HCF of algebraic expressions by division method :

Sometimes the given polynomials are not factorable because of their highest powers. However, the following method gives a systematic way on finding HCF.

**Step 1 :**

Let " f(x) " and " g(x) " be the given polynomials. First, divide f(x) by g(x) to obtain, f(x) = g(x) **x** q(x) + r (x)

So, deg [ g(x) ] > deg [ r(x) ]. If remainder r (x) = 0, then g(x) is the HCF of given polynomials.

**Step 2 :**

If the remainder r(x) is not zero, then divide g(x) by r(x) to obtain g(x) = r(x) **x** q(x) + r**₁** (x).

Where r**₁** (x) is remainder. If it is zero, then r(x) is the required HCF.

**Step 2 :**

If it is not zero, then continue the process until we get zero as remainder.

Question 1 :

Find the HCF of the following pairs of polynomials using division algorithm

x³ - 9 x² + 23 x - 15 , 4 x² - 16 x + 12

**Solution :**

**Let f (x) = **x³ - 9 x² + 23 x - 15, g (x) = 4 x² - 16 x + 12

g (x) = 4 (x² - 4 x + 3)

Since the remainder is 0, HCF of given polynomials is x - 5

Question 2 :

Find the HCF of the following pairs of polynomials using division algorithm

3 x³ + 18 x² + 33 x + 18 , 3 x² + 13 x + 10

Solution:

f (x) = 3 x³ + 18 x² + 33 x + 18

g (x) = 3 x² + 13 x + 10

The remainder is not zero. So, we have to repeat this long division once again.

here r**₁** (x) = (4/3)(x+1)

Now we are taking 4/3 as common from the remainder. So that we are getting (4/3)(x+1)

Therefore HCF is x + 1

Question 3 :

Find the HCF of the following pairs of polynomials using division algorithm

2 x³ + 2 x² + 2 x + 2 , 6 x³ + 12 x² + 6 x + 12

Solution:

f (x) = 2 (x³ + x² + x + 1)

g (x) = 6 (x³ + 2 x² + x + 2)

We factor 2 from f (x) and 6 from g (x)

The remainder is not zero. So, we have to repeat this long division once again

Therefore HCF is 2 (x² + 1)

Question 4 :

Find the HCF of the following pairs of polynomials using division algorithm

x³ - 3 x² + 4 x - 12 , x⁴ + x³ + 4 x² + 4 x

Solution :

f (x) = x³ - 3 x² + 4 x - 12

g (x) = x (x³ + x² + 4 x + 4)

We are taking x from g (x).

The remainder is not zero. So, we have to repeat this long division once again

Therefore HCF is (x² + 4)

- HCF calculator
- HCF for algebraic expressions
- Venn diagram method for hcf and lcm
- Shortcut to find hcf and lcm
- How to solve hcf and lcm problems
- How to solve hcf and lcm word problems
- HCF and lcm worksheets
- Practical use of LCM
- LCM method for time and work
- LCM worksheet
- LCM calculator
- LCM and GCD worksheets

After having gone through the stuff given above, we hope that the students would have understood "HCF of algebraic expressions by division method".

Apart from the stuff given above, if you want to know more about "HCF of algebraic expressions by division method", please click here

Apart from the stuff, "HCF of algebraic expressions by division method", if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**