Easy Algebra Step-by-Step

114 Easy Algebra Step-by-Step

Solution

a.^461

21

xx^32886 x

x

888 x−

Step 1. Using the long division symbol ()) , arrange the terms of both the

dividend and the divisor in descending powers of the variable x.

4 61

21

xx^32886 x

x

888 x−

= (^21) ) 46 − + 81 +
xx^326
− (^1) ) 4 xx+ 8
Step 2. Divide the fi rst term of the dividend by the fi rst term of the divisor
and write the answer as the fi rst term of the quotient.
(^21) ) 4681
x xxx^32668
(^1) ) 4 + 88
2 x^2
Step 3. Multiply 2x – 1 by 2x^2 and enter the product under the dividend.
(^21) ) 4681

2

(^326)
2
x (^1) ) 4 xxx 6 + 888
x
42 xx^32 − 22
Step 4. Subtract 42 xx^3222 from the dividend, being sure to mentally change
the signs of both 4 x^3 and − 2 x^2.
(^21) ) 4681
4
(^326)
32
x xxx 6 8
xx
(^1) ) 4 + 88
2 x^2

2

− 4 x^2

Step 5. Bring down 8x, the next term of the dividend, and repeat steps

2–4.

(^21) ) 4681

2

4

(^326)
2
32
x xxx 6 8
x
xx
(^1) ) 4 + 88
− 2 x

2

−+

−

4 x^2

2

8

422 +

x

xx+ 2

6 x

In long division of polynomials, making

sign errors when subtracting is the most

common mistake.