Question

(2-x²) (1+x²+x³) + (4+x) (3-x-x²) plz answer​

Answer 1

Answer:

(x^2–1)= (x-1)^2

Then you would factorise (x^2–1) by using difference of two squares.

So here is what you are expected to get.

x( x-1) ( x+1 ) = ( x- 1 )^2

Then you would divide both sides by ( x-1 ) to make life easier, and notice that ( x- 1 )^2 is the same as multiplying (x- 1 ) twice. Like this : (x- 1 ) ( x- 1 )

This allow you to cancel out ( x- 1 ) from both sides.

And now the question get simpler and become easier to solve. This is what you should get.

x( x+1) = ( x-1)

The next step would be to Expand the bracket out .

So you have this equation, hopefully.

x^2 + x = x - 1

Bring all the term into one side and makes the equation equal to 0.

You equation will then becomes like this.

x^2 + x - x + 1 = 0 , and the two x(s)will then cancel out and you would be left with an equation :

x^2 + 1= 0

Subtract one from both sides in order to be left with x^2 on one side.

x^2 + 1 - 1 = 0 - 1

x^2 = -1

So now you have x^ 2 on the one side and -1 on the other side.

The final step to get x alone, to square root both sides, to get x by itself.

Square Root of (x )^2 = plus or minus square Root of (-1)

In this case you can’t apply square root on negative numbers. This isn’t possible( mathematically speaking).

E.g if you square any number whether positive or negative, the answer will always be positive so, there is no way that you could square a number and get negative number as a result( in real numbers ).

But COMPLEX Numbers does allow you to have negative number under root sign.

Then if you allow complex number to involve your equation, you will have the answer for x.

X = plus or minus square root of -1. Mathematicians respresent root -1 as lowercase i ( short for imagine numbers )

THEREFORE : The values for x would be plus or minus root -1 or just plus or minus i ( if you want to be more specific )

Edit:

I apologise for giving the incomplete answer to your question. Thanks to Nicholas McConnell for pointing out the mistakes I made in my previous answer. I unconsciously neglect the possible roots when I divides both sides of the expression with x and (x-1). These two were the ones I missed out in my answer.

The complete answers to the question is 0,1,-i,i.

Hope, this help and make you see what I have

Step-by-step explanation:

MAKE ME AS BRAINLIST

Answer 2

$\huge\underbrace\mathfrak\red{answer}$

(2-x²) (1+x²+x³) + (4+x) (3-x-x²)

• After distribution

=> 2 + 2x² + 2x³ + -x² + -x⁴ + -x⁵ + 12 + -4x + -4x² + 3x + -x² + -x³

• After combining like terms the result is,

=> -x⁵ + -x⁴ + ( 2x³ + -x³ ) + ( 2x² + -x² + -4x² + -x² ) + ( -4x + 3x ) + ( 2 + 12 )

=> -x⁵ + -x⁴ + x³ + -4x² + -x + 14

• Now the Final Answer is,

=> -x⁵ - x⁴ + x³ + -4x² -x + 14