FACTORING POLYNOMIALS WITH 4 TERMS BY GROUPING WORKSHEET

Factor the following polynomials by grouping :

Question 1 :

x³ - 2x² - x + 2

Question 2 :

x³ + 3x² - x - 3

Question 3 :

x³ + x² - 4x - 4

Question 4 :

x³ - 3x² + 2x - 6

Question 5 :

x⁴ - x³ - x + x²

Question 6 :

x⁸ - x⁴ - x² + 1

Question 7 :

5a - 5b - xa + xb

Question 8 :

2xy - 4x - 3ay + 6a

1. Answer :

= x³ - 2x² - x + 2

= (x³ - 2x²) + (-x + 2)

 = x²(x - 2) - 1(x - 2)

 =  (x² - 1)(x - 2)

 =  (x² - 1²)(x - 2)

Using algebraic identity a² - b² = (a + b)(a -b),

= (x + 1)(x - 1)(x - 2)

2. Answer :

= x³ + 3x² - x - 3

= (x³ + 3x²) + (-x - 3)

= x²(x + 3) - 1(x + 3)

= (x² - 1)(x + 3)

= (x² - 1²)(x + 3)

Using algebraic identity a² - b² = (a + b)(a -b),

= (x + 1)(x - 1)(x + 3)

3. Answer :

= x³ + x² - 4x - 4

= (x³ + x²) + (-4x - 4)

= x²(x + 1) - 4(x - 1)

= (x² - 4)(x + 1)

= (x² - 2²)(x + 1)

Using algebraic identity a² - b² = (a + b)(a -b),

= (x + 2)(x - 2)(x + 1)

4. Answer :

= x³ - 3x² + 2x - 6

= (x³ - 3x²) + (2x - 6)

= x²(x - 3) + 2(x - 3)

= (x² + 2)(x - 3)

5. Answer :

= x⁴ - x³ - x + x²

Arrange the terms with powers in descending order. 

= x⁴ - x³ + x² - x

= (x⁴ - x³) + (x² - x)

= x³(x - 1) + x(x - 1)

= (x³ + x)(x - 1)

= x(x² + 1)(x - 1)

6. Answer :

= x⁸ - x⁴ + x² + 1

= (x⁸ - x⁴) + (x² + 1)

= x⁴(x⁴ - 1) + 1(x² + 1)

= x⁴(x⁴ - 1) + 1(x² + 1)

= x⁴[(x²)² - 1²] + 1(x² + 1)

= x⁴(x² - 1)(x² + 1) + 1(x² + 1)

= (x² + 1)[x⁴(x² - 1) + 1]

7. Answer :

= 5a - 5b - xa + xb

= (5a - 5b) + (-xa + xb)

= 5(a - b) - x(a - b)

= (a - b)(5 - x)

8. Answer :

= 2xy - 4x - 3ay + 6a

= (2xy - 4x) + (-3ay + 6a)

= 2x(y - 2) - 3a(y - 2)

= (2x - 3a)(y - 2)

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