FACTOR OUT A MONOMIAL WORKSHEET
About "Factor out a monomial worksheet"
Factor out a monomial worksheet :
Here we are going to see some practice questions of factor out a monomial.
Factor out a monomial worksheet - Practice questions
(1) Factor out the greatest common factor
6 x⁴ + 4 x³ y
(2) Factor out the greatest common factor
15x³ + 10x²y - 25x²z
(3) Factor out the greatest common factor
-7 u² - 21 u³
(4) Factor out the greatest common factor
28 m²n² -12 m³n - 20 m³n²
(5) Factor out the greatest common factor
12a²- 21 a b
Factor out a monomial worksheet - Solution
Question 1 :
Factor out the greatest common factor
6 x⁴ + 4 x³ y
Solution :
Step 1 :
There are two terms 6 x⁴ and 4 x³ y in the given polynomial.
By finding greatest common factor, we get
6 x⁴ = 2 ⋅ 3 ⋅ x²⋅ x²
4 x³ y = 2 ⋅ 2 ⋅ x²⋅ x ⋅ y
GCF = 2x²
By writing the given as the multiple of 2x², we get
= 2x² (3x²) + 2x² (2xy)
Step 2 :
Factoring out the greatest common factor,
= 2x² (3x² + 2xy)
Question 2 :
Factor out the greatest common factor
15x³ + 10x²y - 25x²z
Solution :
Step 1 :
There are three terms,
First term = 15x³ = 3 ⋅ 5 ⋅ x²
Second term = 10x²y = 2 ⋅ 5 ⋅ x² ⋅ y
Third term = - 25x²z = -5 ⋅ 5 ⋅ x² ⋅ z
GCF = 5x²
By writing the given as the multiple of 2x², we get
= 5x² (3) + 5x² (2y) + 5x² (-5x²z)
Step 2 :
Factoring out the greatest common factor,
= 5x²(3 + 2y - 5x²z)
Question 3 :
Factor out the greatest common factor
-7 u² - 21 u³
Solution :
Step 1 :
There are two terms,
First term = -7u² = -7⋅ u²
Second term = - 21 u³ = -3 ⋅ 7 ⋅ u² ⋅ u
GCF = -7u²
By writing the given as the multiple of -7u², we get
= -7u² (1) - 7u² (3u)
Step 2 :
Factoring out the greatest common factor,
= -7u²(1 + 3u)
Question 4 :
Factor out the greatest common factor
28 m²n² -12 m³n - 20 m³n²
Solution :
Step 1 :
In the given polynomial , there are three terms,
First term = 28 m²n² = 4 ⋅ 7 ⋅ m² ⋅ n ⋅ n
Second term = -12 m³n = -4 ⋅ 3 ⋅ m² ⋅ m ⋅ n
Third term = - 20 m³n² = -4 ⋅ 5 ⋅ m² ⋅ m ⋅ n ⋅ n
GCF = 4m²n
By writing the given as the multiple of 4m²n, we get
= 4m²n (7n) + 4m²n (-3m) + 4m²n (-5mn)
Step 2 :
Factoring out the greatest common factor,
= 4m²n (7n- 3m - 5mn)
Question 5 :
Factor out the greatest common factor
12a²- 21 a b
Solution :
Step 1 :
In the given polynomial , there are three terms,
First term = 12a² = 4 ⋅ 3 ⋅ a²
Second term = - 21 a b = -3 ⋅ 7 ⋅ a ⋅ b
GCF = 3a
By writing the given as the multiple of 3a, we get
= 3a (4a) + 3a (-7b)
Step 2 :
Factoring out the greatest common factor,
= 3a (4a - 7b)
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