HELP ME!!!

write each polynomial in standard form

1. 4r + 3 - 9r^2 +7r

2. 10x^2+8-6x-10x^2

Simplify each polynomial. Write each in standard form.
HINT: Watch for the operation! Add? Subtract? Or Multiply?
3. (2v^3-v+8)+(-v^3+v-3)

4. (6s^4+7s^2+7)+(8s^4-11s^2+9s)

5. (4h^3+3h+1)-(-5h^3+6h-2)

6. (8z^3-3z^2-7)-(z^3-z^2+9)

7. 5k(3-4k)

8. 4m(2m+9m^2-6)

9. q(11+8q-2q^2 )

10. (x-2)(x+4)

11. (6g+7)(3g-8)

12. (x-1)^2

13. (4y+2)^2

Factor out the GCF (Greatest Common Factor)
Hint: What can you divide every term by?
14. 3b^4-9b^2+6b

15. 4g^2+8g

16. 45c^5-63c^3+27

Factor each polynomial.
HINT: Change from x^2+bx+c to (x+p)(x+q) where p and q are the factors of c that add to b.
17. x^2+8x+12

18. t^2-5t-14

19. p^2-20p+100

20. r^2+6r-40

21. x^2-13x-30

22. d^2-18d+45

It would be amazing if someone could answer these for my portfolio I need to do asap but I just can not figure these out!!!! These are the questions for The Unit 3 Polynomial Sample Work for Algebra 1 Connections Academy

Please post your attempts.

for example
17. x^2+8x+12 = (x+2)(x+6)

I'd be happy to help you with these questions! Let's go through each one step by step.

1. To write the polynomial in standard form, we arrange the terms in descending order according to the exponent of the variable:
4r - 9r^2 + 7r + 3
-9r^2 + (4r + 7r) + 3
-9r^2 + 11r + 3

2. Similarly, for this polynomial:
10x^2 - 6x - 10x^2 + 8
(10x^2 - 10x^2) - 6x + 8
-6x + 8

3. For simplifying the polynomial and writing it in standard form:
(2v^3 - v + 8) + (-v^3 + v - 3)
2v^3 - v^3 - v + v + 8 - 3
v^3 + 5

4. Simplifying and arranging in standard form:
(6s^4 + 7s^2 + 7) + (8s^4 - 11s^2 + 9s)
6s^4 + 8s^4 + 7s^2 - 11s^2 + 9s + 7
14s^4 - 4s^2 + 9s + 7

5. Simplifying and arranging in standard form:
(4h^3 + 3h + 1) - (-5h^3 + 6h - 2)
4h^3 + 5h^3 + 3h - 6h + 1 + 2
9h^3 - 3h + 3

6. Simplifying and arranging in standard form:
(8z^3 - 3z^2 - 7) - (z^3 - z^2 + 9)
8z^3 - z^3 - 3z^2 + z^2 - 7 - 9
7z^3 - 2z^2 - 16

7. Applying distribution to simplify:
5k(3 - 4k)
15k - 20k^2

8. Similarly, simplify:
4m(2m + 9m^2 - 6)
8m^2 + 36m^3 - 24m

9. Simplifying and arranging in standard form:
q(11 + 8q - 2q^2)
11q + 8q^2 - 2q^3

10. To expand the given product:
(x - 2)(x + 4)
x(x) + x(4) - 2(x) - 2(4)
x^2 + 4x - 2x - 8
x^2 + 2x - 8

11. Expanding:
(6g + 7)(3g - 8)
6g(3g) + 6g(-8) + 7(3g) + 7(-8)
18g^2 - 48g + 21g - 56
18g^2 - 27g - 56

12. Expanding:
(x - 1)(x - 1)
x(x) - x(1) - 1(x) + 1(1)
x^2 - x - x + 1
x^2 - 2x + 1

13. Expanding:
(4y + 2)(4y + 2)
4y(4y) + 4y(2) + 2(4y) + 2(2)
16y^2 + 8y + 8y + 4
16y^2 + 16y + 4

14. Factoring out the GCF:
3b^4 - 9b^2 + 6b
3b(b^3 - 3b + 2)

15. Similarly, factoring:
4g^2 + 8g
4g(g + 2)

16. Factoring:
45c^5 - 63c^3 + 27
9(5c^5 - 7c^3 + 3)

17. Factoring:
x^2 + 8x + 12
(x + 2)(x + 6)

18. Factoring:
t^2 - 5t - 14
(t - 7)(t + 2)

19. Factoring:
p^2 - 20p + 100
(p - 10)^2

20. Factoring:
r^2 + 6r - 40
(r - 4)(r + 10)

21. Factoring:
x^2 - 13x - 30
(x - 15)(x + 2)

22. Factoring:
d^2 - 18d + 45
(d - 3)(d - 15)

I hope this helps you with your portfolio! Let me know if you have any further questions.