Factorising

I am having trouble factorising this equation. I don't know how to solve this equation. It would be much appreciated if you could explain to me step by step on how to solve this question:

(X+5)+3(x+5)^2

Thanks.

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Reply 1

Pheylan

If you had

y+3y^2

instead, would you be able to see what to do?

Reply 2

elldeegee

Original post by zed963

either:
expand brackets, simplify, and then factorise again.

or

take out a factor of (x+5)

the latter is what i think the previous poster was getting at,

y +3y^2

becomes

y (1 +3y)

and is therefore factorised.

Reply 3

zed963

Original post by elldeegee

either:
expand brackets, simplify, and then factorise again.

or

take out a factor of (x+5)

the latter is what i think the previous poster was getting at,

y +3y^2

becomes

y (1 +3y)

and is therefore factorised.

So we know that a common factor is (x+5) so now I'm left with 3x+15.

Reply 4

elldeegee

Original post by zed963

So we know that a common factor is (x+5) so now I'm left with 3x+15.

(X+5)+3(x+5)^2
taking out a common factor of (x+5) leaves:

(x+5) (1 + 3(x+5))

See where your mistake would have been when saying you're left with 3x+15?
it's an easy mistake to make :smile:

Reply 5

zed963

Original post by elldeegee

(X+5)+3(x+5)^2
taking out a common factor of (x+5) leaves:

(x+5) (1 + 3(x+5))

See where your mistake would have been when saying you're left with 3x+15?
it's an easy mistake to make :smile:

How does the 1 come into play?

Reply 6

Math12345

(x+5)+3(x+5)^2

The first thing you should do is make (x+5)^2 into (x+5)(x+5) to make it easier.

(x+5)+3(x+5)(x+5)

The common factor is (x+5) as you can see.

What times (x+5) equals (x+5)?
And what times (x+5) equals 3(x+5)(x+5)?

This is what you should get:

(x+5)(1+3(x+5))
(x+5)(1+3x+15)

Reply 7

zed963

If I was to expand this whole number fully would it become x+5 +3x+15 ?

Reply 8

elldeegee

Original post by zed963

How does the 1 come into play?

say we had the one from before y+3y^2
to factorise this, take out a factor of y:

y(1+ 3y)
because from original

y \div y = 1

and

3y^2 \div y = 3y

so in this case,

you've take out a factor of

(x+5)

(x+5) \div (x+5) = 1

and

3(x+5)^2 \div (x+5) = 3(x+5)

thus,

(x+5)+3(x+5)^2

becomes

(x+5)(1+3(x+5))

simplifying this last bit gives

(x+5) (1+3x+15) = (x+5)(3x+16)

(edited 12 years ago)

Reply 9

TenOfThem

Original post by zed963

If I was to expand this whole number fully would it become x+5 +3x+15 ?

Reply 10

zed963

Original post by Math12345

This is the bit that I am not understanding completelym.

What times (x+5) equals (x+5)?
And what times (x+5) equals 3(x+5)(x+5)?

Reply 11

Math12345

Original post by zed963

This is the bit that I am not understanding completelym.

What times (x+5) equals (x+5)?
And what times (x+5) equals 3(x+5)(x+5)?

(x+5)*y=(x+5)
(x+5)*z=3(x+5)(x+5)

y=1
z=3(x+5)

Reply 12

TenOfThem

Original post by zed963

This is the bit that I am not understanding completelym.

What times (x+5) equals (x+5)?
And what times (x+5) equals 3(x+5)(x+5)?

Start with some easy examples

Can you factorise

3y + 5y^2

3y + y^2

y + 5y^2

Reply 13

elldeegee

Original post by zed963

This is the bit that I am not understanding completelym.

What times (x+5) equals (x+5)?
And what times (x+5) equals 3(x+5)(x+5)?

say if we had something like

2x+6

how would you factorise this? you'd say to yourself, what is a factor of both "2x" and "6", or "what goes into "2x" and "6""

The answer would be 2, because 2 is a factor of 2x and 2 is a factor of 6.

so 2x+6 factorised becomes 2(x+3)
and then multiplying this out would give

2 \times x = 2x

and

2 \times +3 = +6

and putting them together gives 2x+6, which is the original before factorisation.

P.s i have a feeling this may be confusing, so much easier to explain this stuff faceto face :tongue:

Reply 14

zed963

Original post by TenOfThem

Start with some easy examples

Can you factorise

3y + 5y^2

3y + y^2

y + 5y^2

y(3+5y)

y(3+y)

y(1+5y)

Reply 15

zed963

Original post by elldeegee

2 \times x = 2x

and

2 \times +3 = +6

and putting them together gives 2x+6, which is the original before factorisation.

P.s i have a feeling this may be confusing, so much easier to explain this stuff faceto face :tongue:

I know how to do basic factorising but not when it comes to these complicated questions.