Question

1. which of the following is the sum of (7x^{2}-3x + 2) and (8x^{2}+9x - 3)?

(1) (15x^{2}+6x - 1)
(2) (15x^{4}+6x^{2}-1)
(3) (x^{2}-12x + 5)
(4) (x^{4}-12x^{2}+5)

1. when the polynomial (6x - 5x^{2}+x^{3}-7) is added to (10 + 4x^{2}-x - 5x^{3}) the resulting polynomial has which of the following as its leading coefficient?

(1) (-1)
(3) (3)
(2) (16)
(4) (-4)

1. subtracting the polynomial (5x^{2}-6x - 3) from another polynomial is equivalent to adding which of the following?

(1) (-5x^{2}-6x - 3)
(2) (5x^{2}+6x + 3)
(3) (-5x^{2}+6x + 3)
(4) (5x^{2}-6x + 3)

1. which of the following is equivalent to the difference: (left(-3x^{2}+5x - 1

ight)-left(4x^{2}-3x + 7
ight))?
(1) (7x^{2}-8x + 8)
(2) (-7x^{2}+8x - 8)
(3) (x^{2}+2x - 8)
(4) (-x^{2}-2x + 8)

1. when the polynomial (x^{2}-4x + 9) is subtracted from the polynomial (x^{2}+8x - 3) the result is?

(1) (-2x^{2}+12x + 6)
(2) (12x - 12)
(3) (-12x + 12)
(4) (2x^{2}-12x - 6)

Explanation:

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Problem 1

Step1: Group like terms

$(7x^2 + 8x^2) + (-3x + 9x) + (2 - 3)$

Step2: Combine like terms

$15x^2 + 6x - 1$

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Problem 2

Step1: Group like terms by degree

$(x^3 - 5x^3) + (-5x^2 + 4x^2) + (6x - x) + (-7 + 10)$

Step2: Combine like terms

$-4x^3 - x^2 + 5x + 3$

Step3: Identify leading coefficient

The term with the highest degree is $-4x^3$, so its coefficient is $-4$.

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Problem 3

Step1: Apply subtraction rule

Subtracting a polynomial is adding its additive inverse: $-(5x^2 - 6x - 3)$

Step2: Distribute the negative sign

$-5x^2 + 6x + 3$

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Problem 4

Step1: Distribute the negative sign

$-3x^2 + 5x - 1 - 4x^2 + 3x - 7$

Step2: Group like terms

$(-3x^2 - 4x^2) + (5x + 3x) + (-1 - 7)$

Step3: Combine like terms

$-7x^2 + 8x - 8$

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Problem 5

Step1: Write the subtraction expression

$(x^2 + 8x - 3) - (x^2 - 4x + 9)$

Step2: Distribute the negative sign

$x^2 + 8x - 3 - x^2 + 4x - 9$

Step3: Group like terms

$(x^2 - x^2) + (8x + 4x) + (-3 - 9)$

Step4: Combine like terms

$12x - 12$

Answer:

1. (1) $15x^2 + 6x - 1$
2. (4) $-4$
3. (3) $-5x^2 + 6x + 3$
4. (2) $-7x^2 + 8x - 8$
5. (2) $12x - 12$