((Look at the image))

  a)  y = 2x⁴ -18x² +8x +24

  b)  4th degree; tends toward +∞ when |x| gets large

Step-by-step explanation:

a) When r is a root of the polynomial, (x -r) is a factor. The given roots mean the factors are ...

  y = a(x -(-1))(x -(-3))(x -2)(x -2) = a(x+1)(x+3)(x-2)²

The product of the constant terms is a(1)(3)(2²) = 12a. This is the y-intercept, which is said to be 24. So ...

  12a = 24   ⇒   a = 2

The polynomial function is then ...

  y = 2(x +1)(x +3)(x -2)²

  y = 2x⁴ -18x² +8x +24

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b) The leading coefficient of this 4th-degree polynomial is positive, so when x has large positive or negative values, the function value will tend toward positive infinity.

Missing Part of the Question

Step-by-step explanation:

Given

y = 3

Required

Which pair of expression are equal

To get the pair of expression that are equal; we simply substitute 3 for y in each of the expressions

3 (4 - y) -7 and 5 + 3y

Substitute 3 for y in 3 (4 - y) -7

This gives 3(4 - 3) -7

= 3(1) - 7

= 3 - 7

= -4

Then Substitute 3 for y in 5 + 3y

This gives  5 + 3(3)

= 5 + 9

= 14

-4 and 14 are not equal

9 + y + 4y - 2 - 3y; -2y + 7

Substitute 3 for y in 9 + y + 4y - 2 - 3y

This gives 9 + 3 + 4(3) - 2 - 3(3)

= 9 + 3 + 12 - 2 - 9

= 13

Then Substitute 3 for y in -2y + 7

This gives  -2(3) + 7

= -6 + 7

= 1

13 and 1 are not equal

5 + y - 2 - 6y + y; 8y + 3

Substitute 3 for y in 5 + y - 2 - 6y + y

This gives 5 + 3 - 2 - 6(3) + 3

= 5 + 3 - 2 - 18 + 3

= -9

Then Substitute 3 for y in 8y + 3

This gives  8(3) + 3

= 24 + 3

= 27

-9 and 27 are not equal

2y + 7 + y - 2 + y; 4y + 5

Substitute 3 for y in 2y + 7 + y - 2 + y

This gives 2(3) + 7 + 3 - 2 + 3

= 6 + 7 + 3 - 2 + 3

= 17

Then Substitute 3 for y in 4y + 5

This gives  4(3) + 5

= 12 + 5

= 17

17 and 17 are equal

Hence, Option D is correct