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Please help!!! Brainliest given!!

1. Which of the following polynomial equations are valid identities?
A. m3 - 1 = (m - 1) (1 + m + m2)
B.(n + 3)2 + 2n = 81 +13

A. Only B
B. Only A
C. Neither A nor B
D. Both A and B

2. Select the polynomial that has (x-3) as a factor.

A. p(x)=x^4-2x^3-25
B. p(x)=x^3+3x^2-2x-6
C. p(x)=x^3-2x^2-4x+3
D. p(x)=x^4-20x-23

3. Find the remainder when x^4-2x^3+x^2-5x+3 is divided by x+1
A. 3
B. 8
C. 12
D. -2​

Respuesta :

shinomiya

Answer:

1: A

2: C

3: I have no clue (Sorry)

Step-by-step explanation:

mhanifa

Answer:

  • 1. A
  • 2. C
  • 3. C

Step-by-step explanation:

1. ................................................

A. m^3 - 1 = (m - 1)( 1 + m + m^2)

  • When we open parenthesis we get both sides equal. YES

B. (n + 3)^2 + 2n = 81 + 13

  • Left side has variables, right side not. NO

2. Polynomial that has (x - 3) as a factor

A. p(x)=x^4-2x^3-25

  • x^4 - 3x^3 + x^3 - 27 + 2
  • x^3(x-3) + (x - 3)(x^2 + 3x + 9) + 2
  • It can' be factored without remainder. NO

B. p(x)=x^3+3x^2-2x-6

  • x^2(x+3) -2(x+3).
  • It has (x+3) as a factor. NO

C. p(x)=x^3-2x^2-4x+3

  • x^3 - 3x^2 + x^2 - 3x - x +3 =
  • x^2(x - 3) + x(x - 3) - (x - 3)
  • It has a (x - 3) as a factor. YES

D. p(x)=x^4-20x-23

  • x^4 - 27 x + 7 x - 23 =
  • x(x-3)(x+3x + 9) + 7( x - 3) - 2
  • It can' be factored without remainder. NO

3. x^4-2x^3+x^2-5x+3 is divided by x+1, find remainder

  • x^4 + x^3 - 3x^3 - 3x^2 + 4x^2 + 4x - 9x - 9 + 12=
  • x^3 (x + 1) - x^2(x + 1) + 4x(x + 1) - 9(x + 1) + 12
  • The remainder is 12. Option C

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