# 10 points! factor the polynomial show work?

1.) 125x^3-8

2.) 2x^3-5x^2+18x-45

3.) x^4+3x^2+2

Relevance

1, 125x^(3)-8

The binomial can be factored using the difference of cubes formula, because both terms are perfect cubes. The difference of cubes formula is a^(3)-b^(3)=(a-b)(a^(2)+ab+b^(2)).

(5x-2)(25x^(2)+10x+4)

2, 2x^(3)-5x^(2)+18x-45

Factor the greatest common factor (GCF) from each group.

(x^(2)(2x-5)+9(2x-5))

Factor the polynomial by grouping the first two terms together and finding the greatest common factor (GCF). Next, group the second two terms together and find the GCF. Since both groups contain the factor (2x-5), they can be combined.

(x^(2)+9)(2x-5)

3, x^(4)+3x^(2)+2

For a polynomial of the form x^(2)+bx+c, find two factors of c (2) that add up to b (3). In this problem 2*1=2 and 2+1=3, so insert 2 as the right hand term of one factor and 1 as the right-hand term of the other factor.

(x^(2)+2)(x^(2)+1)

• Write down components of 40 5: a million, 3, 5, 9 , 15 -a million, -3, -5, -9, -15 Plug in one indoors the expression till you get a 0 answer attempt 5: 5^3 - 5 x 5^2 - 9 x 5 + 40 5 = 0. So (x - 5) is a ingredient. you need to then divide x^3-5x^2-9x+40 5 by skill of using x - 5 to get the a number of components, or you need to save on plugging indoors the climate of 40 5 till you get 0. even yet it quite is time-eating. attempt 3: 3^3 - 5 x 3^2 - 9 x 3 + 40 5 = 0. So (x - 3) is a ingredient. attempt -3: -3^3 - 5 x -3^2 - 9 x -3 + 40 5 = 0. So (x + 3) is a ingredient. x^3-5x^2-9x+40 5 = (x - 5) (x + 3) (x - 3). attempt the long branch technique of get a quadratic, then ingredient the quadratic. it quite is quicker that way.