At Westonci.ca, we provide reliable answers to your questions from a community of experts. Start exploring today! Experience the ease of finding accurate answers to your questions from a knowledgeable community of professionals. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
Certainly! To find two monomials whose product is a given monomial, we need to consider the different ways we can split the given monomial into two factors with positive integer coefficients. Let's go through each case step-by-step:
### (i) [tex]\( abc \)[/tex]
To factorize [tex]\( abc \)[/tex], we look for pairs of monomials whose product is [tex]\( abc \)[/tex]. The possible pairs are:
1. [tex]\( a \times bc \)[/tex]:
- First monomial: [tex]\( a \)[/tex]
- Second monomial: [tex]\( bc \)[/tex]
2. [tex]\( b \times ac \)[/tex]:
- First monomial: [tex]\( b \)[/tex]
- Second monomial: [tex]\( ac \)[/tex]
3. [tex]\( c \times ab \)[/tex]:
- First monomial: [tex]\( c \)[/tex]
- Second monomial: [tex]\( ab \)[/tex]
4. [tex]\( 1 \times abc \)[/tex]:
- First monomial: [tex]\( 1 \)[/tex]
- Second monomial: [tex]\( abc \)[/tex]
So, the factor pairs for [tex]\( abc \)[/tex] are:
[tex]\[ (a, bc), (b, ac), (c, ab), (1, abc) \][/tex]
### (ii) [tex]\( xyz \)[/tex]
To factorize [tex]\( xyz \)[/tex], we look for pairs of monomials whose product is [tex]\( xyz \)[/tex]. The possible pairs are:
1. [tex]\( x \times yz \)[/tex]:
- First monomial: [tex]\( x \)[/tex]
- Second monomial: [tex]\( yz \)[/tex]
2. [tex]\( y \times xz \)[/tex]:
- First monomial: [tex]\( y \)[/tex]
- Second monomial: [tex]\( xz \)[/tex]
3. [tex]\( z \times xy \)[/tex]:
- First monomial: [tex]\( z \)[/tex]
- Second monomial: [tex]\( xy \)[/tex]
4. [tex]\( 1 \times xyz \)[/tex]:
- First monomial: [tex]\( 1 \)[/tex]
- Second monomial: [tex]\( xyz \)[/tex]
So, the factor pairs for [tex]\( xyz \)[/tex] are:
[tex]\[ (x, yz), (y, xz), (z, xy), (1, xyz) \][/tex]
### (iii) [tex]\( a^2 b c \)[/tex]
To factorize [tex]\( a^2 b c \)[/tex], we look for pairs of monomials whose product is [tex]\( a^2 b c \)[/tex]. The possible pairs are:
1. [tex]\( a \times a bc \)[/tex]:
- First monomial: [tex]\( a \)[/tex]
- Second monomial: [tex]\( a bc \)[/tex]
2. [tex]\( a^2 \times bc \)[/tex]:
- First monomial: [tex]\( a^2 \)[/tex]
- Second monomial: [tex]\( bc \)[/tex]
3. [tex]\( b \times a^2 c \)[/tex]:
- First monomial: [tex]\( b \)[/tex]
- Second monomial: [tex]\( a^2 c \)[/tex]
4. [tex]\( c \times a^2 b \)[/tex]:
- First monomial: [tex]\( c \)[/tex]
- Second monomial: [tex]\( a^2 b \)[/tex]
5. [tex]\( 1 \times a^2 b c \)[/tex]:
- First monomial: [tex]\( 1 \)[/tex]
- Second monomial: [tex]\( a^2 b c \)[/tex]
So, the factor pairs for [tex]\( a^2 b c \)[/tex] are:
[tex]\[ (a, a bc), (a^2, bc), (b, a^2 c), (c, a^2 b), (1, a^2 b c) \][/tex]
### (iv) [tex]\( 7 a b c \)[/tex]
To factorize [tex]\( 7 a b c \)[/tex], we look for pairs of monomials whose product is [tex]\( 7 a b c \)[/tex]. The possible pairs are:
1. [tex]\( 7 \times a bc \)[/tex]:
- First monomial: [tex]\( 7 \)[/tex]
- Second monomial: [tex]\( a bc \)[/tex]
2. [tex]\( 7a \times bc \)[/tex]:
- First monomial: [tex]\( 7a \)[/tex]
- Second monomial: [tex]\( bc \)[/tex]
3. [tex]\( 7b \times ac \)[/tex]:
- First monomial: [tex]\( 7b \)[/tex]
- Second monomial: [tex]\( ac \)[/tex]
4. [tex]\( 7c \times ab \)[/tex]:
- First monomial: [tex]\( 7c \)[/tex]
- Second monomial: [tex]\( ab \)[/tex]
5. [tex]\( 1 \times 7 a b c \)[/tex]:
- First monomial: [tex]\( 1 \)[/tex]
- Second monomial: [tex]\( 7 a b c \)[/tex]
So, the factor pairs for [tex]\( 7 a b c \)[/tex] are:
[tex]\[ (7, a bc), (7a, bc), (7b, ac), (7c, ab), (1, 7 a b c) \][/tex]
### (i) [tex]\( abc \)[/tex]
To factorize [tex]\( abc \)[/tex], we look for pairs of monomials whose product is [tex]\( abc \)[/tex]. The possible pairs are:
1. [tex]\( a \times bc \)[/tex]:
- First monomial: [tex]\( a \)[/tex]
- Second monomial: [tex]\( bc \)[/tex]
2. [tex]\( b \times ac \)[/tex]:
- First monomial: [tex]\( b \)[/tex]
- Second monomial: [tex]\( ac \)[/tex]
3. [tex]\( c \times ab \)[/tex]:
- First monomial: [tex]\( c \)[/tex]
- Second monomial: [tex]\( ab \)[/tex]
4. [tex]\( 1 \times abc \)[/tex]:
- First monomial: [tex]\( 1 \)[/tex]
- Second monomial: [tex]\( abc \)[/tex]
So, the factor pairs for [tex]\( abc \)[/tex] are:
[tex]\[ (a, bc), (b, ac), (c, ab), (1, abc) \][/tex]
### (ii) [tex]\( xyz \)[/tex]
To factorize [tex]\( xyz \)[/tex], we look for pairs of monomials whose product is [tex]\( xyz \)[/tex]. The possible pairs are:
1. [tex]\( x \times yz \)[/tex]:
- First monomial: [tex]\( x \)[/tex]
- Second monomial: [tex]\( yz \)[/tex]
2. [tex]\( y \times xz \)[/tex]:
- First monomial: [tex]\( y \)[/tex]
- Second monomial: [tex]\( xz \)[/tex]
3. [tex]\( z \times xy \)[/tex]:
- First monomial: [tex]\( z \)[/tex]
- Second monomial: [tex]\( xy \)[/tex]
4. [tex]\( 1 \times xyz \)[/tex]:
- First monomial: [tex]\( 1 \)[/tex]
- Second monomial: [tex]\( xyz \)[/tex]
So, the factor pairs for [tex]\( xyz \)[/tex] are:
[tex]\[ (x, yz), (y, xz), (z, xy), (1, xyz) \][/tex]
### (iii) [tex]\( a^2 b c \)[/tex]
To factorize [tex]\( a^2 b c \)[/tex], we look for pairs of monomials whose product is [tex]\( a^2 b c \)[/tex]. The possible pairs are:
1. [tex]\( a \times a bc \)[/tex]:
- First monomial: [tex]\( a \)[/tex]
- Second monomial: [tex]\( a bc \)[/tex]
2. [tex]\( a^2 \times bc \)[/tex]:
- First monomial: [tex]\( a^2 \)[/tex]
- Second monomial: [tex]\( bc \)[/tex]
3. [tex]\( b \times a^2 c \)[/tex]:
- First monomial: [tex]\( b \)[/tex]
- Second monomial: [tex]\( a^2 c \)[/tex]
4. [tex]\( c \times a^2 b \)[/tex]:
- First monomial: [tex]\( c \)[/tex]
- Second monomial: [tex]\( a^2 b \)[/tex]
5. [tex]\( 1 \times a^2 b c \)[/tex]:
- First monomial: [tex]\( 1 \)[/tex]
- Second monomial: [tex]\( a^2 b c \)[/tex]
So, the factor pairs for [tex]\( a^2 b c \)[/tex] are:
[tex]\[ (a, a bc), (a^2, bc), (b, a^2 c), (c, a^2 b), (1, a^2 b c) \][/tex]
### (iv) [tex]\( 7 a b c \)[/tex]
To factorize [tex]\( 7 a b c \)[/tex], we look for pairs of monomials whose product is [tex]\( 7 a b c \)[/tex]. The possible pairs are:
1. [tex]\( 7 \times a bc \)[/tex]:
- First monomial: [tex]\( 7 \)[/tex]
- Second monomial: [tex]\( a bc \)[/tex]
2. [tex]\( 7a \times bc \)[/tex]:
- First monomial: [tex]\( 7a \)[/tex]
- Second monomial: [tex]\( bc \)[/tex]
3. [tex]\( 7b \times ac \)[/tex]:
- First monomial: [tex]\( 7b \)[/tex]
- Second monomial: [tex]\( ac \)[/tex]
4. [tex]\( 7c \times ab \)[/tex]:
- First monomial: [tex]\( 7c \)[/tex]
- Second monomial: [tex]\( ab \)[/tex]
5. [tex]\( 1 \times 7 a b c \)[/tex]:
- First monomial: [tex]\( 1 \)[/tex]
- Second monomial: [tex]\( 7 a b c \)[/tex]
So, the factor pairs for [tex]\( 7 a b c \)[/tex] are:
[tex]\[ (7, a bc), (7a, bc), (7b, ac), (7c, ab), (1, 7 a b c) \][/tex]
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.
