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Found 466 Articles for Mathematics
146 Views
Given:The given quadratic trinomials are:(i) $12x^2-17xy+6y^2$(ii) $6x^2-5xy-6y^2$To do:We have to factorize the given quadratic trinomials.Solution:Factorizing algebraic expressions:Factorizing an algebraic expression implies writing the expression as a product of two or more factors. Factorization is the reverse of distribution. An algebraic expression is factored completely when it is written as a product of prime factors.(i) The given expression is $12x^2-17xy+6y^2$.We can factorize the given expression by splitting the middle term. Splitting the middle term means we have to rewrite the middle term as the sum or difference of the two terms.Here, The coefficient of $x^2$ is $12$The coefficient of $x$ is $-17y$The constant ... Read More
143 Views
Given:The given quadratic trinomials are:(i) $11x^2-54x+63$(ii) $7x-6x^2+20$(iii) $3x^2+22x+35$To do:We have to factorize the given quadratic trinomials.Solution:Factorizing algebraic expressions:Factorizing an algebraic expression implies writing the expression as a product of two or more factors. Factorization is the reverse of distribution. An algebraic expression is factored completely when it is written as a product of prime factors.(i) The given expression is $11x^2-54x+63$.We can factorize the given expression by splitting the middle term. Splitting the middle term means we have to rewrite the middle term as the sum or difference of the two terms.Here, The coefficient of $x^2$ is $11$The coefficient of $x$ is $-54$The ... Read More
168 Views
Given:The given quadratic trinomials are:(i) $28-31x-5x^2$(ii) $3+23y-8y^2$To do:We have to factorize the given quadratic trinomials.Solution:Factorizing algebraic expressions:Factorizing an algebraic expression implies writing the expression as a product of two or more factors. Factorization is the reverse of distribution. An algebraic expression is factored completely when it is written as a product of prime factors.(i) The given expression is $28-31x-5x^2$.We can factorize the given expression by splitting the middle term. Splitting the middle term means we have to rewrite the middle term as the sum or difference of the two terms.Here, The coefficient of $x^2$ is $-5$The coefficient of $x$ is $-31$The constant ... Read More
78 Views
Given:The given quadratic trinomials are:(i) $3x^2+10x+3$(ii) $7x-6-2x^2$(iii) $7x^2-19x-6$To do:We have to factorize the given quadratic trinomials.Solution:Factorizing algebraic expressions:Factorizing an algebraic expression implies writing the expression as a product of two or more factors. Factorization is the reverse of distribution. An algebraic expression is factored completely when it is written as a product of prime factors.(i) The given expression is $3x^2+10x+3$.We can factorize the given expression by splitting the middle term. Splitting the middle term means we have to rewrite the middle term as the sum or difference of the two terms.Here, The coefficient of $x^2$ is $3$The coefficient of $x$ is $10$The ... Read More
143 Views
Given:The given quadratic trinomials are:(i) $2x^2+5x+3$(ii) $2x^2-3x-2$To do:We have to factorize the given quadratic trinomials.Solution:Factorizing algebraic expressions:Factorizing an algebraic expression implies writing the expression as a product of two or more factors. Factorization is the reverse of distribution. An algebraic expression is factored completely when it is written as a product of prime factors.(i) The given expression is $2x^2+5x+3$.We can factorize the given expression by splitting the middle term. Splitting the middle term means we have to rewrite the middle term as the sum or difference of the two terms.Here, The coefficient of $x^2$ is $2$The coefficient of $x$ is $5$The constant ... Read More
133 Views
Given:The given expressions are:(i) $y^2+5y-36$(ii) $(a^2-5a)^2-36$(iii) $(a+7)(a-10)+16$To do:We have to factorize the given algebraic expressions.Solution:Factorizing algebraic expressions:Factorizing an algebraic expression implies writing the expression as a product of two or more factors. Factorization is the reverse of distribution. An algebraic expression is factored completely when it is written as a product of prime factors.(i) The given expression is $y^2+5y-36$.We can factorize the given expression by splitting the middle term. Splitting the middle term means we have to rewrite the middle term as the sum or difference of the two terms.$y^2+5y-36$ can be written as, $y^2+5y-36=y^2+9y-4y-36$ [Since ... Read More
80 Views
Given:The given expressions are:(i) $a^2+2a-3$(ii) $a^2+14a+48$(iii) $x^2-4x-21$To do:We have to factorize the given algebraic expressions.Solution:Factorizing algebraic expressions:Factorizing an algebraic expression implies writing the expression as a product of two or more factors. Factorization is the reverse of distribution. An algebraic expression is factored completely when it is written as a product of prime factors.(i) The given expression is $a^2+2a-3$.We can factorize the given expression by splitting the middle term. Splitting the middle term means we have to rewrite the middle term as the sum or difference of the two terms.$a^2+2a-3$ can be written as, $a^2+2a-3=a^2+3a-a-3$ [Since ... Read More
562 Views
Given:The given expressions are:(i) $x^2-22x+120$(ii) $x^2-11x-42$To do:We have to factorize the given algebraic expressions.Solution:Factorizing algebraic expressions:Factorizing an algebraic expression implies writing the expression as a product of two or more factors. Factorization is the reverse of distribution. An algebraic expression is factored completely when it is written as a product of prime factors.(i) The given expression is $x^2-22x+120$.We can factorize the given expression by splitting the middle term. Splitting the middle term means we have to rewrite the middle term as the sum or difference of the two terms.$x^2-22x+120$ can be written as, $x^2-22x+120=x^2-12x-10x+120$ [Since $-22x=-12x-10x$ ... Read More
144 Views
Given:The given expressions are:(i) $a^2+3a-88$(ii) $a^2-14a-51$(iii) $x^2+14x+45$To do:We have to factorize the given algebraic expressions.Solution:Factorizing algebraic expressions:Factorizing an algebraic expression implies writing the expression as a product of two or more factors. Factorization is the reverse of distribution. An algebraic expression is factored completely when it is written as a product of prime factors.(i) The given expression is $a^2+3a-88$.We can factorize the given expression by splitting the middle term. Splitting the middle term means we have to rewrite the middle term as the sum or difference of the two terms.$a^2+3a-88$ can be written as, $a^2+3a-88=a^2+11a-8a-88$ [Since ... Read More
585 Views
Given:The given expressions are:(i) $x^2+12x-45$(ii) $40+3x-x^2$To do:We have to factorize the given algebraic expressions.Solution:Factorizing algebraic expressions:Factorizing an algebraic expression implies writing the expression as a product of two or more factors. Factorization is the reverse of distribution. An algebraic expression is factored completely when it is written as a product of prime factors.(i) The given expression is $x^2+12x-45$.We can factorize the given expression by splitting the middle term. Splitting the middle term means we have to rewrite the middle term as the sum or difference of the two terms.$x^2+12x-45$ can be written as, $x^2+12x-45=x^2+15x-3x-45$ [Since $12x=15x-3x$ ... Read More