# FACTOR IN ONE VARIABLE

Factorize the following algebraic expressions

Problem 1 :

-3x + 21

Solution :

= -3x + 21

= -3x + 3 ⋅ 7

= 3(-x + 7)

Problem 2 :

6x² + 3x

Solution :

= 6x² + 3x

= 2 3x² + 3x

= 3x (2x + 1)

Problem 3 :

18x² + 12xy

Solution :

= 18x² + 12xy

= 6 ⋅ 3x² + 6 ⋅ 2 xy

= 6x (3x + 2y)

Problem 4 :

6tm - 24m²

Solution :

= 6tm - 24m²

= -24m² + 6tm

= 6 ⋅ -4m² + 6tm

= 6m (-4m + t)

Problem 5 :

8x + 12y + 10x + 15y

Solution :

= 8x + 12y + 10x + 15y

= 18x + 27y

= 9 (2x + 3y)

Problem 6 :

x² - 7x + 3x - 21

Solution :

= x² - 7x + 3x - 21

=x(x - 7) + 3(x - 7)

= (x + 3) (x - 7)

Problem 7 :

7x + 4

Solution :

= 7x + 4

There is no numerical value in common in 7 and 4. So, we cannot factor this.

Problem 8 :

20x - 10

Solution :

= 20x - 10

Factoring 10 from these two terms.

= 10 (2x - 1)

Problem 9 :

18xy - 3yz

Solution :

= 18xy - 3yz

= 3y (6x - z)

Problem 10 :

12mn + 18mp

Solution :

= 12mn + 18mp

= 12mn + 18mp

= 6m (2n + 3p)

Problem 11 :

16m² - 4m

Solution :

= 16m² - 4m

= 4m(4m - 1)

Problem 12 :

3x² + 6x - 18

Solution :

= 3x² + 6x - 18

= 3(x² + 2x - 6)

Problem 13 :

-6x - 24

Solution :

= -6x - 24

= -6(x + 4)

Problem 14 :

-2xy - 8x

Solution :

= -2xy - 8x

= -2x(y + 4)

Problem 15 :

24mn - 16m²n

Solution :

= 24mn - 16m²n

= -16m²n + 24mn

= 8mn (-2m + 3)

Problem 16 :

-x²y - y²x

Solution :

= -x²y - y²x

= -xy (x + y)

Problem 17 :

12m²n + 24m²n²

Solution :

= 12m²n + 24m²n²

= 24m²n² + 12m²n

= 12m²n (2n + 1)

Problem 18 :

72y²p - 18y³p²

Solution :

= 72y²p - 18y³p²

= - 18p²y³ + 72py²

= 18py² (-py + 4)

Problem 19 :

4(x + 3) + m(x + 3)

Solution :

= 4(x + 3) + m(x + 3)

= (x + 3) (m + 4)

Problem 20 :

x(x - 1) + 5(x - 1)

Solution :

= x(x - 1) + 5(x - 1)

= (x - 1) (x + 5)

Problem 21 :

y(y + 4) - 6(y + 4)

Solution :

= y(y + 4) - 6(y + 4)

= (y + 4) (y - 6)

Problem 22 :

x² (x + 7) + x (x + 7)

Solution :

= x² (x + 7) + x (x + 7)

=  (x + 7) (x² + x)

=  (x + 7) x(+ 1)

= x(x + 1) (x + 7)

Problem 23 :

3x(x - 4) - 7(x - 4)

Solution :

= 3x(x - 4) - 7(x - 4)

= (x - 4)(3x - 7)

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