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polynomial operations your turn: add the following polynomials. write t…

Question

polynomial operations
your turn:
add the following polynomials. write the answers in standard form.

  1. $(7j^3 - 2) + (5j^3 - j - 3)$
  2. $(8a^5 - 4) + (3a^5 + a - 2)$
  3. $(6m^5 + 1) + (2m^5 + 9m - 1)$
  4. $(3m^5 + 1) + (9m^5 + 3m - 2)$
  5. $(-5x^2 - x + 4) + (-3x^2 - 5x + 2)$
  6. $(-4x + 4x^3 + 7) + (3x^3 - 9 - 3x)$
  7. $(3x^2 - 2x + 1) + (-x^2 + 3x + 1)$

subtract the following polynomials. write the answers in standard form.

  1. $(-x^2 + x - 4) - (3x^2 - 8x - 2)$
  2. $(8x^2 - 3x) - (5x - 5 - 8x^2)$
  3. $(-x^2 - 5x - 3) - (-7x^2 - 8x - 8)$
  4. $(-2x^3 + x) - (7x - 3 - 7x^3)$
  5. $(3x^3 + 3x^2 + 9) - (5x^3 - 7x^2 + 6x - 9)$
  6. $(5x^3 + 5x^2 + 5) - (6x^3 - 6x^2 + 8x - 5)$
  7. $(5x^3 + 3x^2 + 5) - (7x^3 - 9x^2 + 8x - 5)$

complete the combined operations:

  1. $(3x^2 - 4x) - (2x^2 + 3x - 7) + (4x + 19)$
  2. $(3x^2 - 4x) + (2x^2 + 3x - 7) - (4x + 19)$

Explanation:

Response
Addition of Polynomials (1-7)

Step1: Combine like terms

Group same-degree terms together.

Step2: Simplify coefficients

Add coefficients of like terms.

Step3: Write in standard form

Order terms from highest to lowest degree.

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  1. Problem: $(7j^3 - 2) + (5j^3 - j - 3)$

Step1: Group like terms

$(7j^3 + 5j^3) + (-j) + (-2 - 3)$

Step2: Simplify

$12j^3 - j - 5$

Step1: Distribute the negative sign

Flip signs of all terms in the subtracted polynomial.

Step2: Combine like terms

Group same-degree terms together.

Step3: Simplify coefficients

Add coefficients of like terms.

Step4: Write in standard form

Order terms from highest to lowest degree.

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  1. Problem: $(-x^2 + x - 4) - (3x^2 - 8x - 2)$

Step1: Distribute negative sign

$-x^2 + x - 4 - 3x^2 + 8x + 2$

Step2: Group like terms

$(-x^2 - 3x^2) + (x + 8x) + (-4 + 2)$

Step3: Simplify

$-4x^2 + 9x - 2$

Step1: Distribute signs

Flip signs for terms subtracted, keep signs for terms added.

Step2: Combine like terms

Group same-degree terms together.

Step3: Simplify coefficients

Add coefficients of like terms.

Step4: Write in standard form

Order terms from highest to lowest degree.

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  1. Problem: $(3x^2 - 4x) - (2x^2 + 3x - 7) + (4x + 19)$

Step1: Distribute signs

$3x^2 - 4x - 2x^2 - 3x + 7 + 4x + 19$

Step2: Group like terms

$(3x^2 - 2x^2) + (-4x - 3x + 4x) + (7 + 19)$

Step3: Simplify

$x^2 - 3x + 26$

Answer:

$12j^3 - j - 5$

  1. Problem: $(8a^5 - 4) + (3a^5 + a - 2)$

Step1: Group like terms

$(8a^5 + 3a^5) + (a) + (-4 - 2)$

Step2: Simplify

$11a^5 + a - 6$