Question

*y-3 is one of the factors of the algebraic expression-* 1️⃣ y³-3 2️⃣ y² - 9 3️⃣ y² + 3 4️⃣ y²- 7²

Answer 1

Given :  Expressions

To Find : y-3 is one of the factors  of which expression

1️⃣ y³-3

2️⃣ y² - 9

3️⃣ y² + 3

4️⃣ y²- 7²

Solution:

Using a² - b² = (a + b)(a - b)

1️⃣ y³- 3

can not be further factorized

Hence (y - 3) is  not a factor

2️⃣ y² - 9

= y² - ( 3)²

= ( y +  3)(y -  3)

Hence (y - 3) is   a factor

3️⃣ y² + 3

can not be further factorized

Hence (y - 3) is  not a factor

4️⃣ y²- 7²

= (y + 7)(y - 7)

Hence (y - 3) is  not a factor

Hence y -3 is one on the factor of   the algebraic expression  y² - 9

Correct option is  2️⃣ y² - 9

Another method:

y - 3 is factors if substituting y = 3 in the expression will lead to zero

Check

1️⃣ y³-3  = 3³ -3 = 27 - 3 = 24 ≠ 0

2️⃣ y² - 9  = 3² - 9 = 9 - 9 = 0   Hence y - 3 is factor

3️⃣ y² + 3  = 3² + 3 = 9 + 3 = 12

4️⃣ y²- 7²   = 3² - 7² = 9 - 49 = - 40

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Answer 2

Finding Factors

Given:

A factor (y - 3) and four expressions as follows:

1. y³-3
2. y² - 9
3. y² + 3
4. y²- 7²

To Find:

Its corresponding expression

Solution:

In order to find out the correct corresponding algebraic expression to the given factor, we need to factorize the expressions given.

(1)  y³-3

→ This is the simplest factorized form of this expression. We cannot factorize it further. Hence, (y - 3) is not the factor of the given expression.

(2)  y² - 9

      = y² - 3²

      = (y + 3)(y - 3)

→ (y - 3) is a factor of the given expression.

(3)  y² + 3

→ This is the simplest factorized form of this expression. We cannot factorize it further. Hence, (y - 3) is not the factor of the given expression.

(4) y² - 7²

     = (y +7)(y - 7)

→ (y - 3) is not  a factor of the given expression.

     

→ After above calculations it is clear that (y - 3) is the factor of y² - 9.

Final Answer:

Hence, Option (2) y² - 9 is the correct option.

 

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