Question

factorise the given term X raise to power 3 + 3 X raise to power 2 +3x -7​

Answer 1

Step-by-step explanation:

Because the

x

4

coefficient is

1

we know the coefficient for the

x

2

terms in the factor will also be

1

:

(

x

2

)

(

x

2

)

Because the constant is a negative and the coefficient for the

x

term is a negative we know the sign for the constants in the factors will have one positive and one negative:

(

x

2

+

)

(

x

2

−

)

Now we need to determine the factors which multiply to -4 and also add to -3:

1

×

−

4

=

−

4

;

1

−

4

=

−

3

<- this IS the factor

(

x

2

+

1

)

(

x

2

−

4

)

The factor

(

x

2

−

4

)

is a special form of the quadratic:

x

2

−

y

2

=

(

x

+

y

)

(

x

−

y

)

We can factor this term as:

(

x

2

+

1

)

(

x

+

2

)

(

x

−

2

)

Answer 2

Step-by-step explanation:

By putting x=1, we get,

${1}^{3} + 3 \times 1^{2} + 3 \times 1 - 7 \\ = 1 + 3 + 3 - 7 \\ = 0$

x=1 is a solution of above equation.

now,

$= x^{2} ( x - 1) + 4x(x - 1) + 7(x - 1) \\ = (x - 1)(x^{2} + 4x + 7)$

solving

$solving \: x ^{2} + 4x + 7$

we get,

x= {-4±(square root) (16-28)}÷2

x= -2±i(square root)(3)

which are imaginary roots

therefore, x= 1 is the only real root of the equation.

Hope it helps.

Thank you:)