Question

Factorize x^4 + 2x63 -7x^2 – 8x +12

Answer 1

Answer:

(x)=x^4+2x^3+x^2+8x-12

I need to find all of the actual zeros of this function, including the complex. Thanks.

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= .

It is easy to check that x = 1 is the root.

It means that the left side polynomial has the factor (x-1).

Make long division of by (x-1). You will get

= .

The polynomial has the root x = -3. (Check it).

Then this polynomial has the factor (x+3).

Make the long division again and get the quotient, which is the quadratic polynomial this time.

I hope that you can complete yourself the assignment from this point.

Answer 2

Step-by-step explanation:

Since power is 4, there are 4 factors.

Take x=1 and put x=1 in this polynomial

you will get = 0

So x - 1 is a factor.

Now divide the polynomial by x-1

You will get

x^3+3x^2-4x-12

Now take x=2and put x=2 in the polynomial

x^3+3x^2-4x-12

you will get 0

So x-2 is one factor

Again divide like this

(x^3+3x^2-4x-12)÷(x-2)=x^2+5x+6

x^2+5x+6=(x+2)(x+3) {by middle term splitting}

So 4 factors are

(x-1), (x-2), (x+2) and (x+3) Ans