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27 votes
Factorize :3y²-54y+343​

User Mohit Tanwani
by
2.4k points

1 Answer

8 votes
8 votes

1 In general, given

a

x

2

+

b

x

+

c

ax

2

+bx+c, the factored form is:

a

(

x

b

+

b

2

4

a

c

2

a

)

(

x

b

b

2

4

a

c

2

a

)

a(x−

2a

−b+

b

2

−4ac

)(x−

2a

−b−

b

2

−4ac

)

2 In this case,

a

=

3

a=3,

b

=

54

b=−54 and

c

=

343

c=343.

3

(

y

54

+

(

54

)

2

4

×

3

×

343

2

×

3

)

(

y

54

(

54

)

2

4

×

3

×

343

2

×

3

)

3(y−

2×3

54+

(−54)

2

−4×3×343

)(y−

2×3

54−

(−54)

2

−4×3×343

)

3 Simplify.

3

(

y

54

+

20

3

ı

6

)

(

y

54

20

3

ı

6

)

3(y−

6

54+20

3

)(y−

6

54−20

3

)

4 Factor out the common term

2

2.

3

(

y

2

(

27

+

10

3

ı

)

6

)

(

y

54

20

3

ı

6

)

3(y−

6

2(27+10

3

)

)(y−

6

54−20

3

)

5 Simplify

2

(

27

+

10

3

ı

)

6

6

2(27+10

3

)

to

27

+

10

3

ı

3

3

27+10

3

.

3

(

y

27

+

10

3

ı

3

)

(

y

54

20

3

ı

6

)

3(y−

3

27+10

3

)(y−

6

54−20

3

)

6 Factor out the common term

2

2.

3

(

y

27

+

10

3

ı

3

)

(

y

2

(

27

10

3

ı

)

6

)

3(y−

3

27+10

3

)(y−

6

2(27−10

3

)

)

7 Simplify

2

(

27

10

3

ı

)

6

6

2(27−10

3

)

to

27

10

3

ı

3

3

27−10

3

.

3

(

y

27

+

10

3

ı

3

)

(

y

27

10

3

ı

3

)

3(y−

3

27+10

3

)(y−

3

27−10

3

I hope this help you

User Theowi
by
2.9k points