# The factors of the expression 4 x 2 − 25 .

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1, Problem 7T

(a)

To determine

## The factors of the expression 4x2−25 .

Expert Solution

The factors of the expression 4x225 is (2x5)(2x+5) .

### Explanation of Solution

Given:

The expression is 4x225 .

Calculation:

The formula of difference of squares is,

A2B2=(AB)(A+B) (1)

Rearrange the given expression,

4x225=(2x)2(5)2

Substitute 2x for A and 5 for B in the equation (1) to get factors,

(2x)2(5)2=(2x5)(2x+5)

Thus, the factors of the expression 4x225 is (2x5)(2x+5) .

(b)

To determine

### The factors of the expression 2x2+5x−12 .

Expert Solution

The factors of the expression 2x2+5x12 is (2x3)(x+4) .

### Explanation of Solution

Given:

The expression is 2x2+5x12 .

Calculation:

Solve the given expression to get factors,

2x2+5x12=2x2+8x3x12

The greatest common factor of terms 2x2 and 8x is 2x and the terms 3x and 12 is 3 to solve the above expression,

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

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

(c)

To determine

### The factors of the polynomial expression x3−3x2−4x+12 .

Expert Solution

The factors of the polynomial expression x33x24x+12 is (x3)(x2)(x+2) .

### Explanation of Solution

Given:

The polynomial expression is x33x24x+12 .

Calculation:

First, factor the group terms than factor out common factor in the above expression,

x33x24x+12=x2(x3)4(x3)=(x2(2)2)(x3)=(x2)(x+2)(x3)

Thus, the factors of the polynomial expression x33x24x+12 is (x3)(x2)(x+2) .

(d)

To determine

### The factors of the expression x4+27x .

Expert Solution

The factors of the expression x4+27x is x(x+3)(x23x+9) .

### Explanation of Solution

Given:

The expression is x4+27x .

Calculation:

The greatest common factor of terms x4 and 27x is x to solve the above expression,

x4+27x=x(x3+(3)3)

The formula of sum of cubes is,

A3+B3=(A+B)(A2AB+B2)

Substitute x for A and 3 for B in above formula,

x4+27x=x(x3+(3)3)=x{(x+3)(x2x3+32)}=x(x+3)(x23x+9)

Thus, the factors of the expression x4+27x is x(x+3)(x23x+9) .

(e)

To determine

### The factors of the expression 3x3/2−9x1/2+6x−1/2 .

Expert Solution

The factors of the expression 3x3/29x1/2+6x1/2 is 3x1/2(x1)(x2) .

### Explanation of Solution

Given:

The expression is 3x3/29x1/2+6x1/2 .

Calculation:

First, factor out the power of x with the smallest exponent that is x1/2 than solve the given expression,

3x3/29x1/2+6x1/2=3x1/2(x23x+2)=3x1/2(x22xx+2)=3x1/2{x(x2)1(x2)}=3x1/2(x1)(x2)

Thus, the factors of the expression 3x3/29x1/2+6x1/2 is 3x1/2(x1)(x2) .

(f)

To determine

### The factors of the expression x3y−4xy .

Expert Solution

The factors of the expression x3y4xy is xy(x2)(x+2) .

### Explanation of Solution

Given:

The expression is x3y4xy .

Calculation:

First, factor out the power of x and y with the smallest exponent that is xy than solve the given expression,

x3y4xy=xy(x2(2)2)=xy(x2)(x+2)

Thus, the factors of the expression x3y4xy is xy(x2)(x+2) .

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