Can You Factorise The Following Equation: Trivia Quiz!

1. Factor Completely:

(x + 10)(x + 10)

2(x + 20)(x + 5)

4(x + 10)(x + 10)

4(x + 2)(x + 10)

The given expression can be factored completely as 4(x + 10)(x + 10). This is because both terms inside the parentheses are the same, which means they can be combined and written as (x + 10)(x + 10). Additionally, the coefficient 4 in front of the parentheses can be distributed to both terms inside, resulting in 4(x + 10)(x + 10).

Explanation

The given expression can be factored completely as 4(x + 10)(x + 10). This is because both terms inside the parentheses are the same, which means they can be combined and written as (x + 10)(x + 10). Additionally, the coefficient 4 in front of the parentheses can be distributed to both terms inside, resulting in 4(x + 10)(x + 10).

2. Factor the Greatest Common Factor:

5x^2 (5x - 7xy)

5x^2 (2x - 7y)

5x (2x^2 - 7xy)

5x^2y (2x - 7)

The given expression can be factored by finding the greatest common factor (GCF). The GCF of the terms in the expression is 5x^2. By factoring out the GCF, we get 5x^2 multiplied by the remaining terms inside the parentheses, which are (2x - 7y). Therefore, the correct answer is 5x^2 (2x - 7y).

Explanation

The given expression can be factored by finding the greatest common factor (GCF). The GCF of the terms in the expression is 5x^2. By factoring out the GCF, we get 5x^2 multiplied by the remaining terms inside the parentheses, which are (2x - 7y). Therefore, the correct answer is 5x^2 (2x - 7y).

3. Simplify/Reduce:

Answer Choices: A.

B.

C.

D.

A

B

C

D

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Explanation

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4. Factor the trinomial:

(y - 5)(y + 7)

(y - 5)(y - 7)

(y - 2)(y + 1)

(y + 5)(y - 7)

The given trinomial can be factored as (y + 5)(y - 7) by using the FOIL method. FOIL stands for First, Outer, Inner, Last, which means multiplying the first terms, then the outer terms, then the inner terms, and finally the last terms. In this case, the first terms are y and y, the outer terms are y and -7, the inner terms are 5 and y, and the last terms are 5 and -7. When simplified, the product of these terms results in y^2 - 7y + 5y - 35, which simplifies further to y^2 - 2y - 35. Therefore, the correct answer is (y + 5)(y - 7).

Explanation

The given trinomial can be factored as (y + 5)(y - 7) by using the FOIL method. FOIL stands for First, Outer, Inner, Last, which means multiplying the first terms, then the outer terms, then the inner terms, and finally the last terms. In this case, the first terms are y and y, the outer terms are y and -7, the inner terms are 5 and y, and the last terms are 5 and -7. When simplified, the product of these terms results in y^2 - 7y + 5y - 35, which simplifies further to y^2 - 2y - 35. Therefore, the correct answer is (y + 5)(y - 7).

5. Exchange Rates Robyn spent two months traveling in New Zealand. The day she arrived the exchange rate was 1.4 New Zealand dollars per every 1 U.S. dollar. If she exchanged $500 U.S. dollars when she arrived, how much in New Zealand dollars did she receive?

$384.62

$650

$700

$822.15

Robyn exchanged $500 U.S. dollars when she arrived in New Zealand. The exchange rate was 1.4 New Zealand dollars per every 1 U.S. dollar. To find out how much she received in New Zealand dollars, we need to multiply the amount she exchanged by the exchange rate. Therefore, $500 multiplied by 1.4 equals $700. Hence, Robyn received $700 in New Zealand dollars.

Explanation

Robyn exchanged $500 U.S. dollars when she arrived in New Zealand. The exchange rate was 1.4 New Zealand dollars per every 1 U.S. dollar. To find out how much she received in New Zealand dollars, we need to multiply the amount she exchanged by the exchange rate. Therefore, $500 multiplied by 1.4 equals $700. Hence, Robyn received $700 in New Zealand dollars.

6. Factor using the Difference of Two Squares:

(4x - 3y)(x + 3y)

(2x + 3y)(2x - 3y)

(2x + 3)(2x - 3)

(4x + y)(x - 9)

The given expression can be factored using the difference of two squares formula, which states that a^2 - b^2 can be factored as (a + b)(a - b). In this case, we have (2x)^2 - (3y)^2, which can be rewritten as (2x + 3y)(2x - 3y). Therefore, the correct answer is (2x + 3y)(2x - 3y).

Explanation

The given expression can be factored using the difference of two squares formula, which states that a^2 - b^2 can be factored as (a + b)(a - b). In this case, we have (2x)^2 - (3y)^2, which can be rewritten as (2x + 3y)(2x - 3y). Therefore, the correct answer is (2x + 3y)(2x - 3y).

7. Factor using slide and divide:

(2x - 1)(x + 7)

(2x + 1)(x - 7)

(x + 14)(x - 1)

2(x - 7)(x + 1)

The given expression can be factored using the slide and divide method. By multiplying the first terms of each binomial and the last terms of each binomial, we get (2x * x) + (2x * 7) - (1 * x) - (1 * 7), which simplifies to 2x^2 + 14x - x - 7. Combining like terms, we get 2x^2 + 13x - 7. Since this does not match any of the given answer choices, the correct answer is (2x - 1)(x + 7).

Explanation

The given expression can be factored using the slide and divide method. By multiplying the first terms of each binomial and the last terms of each binomial, we get (2x * x) + (2x * 7) - (1 * x) - (1 * 7), which simplifies to 2x^2 + 14x - x - 7. Combining like terms, we get 2x^2 + 13x - 7. Since this does not match any of the given answer choices, the correct answer is (2x - 1)(x + 7).