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) 12xy
^{2}
(d) 24x
^{2}y
(e) 5xy
^{2}z
^{2}
2. Find the H.C.F. of the monomials:
(a) 4x
^{2} and 10xy
(b) 21a
^{2}b and 49ab
^{2}
(c) x
^{3}y
^{2} and – 5y
^{2}
(d) 4x
^{3}, 6y
^{2} and 8z
(e) 2x
^{2}y
^{3}, 10x
^{3}y
^{2} and 14xy
(f) 5x
^{3}, -15x
^{2} and 45x
3. Find the common factors of the given terms.
(a) 3x
^{2}, 15xy
(b) 33x
^{2}y, - 77xy
^{2}
(c) 9x
^{2}y
^{2}z, 54xyz
^{2}
(d) x
^{3}y
^{2}, - 5y
^{2}
(e) 4x
^{3}, 10y
^{3}, 6z
^{3}
(f) 2xyz
^{3}, 3x
^{2}y
^{2}z, 5xyz
4. Find the H.C.F. of the terms of the expression:
(a) – 2x
^{2} - 8x
^{3} - 20x
^{4}
(b) 3xy
^{2} + 9x
^{2}y
^{2} – 6x
^{2}y
(c) 5x
^{2} + 25x + 50
(d) x
^{3}y
^{2} – 8y
^{2}
5. Find the factors of the expression:
(a) 3x
^{4} – 9x
^{5} – 15x
^{3}
(b) – 10ab
^{3} + 30ba
^{3} – 50a
^{2}b
^{3}
(c) 15a
^{2} – 20b
^{2} + 25c
^{2}
(d) x
^{3}yz + 5xy
^{3}+ 9x
^{3}y
(e) 3x
^{2} – 9x
^{2}y - 27x
^{3}z
(f) 7x
^{3} + 7xy
^{2} + 7xz
^{2}
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, y
^{2}, xy
^{2}, xy, 2x, 2y, 2y
^{2}, 2xy, 2xy
^{2}, 3x, 3y, 3y
^{2}, 3xy, 3xy
^{2}, 4x, 4y, 4y
^{2}, 4xy, 4xy
^{2}, 6x, 6y, 6y
^{2}, 6xy, 6xy
^{2}, 12x, 12y, 12y
^{2}, 12xy and 12xy
^{2}
(d) 1, 2, 3, 4, 6, 8, 12, 24, x, x
^{2}, y, xy, xy
^{2}, 2x, 2x
^{2}, 2y, 2xy, 2xy
^{2}, 3x, 3x
^{2}, 3y, 3xy, 3xy
^{2}, 4x, 4x
^{2}, 4y, 4xy, 4xy
^{2}, 6x, 6x
^{2}, 6y, 6xy, 6xy
^{2}, 8x, 8x
^{2}, 8y, 8xy, 8xy
^{2}, 12x, 12x
^{2}, 12y, 12xy, 12xy
^{2}, 24x, 24x
^{2}, 24y, 24xy and 24xy
^{2}.
(e) 1, 5, x, y, y
^{2}, z, z
^{2}, xy, xy
^{2}, yz, yz
^{2}, xz, xz
^{2}, y
^{2}z
^{2}, 5x, 5y, 5y
^{2}, 5z, 5z
^{2}, 5xy, 5xy
^{2}, 5yz, 5yz
^{2}, 5xz, 5xz
^{2}, 5y
^{2}z
^{2}.
2. (a) 2x
(b) 7ab
(c) y
^{2}
(d) 2
(e) 2xy
(f) 5x
3. (a) 3x
(b) 11xy
(c) 9xyz
(d) y
^{2}
(e) 2
(f) xyz
4. (a) -2x
^{2}
(b) 3xy
(c) 5
(d) y
^{2}
5. (a) 3x
^{3}(x - 3x
^{2} - 5)
(b) -10ab(b
^{2} - 3a
^{2} + 5ab
^{2})
(c) 5(3a
^{2} - 4b
^{2} + 5c
^{2})
(d) x(x
^{2}yz + 5y
^{3} + 9x
^{2}z)
(e) 3x
^{2}(1- 3y - 9xz)
(f) 7x(x
^{2} + y
^{2} + z
^{2})
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