–7x(5x + 2)

7(5x^2–2x)

7(5x–2x)

7x(5x–2)

The given expression, 35x^2 - 14x, can be factored by taking out the greatest common factor, which is 7x. This leaves us with 7x(5x - 2), which is the fully factored form of the polynomial.

Explanation

The given expression, 35x^2 - 14x, can be factored by taking out the greatest common factor, which is 7x. This leaves us with 7x(5x - 2), which is the fully factored form of the polynomial.

6. Which shows the missing factor? 12b² – 72b = 12b(?)

B^2 – 6b

–b + 6

6b

B – 6

The missing factor in the expression 12b^2 - 72b = 12b(b - 6). This can be determined by factoring out the greatest common factor, which is 12b. The remaining factor is (b - 6), resulting in the expression 12b(b - 6).

Explanation

The missing factor in the expression 12b^2 - 72b = 12b(b - 6). This can be determined by factoring out the greatest common factor, which is 12b. The remaining factor is (b - 6), resulting in the expression 12b(b - 6).

7.

A parallelogram has a height of x+3 and an area of 25x²+75x. What is the measure of the base?

5x^2

25x

X+25

25

The area of a parallelogram is given by the formula base times height. In this case, the area is given as 25x^2 + 75x and the height is x+3. To find the base, we can rearrange the formula and solve for it. So, base = (area)/(height) = (25x^2 + 75x)/(x+3). Simplifying this expression further is not possible without additional information, so the answer remains as 25x.

Explanation

The area of a parallelogram is given by the formula base times height. In this case, the area is given as 25x^2 + 75x and the height is x+3. To find the base, we can rearrange the formula and solve for it. So, base = (area)/(height) = (25x^2 + 75x)/(x+3). Simplifying this expression further is not possible without additional information, so the answer remains as 25x.

8. Which shows the polynomial fully factored? 2x(4x–3) – 5(4x – 3)

(4x – 3)(2x+5)

(8x^2–6x)–(20x–15)

(4x–3)(2x–5)

–10x(4x–3)

The given expression can be fully factored as (4x – 3)(2x – 5). This is because both terms in the expression have a common factor of (4x – 3), which can be factored out. The remaining terms after factoring out (4x – 3) are (2x) and (-5), which gives us (4x – 3)(2x – 5).

Explanation

The given expression can be fully factored as (4x – 3)(2x – 5). This is because both terms in the expression have a common factor of (4x – 3), which can be factored out. The remaining terms after factoring out (4x – 3) are (2x) and (-5), which gives us (4x – 3)(2x – 5).

9. The formula for the surface area of a sphere is SA = 4πr². If the surface area of the sphere is 4πx^2–8πx+4π, what is the measure of the radius?

X+1

2x–1

X–2

X–1

To find the measure of the radius, we need to equate the given surface area formula to the given expression: 4πx^2–8πx+4π = 4πr^2. By comparing the coefficients, we can see that r^2 = x^2, which means r = x. However, we need to find the measure of the radius, not the variable x. The only option that represents the measure of the radius is x–1, so the correct answer is x–1.

Explanation

To find the measure of the radius, we need to equate the given surface area formula to the given expression: 4πx^2–8πx+4π = 4πr^2. By comparing the coefficients, we can see that r^2 = x^2, which means r = x. However, we need to find the measure of the radius, not the variable x. The only option that represents the measure of the radius is x–1, so the correct answer is x–1.

10. Classify the following equation: 8x²–4x+9

Trinomial

Monomial

Binomial

Quadratic polynomial

The given equation, 8x^2 - 4x + 9, is classified as a quadratic polynomial. This is because it is a polynomial of degree 2, meaning the highest power of x is 2. It consists of three terms, each with different powers of x, and does not fit the definitions of a monomial, binomial, or trinomial. Therefore, the correct classification is a quadratic polynomial.

Explanation

The given equation, 8x^2 - 4x + 9, is classified as a quadratic polynomial. This is because it is a polynomial of degree 2, meaning the highest power of x is 2. It consists of three terms, each with different powers of x, and does not fit the definitions of a monomial, binomial, or trinomial. Therefore, the correct classification is a quadratic polynomial.