Worksheet on Factoring Algebraic Expression

Practice the worksheet on factoring algebraic expression. The questions are based on possible factors, H.C.F. of the monomials, common factors and factors of the expression.

1. Write all the possible factors of:

(a) 4x                    

(b) 10xy       

(c) 12xy2

(d) 24x2y

(e) 5xy2z2

2. Find the H.C.F. of the monomials:

(a) 4x2 and 10xy

(b) 21a2b and 49ab2

(c) x3y2 and – 5y2

(d) 4x3, 6y2 and 8z

(e) 2x2y3, 10x3y2 and 14xy

(f) 5x3, -15x2 and 45x

3. Find the common factors of the given terms.

(a) 3x2, 15xy

(b) 33x2y, - 77xy2

(c) 9x2y2z, 54xyz2

(d) x3y2, - 5y2

(e) 4x3, 10y3, 6z3

(f) 2xyz3, 3x2y2z, 5xyz

4. Find the H.C.F. of the terms of the expression:

(a) – 2x2 - 8x3 - 20x4

(b) 3xy2 + 9x2y2 – 6x2y

(c) 5x2 + 25x + 50

(d) x3y2 – 8y2

5. Find the factors of the expression:

(a) 3x4 – 9x5 – 15x3

(b) – 10ab3 + 30ba3 – 50a2b3

(c) 15a2 – 20b2 + 25c2

(d) x3yz + 5xy3+ 9x3y

(e) 3x2 – 9x2y - 27x3z

(f) 7x3 + 7xy2 + 7xz2

Answers for the worksheet on factoring algebraic expression are given below to check the exact answers of the above factors.


1. (a)  1, 4, x, 4x 

(b) 1, 2, 5, 10, x, y, xy, 2x, 2y, 2xy, 5x, 5y, 5xy, 10x, 10y, 10xy

(c) 1, 2, 3, 4, 6, 12, x, y, y2, xy2, xy, 2x, 2y, 2y2, 2xy, 2xy2, 3x, 3y, 3y2, 3xy, 3xy2, 4x, 4y, 4y2, 4xy, 4xy2, 6x, 6y, 6y2, 6xy, 6xy2, 12x, 12y, 12y2, 12xy and 12xy2

(d) 1, 2, 3, 4, 6, 8, 12, 24, x, x2, y, xy, xy2, 2x, 2x2, 2y, 2xy, 2xy2, 3x, 3x2, 3y, 3xy, 3xy2, 4x, 4x2, 4y, 4xy, 4xy2, 6x, 6x2, 6y, 6xy, 6xy2, 8x, 8x2, 8y, 8xy, 8xy2, 12x, 12x2, 12y, 12xy, 12xy2, 24x, 24x2, 24y, 24xy and 24xy2.

(e) 1, 5, x, y, y2, z, z2, xy, xy2, yz, yz2, xz, xz2, y2z2, 5x, 5y, 5y2, 5z, 5z2, 5xy, 5xy2, 5yz, 5yz2, 5xz, 5xz2, 5y2z2.

2. (a) 2x

(b) 7ab

(c) y2

(d) 2

(e) 2xy

(f) 5x

3. (a) 3x

(b) 11xy

(c) 9xyz

(d) y2

(e) 2

(f) xyz

4. (a) -2x2

(b) 3xy

(c) 5

(d) y2

5. (a) 3x3(x - 3x2 - 5)

(b) -10ab(b2 - 3a2 + 5ab2)

(c) 5(3a2 - 4b2 + 5c2)

(d) x(x2yz + 5y3 + 9x2z)

(e) 3x2(1- 3y - 9xz)

(f) 7x(x2 + y2 + z2)

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