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Which equation could have the graph shown below? y = (x – 4)(x – 1)(2 + x)(3 + x) y = (x – 4)(1 – x)(2 + x)(3 + x) y = (x + 4)(x + 1)(2 – x)(3 – x) y = (x + 4)(x + 1)(2 – x)(x – 3)



1 Answer

3 votes

Answer: (x-4)2•(x-1)2•(x+2)2•(x+3)2•(x+4)2•(x+1)2•(x-2)2•(x-3)2

Step-by-step explanation: Step by Step Solution

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STEP

1

:

Equation at the end of step 1

((((((((((((((x-4)•(x-1)•(x+2))•(x+3))•(x-4))•(1-x))•(x+2))•(x+3))•(x+4))•(x+1))•(2-x))•(3-x))•(x+4))•(x+1))•(2-x))•(x-3)

STEP

2

:

Equation at the end of step 2

(((((((((((((x-4)•(x-1)•(x+2)•(x+3))•(x-4))•(1-x))•(x+2))•(x+3))•(x+4))•(x+1))•(2-x))•(3-x))•(x+4))•(x+1))•(2-x))•(x-3)

STEP

3

:

Equation at the end of step 3

((((((((((((x-4)•(x-1)•(x+2)•(x+3)•(x-4))•(1-x))•(x+2))•(x+3))•(x+4))•(x+1))•(2-x))•(3-x))•(x+4))•(x+1))•(2-x))•(x-3)

STEP

4

:

Multiplying Exponential Expressions:

4.1 Multiply (x-4) by (x-4)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is (x-4) and the exponents are :

1 , as (x-4) is the same number as (x-4)1

and 1 , as (x-4) is the same number as (x-4)1

The product is therefore, (x-4)(1+1) = (x-4)2

Equation at the end of step

4

:

(((((((((((x-4)2•(x-1)•(x+2)•(x+3)•(1-x))•(x+2))•(x+3))•(x+4))•(x+1))•(2-x))•(3-x))•(x+4))•(x+1))•(2-x))•(x-3)

STEP

5

:

5.1 Rewrite (1-x) as (-1) • (x-1)

Multiplying Exponential Expressions:

5.2 Multiply (x-1) by (x-1)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is (x-1) and the exponents are :

1 , as (x-1) is the same number as (x-1)1

and 1 , as (x-1) is the same number as (x-1)1

The product is therefore, (x-1)(1+1) = (x-1)2

STEP

7

:

Pulling out like terms

7.1 Pull out like factors :

-x - 2 = -1 • (x + 2)

Multiplying Exponential Expressions:

7.2 Multiply (x + 2) by (x + 2)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is (x+2) and the exponents are :

1 , as (x+2) is the same number as (x+2)1

and 1 , as (x+2) is the same number as (x+2)1

The product is therefore, (x+2)(1+1) = (x+2)2

STEP

9

:

Pulling out like terms

9.1 Pull out like factors :

-x - 3 = -1 • (x + 3)

Multiplying Exponential Expressions:

9.2 Multiply (x + 3) by (x + 3)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is (x+3) and the exponents are :

1 , as (x+3) is the same number as (x+3)1

and 1 , as (x+3) is the same number as (x+3)1

The product is therefore, (x+3)(1+1) = (x+3)

((((((((x-4)2•(x-1)2•(x+2)2•-1•(x+3)2•(x+4))•(x+1))•(2-x))•(3-x))•(x+4))•(x+1))•(2-x))•(x-3)

STEP

10

:

Equation at the end of step 10

(((((((x-4)2•(x-1)2•(x+2)2•(x+3)2•(-x-4)•(x+1))•(2-x))•(3-x))•(x+4))•(x+1))•(2-x))•(x-3)

STEP

11

:

STEP

12

:

Pulling out like terms

12.1 Pull out like factors :

-x - 4 = -1 • (x + 4)

Equation at the end of step

12

:

((((((x-4)2•(x-1)2•(x+2)2•(x+3)2•(-x-4)•(x+1)•(2-x))•(3-x))•(x+4))•(x+1))•(2-x))•(x-3)

STEP

13

:

STEP

14

:

Pulling out like terms

14.1 Pull out like factors :

-x - 4 = -1 • (x + 4)

Equation at the end of step

14

STEP

15

STEP

16

:

Pulling out like terms

16.1 Pull out like factors :

-x - 4 = -1 •

Equation at the end of step

16

:

STEP

17

:

STEP

18

:

Pulling out like terms

18.1 Pull out like factors :

-x - 4 = -1 • (x + 4)

Multiplying Exponential Expressions:

18.2 Multiply (x + 4) by (x + 4)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is (x+4) and the exponents are :

1 , as (x+4) is the same number as (x+4)1

and 1 , as (x+4) is the same number as (x+4)1

The product is therefore, (x+4)(1+1) = (x+4)2

Equation at the end of step

18

:

(((x-4)2•(x-1)2•(x+2)2•(x+3)2•(x+4)2•(-x-1)•(2-x)•(3-x)•(x+1))•(2-x))•(x-3)

STEP

19

:

STEP

20

:

Pulling out like terms

20.1 Pull out like factors :

-x - 1 = -1 • (x + 1)

Multiplying Exponential Expressions:

20.2 Multiply (x + 1) by (x + 1)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is (x+1) and the exponents are :

1 , as (x+1) is the same number as (x+1)1

and 1 , as (x+1) is the same number as (x+1)1

The product is therefore, (x+1)(1+1) = (x+1)2

Equation at the end of step

20

:

((x-4)2•(x-1)2•(x+2)2•(x+3)2•(x+4)2•(x+1)2•(x-2)•(3-x)•(2-x))•(x-3)

STEP

21

:

21.1 Rewrite (2-x) as (-1) • (x-2)

Multiplying Exponential Expressions:

21.2 Multiply (x-2) by (x-2)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is (x-2) and the exponents are :

1 , as (x-2) is the same number as (x-2)1

and 1 , as (x-2) is the same number as (x-2)1

The product is therefore, (x-2)(1+1) = (x-2)2

22.1 Multiply (x-3) by (x-3)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is (x-3) and the exponents are :

1 , as (x-3) is the same number as (x-3)1

and 1 , as (x-3) is the same number as (x-3)1

The product is therefore, (x-3)(1+1) = (x-3)2

Final result :

(x-4)2•(x-1)2•(x+2)2•(x+3)2•(x+4)2•(x+1)2•(x-2)2•(x-3)2

User Shreeharsha
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