Give the solutions from this questions. 50 pointss

7. P(x) = (x³ 1 x² - 10x + 6)

Step-by-step explanation:

The factored form of a polynomial is: a(x - p)(x-q)...(x-z) . where p, q, ..., z are the roots.

Convert the roots into factors, include conjugates of any complex roots, and multiply all of the factors.  Then find the a-value.

roots:       x = 3               x = 2 + √2                    x = 2 - √2     (conjugate)

factors:    x - 3 = 0          x - 2 - √2 = 0               x - 2 + √2 = 0

                             (x - 3)(x - 2 - √2)(x - 2 + √2)

                          multiply the complex roots:      

                               (x + 3)(x² - 4x + 2)

          distribute (x + 3) to find the basic polynomial

                                x³ + x² - 10x + 6

Next, find the a-value:

P(x) = a(x³ + x² - 10x + 6)

P(1) = a(1 - 1 - 10 + 6) = -3

                           -4a = -3

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8. P(x) = (x⁴ + 8)

Step-by-step explanation:

The factored form of a polynomial is: a(x - p)(x-q)...(x-z) . where p, q, ..., z are the roots.

Convert the roots into factors, include conjugates of any complex roots, and multiply all of the factors.  Then find the a-value.

roots:       x = -2               x = 1 + i                    x = 1 - i     (conjugate)

factors:    x + 2 = 0          x - 1 - i = 0               x - 1 + i = 0

The polynomial has a degree of 4, so x = -2 must be a double root.

                              (x + 2)²(x - 1 - i)(x - 1 + i)

               multiply the double root & complex roots:

                             (x² + 4x + 4)(x² - 2x + 2)

           distribute (x² + 4x + 4) to find the basic polynomial

                                         x⁴ + 8

Next, find the a-value:

P(x) = a(x⁴ + 8)

P(0) = a(0 + 8) = 4

                  8a = 4

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9. P(x) = (x⁴ - x³ - 6x²)

Step-by-step explanation:

The factored form of a polynomial is: a(x - p)(x-q)...(x-z) . where p, q, ..., z are the roots. The roots are where the graph crosses the x-axis.

roots:       x = -2               x = 0                   x = 3

factors:    x + 2 = 0          x  = 0                  x - 3 = 0

The graph "touches - not crosses" the x-axis at x = 0 so x = 0 is a double root.

                                 (x + 2)(x)²(x - 3)

               multiply the factors (x + 2)(x - 3):

                                  x²(x² - x - 6)

           distribute (x)² to find the basic polynomial

                                 x⁴ - x³ - 6x²

Next, find the a-value:

P(x) = a(x⁴ - x³ - 6x²)

P(2) = a[(2)⁴ -(2)³ - 6(2)²] = 8

         a(16 - 8 - 24) = 8

                  -16a = 8

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10. P(x) = -(x³ - 2x² + x - 2)

Step-by-step explanation:

The graph displayed is an x³ graph that has been shifted to the left 2 units and reflected over the x-axis.  Only one root is shown, which means the other two roots are complex numbers.  Since P(i) = 0, then another root is: x = i

roots:       x = -2               x =  i                    x =  - i     (conjugate)

factors:    x + 2 = 0          x - i = 0               x + i = 0

                              (x + 2)(x - i)(x + i)

                    multiply the complex roots:

                             (x + 2)(x² + 1)

           distribute (x + 2) to find the basic polynomial

                                    x³  - 2x² + x - 2

Next, reflect over the x-axis:

P(x) = - (x³  - 2x² + x - 2)

answer:   segregation violated the equal protection clause of the 14th amendment, which holds that no state can “deny to any person within its jurisdiction the equal protection of the laws.”

details/explanation:

brown v. board of education of topeka, decided by the us supreme court in 1954, ruled that all americans are entitled to the same civil liberties and protections in regard to access to education. until that decision, it was legal to segregate schools according to race, so that black students could not attend the same schools as white students.   an older supreme court decision, plessy v. ferguson (1896), had said that separate, segregated public facilities were acceptable as long as the facilities offered were equal in quality.   in the case of brown v. board of education, that standard was challenged and defeated.   segregation was shown to create inequality, and the supreme court unanimously ruled segregation to be unconstitutional.

the ruling was important in advancing civil rights because it affirmed that the 14th amendment applies to all rights and privileges of citizens, including access to   education.   this was being violated by states whose laws supported the segregation of schools.   section 1 of the 14th amendment reads as follows:

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step-by-step explanation: