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

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

Answers:

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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