Good at Factorization?

Question

Factorise:
1.) d^4 - d^3 + 2d - 2
2.) g^5 + g + 1

Answer 1

1)

d^4 - d^3 + 2d - 2

We have to use a method called "grouping". Factor the first two terms, and the last two terms.

d^3(d - 1) + 2(d - 1)

Now, factor (d - 1) out of BOTH these terms,

(d - 1)(d^3 + 2)

Answer 2

1) d^4 - d^3 + 2d - 2
(d-1) (d^3+2)

2) g^5 + g + 1
(g^2++g+1) (g^3-g^2+1)

Answer 3

The first one can be factorised as...
d^4-d^3+2d-2
=d(d^3+2)-1(d^3+2)
=(d+1)(d^3+2)

then we can factorise (d^3+2) using the familiar formula
a^3+b^3=(a+b)(a^2-ab+b^2)

Answer 4

1) d^3(d-1) + 2(d-1) = (d-1)(d^3 +2)

Answer 5

1)i use the roots for factorise :find the easy roots;
u know:ax^4+bx^3+cx^2+dx+e if we have:a+b+c+d+e=0 then(x=1)is one of the roots.its correct for all of the polynomials.so:
1-1+2-2=0so the(d=1)is your root.then compute the other factor by:
(d^4-d^3+2d-2)/(d-1)=3d^2+2
2)(d-a(cis108))(d-a(cis180))(d-a(cis(-36)))
(d-a(cis252))(d-acis36))
cis36=cos36+isin36
i=imaginary number
a=the root in R it has that i think it must calculate with computer.
but i know that a is[-1,0].

Answer 6

d⁴ - d³ + 2d - 2

d³(d - 1) + 2(d - 1)

(d³ + 2)(d - 1)

- - - - - - - - -s-

Answer 7

1)d^3(d-1)+2(d-1)
(d^3+2)(d-1)

2)(x^2+x+1)(x^3-x^2+1)

I hope this helps!