# The rational form of expression, x 2 − x − 12 x 2 + 5 x + 6

### 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 1.4, Problem 18E
To determine

## To calculate: The rational form of expression, x2−x−12x2+5x+6

Expert Solution

The simplified form of the given expression is,

(x4)(x+2)

### Explanation of Solution

Given information:

The given expression is as, x2x12x2+5x+6

Formula used:

For the algebraic expression the middle term factorization is as, x2xc

These are the steps to do this ,

Step 1.multiply the coefficient of x2 and the constant c .

Step 2. Then do factor of that number by doing multiplication or division or subtraction or addition got the coefficient of middle term that means x .

Step 3. Then to take common form first to numbers and then from other two numbers.

Step 4. Got four factors in that two pairs are same and another two are same.

Step 5. Get the final two factors.

Calculation :

Consider the expression, x2x12x2+5x+6

Rewrite the numerator in the form of middle term factorization,

x2x12x2+5x+6=x2(4x3x)12x2+(2x+3x)+6=x24x+3x12x2+2x+3x+6=x(x4)+3(x4)x(x+2)+3(x+2)=(x+3)(x4)(x+3)(x+2)

Rewrite the expression, x2x12x2+5x+6=(x4)(x+2)

The above expression can’t be simplified further.

Thus the simplified form of the expression is (x4)(x+2) .

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