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(x+3)(x+2)=0

x = -3

x = -2

x =  0.0000 + 1.0000 i

Step-by-step explanation:

x^4 - 5x^3 +7x^2-5x+6 =0

We need to find the factors for 6 when multiplied together they give us 6

And when they are added they add up to 5

(x+3)(x+2)=0

x = -3

x = -2

x =  0.0000 + 1.0000 i

The Factor Theorem states that if P/Q is root of a polynomial then this polynomial can be divided by q*x-p Note that q and p originate from P/Q reduced to its lowest terms

In our case this means that

 of -x5/ x3-2x2+x-2 and of -x5 / x^2- 2x2 and  x^4-2x2 2x2

Which also separates 7 the same x7- 2x2+x-2 +x-2  and again to make (6 of the 7 )is 2x2 + x  then +x to make 7

The first one can be divided with  x-2 +1

Proof

3.5    Find roots (zeroes) of :       F(x) = x2+1

3.4    Polynomial Long Division

Dividing :  x3-2x2+x-2

                             ("Dividend")

By         :    x-2    ("Divisor")

dividend     x3  -  2x2  +  x  -  2

- divisor  * x2     x3  -  2x2        

remainder             x  -  2

- divisor  * 0x1                

remainder             x  -  2

- divisor  * x0             x  -  2

remainder                0

Quotient :  x2+1  Remainder:  0

    See theory in step 3.1

In this case, the Leading Coefficient is  1  and the Trailing Constant is  1.

The factor(s) are:

of the Leading Coefficient :  1

of the Trailing Constant :  1

Let us test

P    Q    P/Q    F(P/Q)    Divisor

     -1       1        -1.00        24.00    

     -2       1        -2.00        100.00    

     -3       1        -3.00        300.00    

     -6       1        -6.00        2664.00    

     1       1        1.00        4.00    

     2       1        2.00        0.00      x-2

     3       1        3.00        0.00      x-3

     6       1        6.00        444.00  

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it

10.4 inches

step-by-step explanation:

2x2x2.6