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Factorization of Polynomials | Factorization of Polynomials Exercise 3C

Question 61

7(𝑥 − 2𝑦)^2 − 25(𝑥 − 2𝑦) + 12

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  • Solution

  • Transcript

7(𝑥 − 2𝑦)^2 − 25(𝑥 − 2𝑦) + 12

Let us consider x – 2y = z

So we get,

= 7𝑧^2 − 25𝑧 + 12

We can further write it as

= 7𝑧^2 − 21𝑧 − 4𝑧 + 12

By taking out the common terms

= 7z (z – 3) – 4 (z – 3)

= (7z – 4) (z – 3)

Let us replace z by x – 2y

So we get,

7(𝑥 − 2𝑦)^2 − 25(𝑥 − 2𝑦) + 12

Then,

= (7(x – 2y) – 4) ((x – 2y) – 3)

= (7x – 14y – 4) (x – 2y – 3)

"hello everyone i am sumanjali math tutor from leader learning welcome to question answer session given expression is 7 into x minus 2 y whole square minus 25 into x minus 2 y plus 12 we need to factorize this expression factorization is nothing but we need to express this in terms of simple terms or product of factors okay so first of all as as this expression is a bit complicated with the terms x minus 2y isn't it now so let us take in place of x minus 2y so let us take a value z okay a value z okay so the expression can be written as 7 into z square in place of x minus 2y i'm writing z minus 25 into z plus 12 okay plus 12 and as a step 1 in the process of factorization the step one is we need to take the product of a and c a value will be coefficient of x square and c value will be constant so the coefficient of yeah x square or z square it is 7 multiplied by 12 7 12 are 84 and we need to search an another pair of factors for 84 that is 21 forza 21 forcer so that we can get the value of by adding or subtracting this we can get the value of uh we can get the value of 25 okay so we can write minus 25 z as minus 21x 21z minus 4z okay so this is 7z square minus 21z minus 4 z plus 12 i am taking common seven z from the first two terms okay so the first term will be z if we take seven z common z will remains minus three will be remains in the second term and i am taking common the second from the second pair of two terms minus four so that z will be remains in the first term and minus three will be as the fourth raiser 12 minus into minus plus so z minus 3 will be reminds so we can express this as a z minus 3 if we take common that 7 z minus 4 will reminds okay so the term the equation 7 z square minus 25 z plus 12 can be written as z minus 3 into 7 z minus 4 so the factors of the given expression is these two and if we write in terms of x minus 2 by 7 minus 7 into x minus 2 y whole square minus 25 into x minus 2 y plus 12 as so that in place of z value i am writing x minus 2 y minus 3 into 7 into x minus 2 y minus 4 okay so these are the factors for the given expression okay that's all hope you understand if you have further questions reach us at comment section and subscribe to the channel leader learning for further queries thank you "

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Question 61

7(𝑥 − 2𝑦)^2 − 25(𝑥 − 2𝑦) + 12

  • Solution

  • Transcript

7(𝑥 − 2𝑦)^2 − 25(𝑥 − 2𝑦) + 12

Let us consider x – 2y = z

So we get,

= 7𝑧^2 − 25𝑧 + 12

We can further write it as

= 7𝑧^2 − 21𝑧 − 4𝑧 + 12

By taking out the common terms

= 7z (z – 3) – 4 (z – 3)

= (7z – 4) (z – 3)

Let us replace z by x – 2y

So we get,

7(𝑥 − 2𝑦)^2 − 25(𝑥 − 2𝑦) + 12

Then,

= (7(x – 2y) – 4) ((x – 2y) – 3)

= (7x – 14y – 4) (x – 2y – 3)

"hello everyone i am sumanjali math tutor from leader learning welcome to question answer session given expression is 7 into x minus 2 y whole square minus 25 into x minus 2 y plus 12 we need to factorize this expression factorization is nothing but we need to express this in terms of simple terms or product of factors okay so first of all as as this expression is a bit complicated with the terms x minus 2y isn't it now so let us take in place of x minus 2y so let us take a value z okay a value z okay so the expression can be written as 7 into z square in place of x minus 2y i'm writing z minus 25 into z plus 12 okay plus 12 and as a step 1 in the process of factorization the step one is we need to take the product of a and c a value will be coefficient of x square and c value will be constant so the coefficient of yeah x square or z square it is 7 multiplied by 12 7 12 are 84 and we need to search an another pair of factors for 84 that is 21 forza 21 forcer so that we can get the value of by adding or subtracting this we can get the value of uh we can get the value of 25 okay so we can write minus 25 z as minus 21x 21z minus 4z okay so this is 7z square minus 21z minus 4 z plus 12 i am taking common seven z from the first two terms okay so the first term will be z if we take seven z common z will remains minus three will be remains in the second term and i am taking common the second from the second pair of two terms minus four so that z will be remains in the first term and minus three will be as the fourth raiser 12 minus into minus plus so z minus 3 will be reminds so we can express this as a z minus 3 if we take common that 7 z minus 4 will reminds okay so the term the equation 7 z square minus 25 z plus 12 can be written as z minus 3 into 7 z minus 4 so the factors of the given expression is these two and if we write in terms of x minus 2 by 7 minus 7 into x minus 2 y whole square minus 25 into x minus 2 y plus 12 as so that in place of z value i am writing x minus 2 y minus 3 into 7 into x minus 2 y minus 4 okay so these are the factors for the given expression okay that's all hope you understand if you have further questions reach us at comment section and subscribe to the channel leader learning for further queries thank you "

Our top 5% students will be awarded a special scholarship to Lido.

subject-cta
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