IDNLearn.com makes it easy to find accurate answers to your specific questions. Join our interactive Q&A community and access a wealth of reliable answers to your most pressing questions.
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]
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! Thank you for trusting IDNLearn.com with your questions. Visit us again for clear, concise, and accurate answers.
