Found 225 Articles for Class 8

Given:Given polynomials are $14x^3y^5, 10x^5y^3$ and $2x^2y^2$.To do:We have to find the greatest common factor of the given polynomials.Solution:GCF:A common factor of two or more numbers is a factor that is shared by the numbers. The greatest common factor (GCF) of those numbers is found by finding all common factors of the numbers and selecting the largest one.The numerical coefficient of $14x^3y^5$ is $14$The numerical coefficient of $10x^5y^3$ is $10$The numerical coefficient of $2x^2y^2$ is $2$This implies, $14=2\times7$$10=2\times5$$2=2\times1$HCF of $14, 10$ and $2$ is $2$The common variables in the given polynomials are $x$ and $y$The power of $x$ in $14x^3y^5$ is $3$The power of $x$ ... Read More

Given:Given polynomials are $2x^3y^2, 10x^2y^3$ and $14xy$.To do:We have to find the greatest common factor of the given polynomials.Solution:HCF:A common factor of two or more numbers is a factor that is shared by the numbers. The highest common factor (HCF) of those numbers is found by finding all common factors of the numbers and selecting the largest one.The numerical coefficient of $2x^3y^2$ is $2$The numerical coefficient of $10x^2y^3$ is $10$The numerical coefficient of $14xy$ is $14$This implies, $2=2\times1$$10=2\times5$$14=2\times7$HCF of $2, 10$ and $14$ is $2$The common variables in the given polynomials are $x$ and $y$The power of $x$ in $2x^3y^2$ is $3$The power of $x$ ... Read More

Given:Given polynomials are $15a^3, -45a^2$ and $-150a$.To do:We have to find the greatest common factor of the given polynomials.Solution:GCF/HCF:A common factor of two or more numbers is a factor that is shared by the numbers. The greatest/highest common factor (GCF/HCF) of those numbers is found by finding all common factors of the numbers and selecting the largest one.The numerical coefficient of $15a^3$ is $15$The numerical coefficient of $-45a^2$ is $45$The numerical coefficient of $-150a$ is $150$This implies, $15=3\times5$$45=3\times3\times5$$150=2\times3\times5\times5$HCF of $15, 45$ and $150$ is $3\times5=15$The common variable in the given polynomials is $a$.The power of $a$ in $15a^3$ is $3$The power of $a$ in $-45a^2$ ... Read More

Given:Given polynomials are $x^3$ and $-yx^2$.To do:We have to find the greatest common factor of the given polynomials.Solution:GCF:A common factor of two or more numbers is a factor that is shared by the numbers. The greatest common factor (GCF) of those numbers is found by finding all common factors of the numbers and selecting the largest one.The numerical coefficient of $x^3$ is $1$The numerical coefficient of $-yx^2$ is $1$GCF is $1$The common variables in the given polynomials are $x$ and $y$The power of $x$ in $x^3$ is $3$The power of $x$ in $-yx^2$ is $2$The power of $y$ in $x^3$ is $0$The power of $y$ in ... Read More

Given:Given polynomials are $36a^2b^2c^4, 54a^5c^2$ and $90a^4b^2c^2$.To do:We have to find the greatest common factor of the given polynomials.Solution:HCF:A common factor of two or more numbers is a factor that is shared by the numbers. The highest common factor (HCF) of those numbers is found by finding all common factors of the numbers and selecting the largest one.The numerical coefficient of $36a^2b^2c^4$ is $36$The numerical coefficient of $54a^5c^2$ is $54$The numerical coefficient of $90a^4b^2c^2$ is $90$This implies, $36=2\times2\times3\times3$$54=2\times3\times3\times3$$90=2\times3\times3\times5$HCF of $36, 54$ and $90$ is $2\times3\times3=18$The common variables in the given polynomials are $a, b$ and $c$The power of $a$ in $36a^2b^2c^4$ is $2$The power of ... Read More

Given:Given polynomials are $a^2b^3$ and $a^3b^2$.To do:We have to find the greatest common factor of the given polynomials.Solution:GCF/HCF:A common factor of two or more numbers is a factor that is shared by the numbers. The greatest/highest common factor (GCF/HCF) of those numbers is found by finding all common factors of the numbers and selecting the largest one.The numerical coefficient of $a^2b^3$ is $1$The numerical coefficient of $a^3b^2$ is $1$HCF is $1$The common variables in the given polynomials are $a$ and $b$The power of $a$ in $a^2b^3$ is $2$The power of $a$ in $a^3b^2$ is $3$The power of $b$ in $a^2b^3$ is $3$The power of $b$ in ... Read More

Given:Given polynomials are $6x^2y^2, 9xy^3$ and $3x^3y^2$.To do:We have to find the greatest common factor of the given polynomials.Solution:GCF:A common factor of two or more numbers is a factor that is shared by the numbers. The greatest common factor (GCF) of those numbers is found by finding all common factors of the numbers and selecting the largest one.The numerical coefficient of $6x^2y^2$ is $6$The numerical coefficient of $9xy^3$ is $9$The numerical coefficient of $3x^3y^2$ is $3$This implies, $6=2\times3$$9=3\times3$$3=3\times1$GCF of $6, 9$ and $3$ is $3$The common variables in the given polynomials are $x$ and $y$The power of $x$ in $6x^2y^2$ is $2$The power of $x$ ... Read More

Given:Given polynomials are $4a^2b^3, -12a^3b$ and $18a^4b^3$.To do:We have to find the greatest common factor of the given polynomials.Solution:HCF:A common factor of two or more numbers is a factor that is shared by the numbers. The highest common factor (HCF) of those numbers is found by finding all common factors of the numbers and selecting the largest one.The numerical coefficient of $4a^2b^3$ is $4$The numerical coefficient of $-12a^3b$ is $12$The numerical coefficient of $18a^4b^3$ is $18$This implies, $4=2\times2$$12=2\times2\times3$$18=2\times3\times3$HCF of $4, 12$ and $18$ is $2$The common variables in the given polynomials are $a$ and $b$The power of $a$ in $4a^2b^3$ is $2$The power of $a$ ... Read More

Given:Given polynomials are $9x^2, 15x^2y^3, 6xy^2$ and $21x^2y^2$.To do:We have to find the greatest common factor of the given polynomials.Solution:GCF/HCF:A common factor of two or more numbers is a factor that is shared by the numbers. The greatest/highest common factor (GCF/HCF) of those numbers is found by finding all common factors of the numbers and selecting the largest one.The numerical coefficient of $9x^2$ is $9$The numerical coefficient of $15x^2y^3$ is $15$The numerical coefficient of $6xy^2$ is $6$The numerical coefficient of $21x^2y^2$ is $21$This implies, $9=3\times3$$15=3\times5$$6=2\times3$$21=3\times7$HCF of $9, 15, 6$ and $21$ is $3$The common variables in the given polynomials are $x$ and $y$The power ... Read More

Given:Given polynomials are $12ax^2, 6a^2x^3$ and $2a^3x^5$.To do:We have to find the greatest common factor of the given polynomials.Solution:GCF:A common factor of two or more numbers is a factor that is shared by the numbers. The greatest common factor (GCF) of those numbers is found by finding all common factors of the numbers and selecting the largest one.The numerical coefficient of $12ax^2$ is $12$The numerical coefficient of $6a^2x^3$ is $6$The numerical coefficient of $2a^3x^5$ is $2$This implies, $12=2\times2\times3$$6=2\times3$$2=2\times1$GCF of $12, 6$ and $2$ is $2$The common variables in the given polynomials are $a$ and $x$The power of $a$ in $12ax^2$ is $1$The power of $a$ ... Read More