Question

Factorise completely x3 + 4x2 + x – 4, only after finding out what has to be subtracted from it, to make (x + 2) a factor of the given expression.​

Answer 1

Step-by-step explanation:

It is usually really, really hard to factorize a cubic function. However, for this polynomial, we can factor by grouping. We try values for splitting the term

−

4

x

2

.

For example, we split it into

−

2

x

2

−

2

x

2

.

The equation becomes this:

(

x

3

−

2

x

2

)

−

(

2

x

2

−

x

−

6

)

. We can factorize each of the expressions in the parentheses:

x

2

(

x

−

2

)

−

(

x

−

2

)

(

2

x

+

3

)

. There is a common factor

(

x

−

2

)

.

Factoring the common factor out, we get

(

x

−

2

)

(

x

2

−

2

x

−

3

)

. We then factorize

x

2

−

2

x

−

3

to

(

x

−

3

)

(

x

+

1

)

.

The fully factored form is then

(

x

−

2

)

(

x

−

3

)

(

x

+

1

)

.

Answer 2

Answer:

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