# To factor: The expression 4 x 2 − 25 . ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805 ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

(a)

To determine

## To factor: The expression 4x2−25.

Expert Solution

The expression 4x225 is factorized as (2x+5)(2x5).

### Explanation of Solution

Consider the expression 4x225.

Simplify the above expression as follows,

4x225=(2x)2(5)2=(2x+5)(2x5)(a2b2=(a+b)(ab))

Thus, the expression 4x225 is factorized as (2x+5)(2x5).

(b)

To determine

### To factor: The expression 2x2+5x−12.

Expert Solution

The expression 2x2+5x12 is factorized as (x+4)(2x3).

### Explanation of Solution

Consider the expression 2x2+5x12.

Simplify the above expression as follows,

2x2+5x12=2x2+8x3x12=2x(x+4)3(x+4)=(x+4)(2x3)

Thus, the expression 2x2+5x12 is factorized as (x+4)(2x3).

(c)

To determine

### To factor: The expression x3−3x2−4x+12.

Expert Solution

The expression x33x24x+12 is factorized as (x3)(x+2)(x2).

### Explanation of Solution

Consider the expression x33x24x+12.

Simplify the above expression as follows,

x33x24x+12=x2(x3)4(x3)=(x3)(x24)=(x3)(x+2)(x2)(a2b2=(a+b)(ab))

Thus, the expression x33x24x+12 is factorized as (x3)(x+2)(x2).

(d)

To determine

### To factor: The expression x4+27x.

Expert Solution

The expression x4+27x is factorized as x(x+3)(x23x+9).

### Explanation of Solution

Consider the expression x4+27x.

Simplify the above expression as follows,

x4+27x=x(x3+27)=x[(x)3+(3)3]=x(x+3)(x2x×3+32)(a3+b3=(a+b)(a2+ab+b2))=x(x+3)(x23x+9)

Thus, the expression x4+27x is factorized as x(x+3)(x23x+9).

(e)

To determine

### To factor: The expression 3x32−9x12+6x−12.

Expert Solution

The expression 3x329x12+6x12 is factorized as 3x12(x2)(x1).

### Explanation of Solution

Consider the expression 3x329x12+6x12.

Simplify the above expression as follows,

3x329x12+6x12=3x12(x23x+2)=3x12(x22xx+2)=3x12(x(x2)1(x2))=3x12(x2)(x1)

Thus, the expression 3x329x12+6x12 is factorized as 3x12(x2)(x1).

(f)

To determine

### To factor: The expression x3y−4xy.

Expert Solution

The expression x3y4xy is factorized as xy(x+2)(x2).

### Explanation of Solution

Consider the expression x3y4xy.

Simplify the above expression as follows,

x3y4xy=xy(x24)=xy[(x)2(2)2]=xy(x+2)(x2)(a2b2=(a+b)(ab))

Thus, the expression x3y4xy is factorized as xy(x+2)(x2).

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