What is the product of -2x^3+x-5 and x^3-3x-4 ?

-2x^6 + 7x^4 + 3x^3 - 3x^2 + 11x + 20

Step-by-step explanation:

When multiplying two expressions, each part of the expression has to be multiplied by each part of the other expression.

(-2x^3 + x - 5) * (x^3 - 3x - 4)

Let's multiply -2x^3 first.

-2x^3 * x^3 = -2x^6

-2x^3 * -3x = 6x^4

-2x^3 * -4 = 8x^3

Now let's multiply x.

x * x^3 = x^4

x * -3x = -3x^2

x * -4 = -4x

Finally, let's multiply -5.

-5 * x^3 = -5x^3

-5 * -3x = 15x

-5 * -4 = 20

Let's put all of our answers into one expression in descending order of exponents.

-2x^6 + 6x^4 + x^4 + 8x^3 - 5x^3 - 3x^2 - 4x + 15x + 20

Combine like terms:

-2x^6 + 7x^4 + 3x^3 - 3x^2 + 11x + 20

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.