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lisabon 2012 [21]
2 years ago
9

Add or subtract the polynomials (8x3+3x-2)+(9x2-7+3x-2x3)

Mathematics
2 answers:
crimeas [40]2 years ago
4 0

Answer:

10x^3+9x^2-9

Step-by-step explanation:

8x^3+2x-2+9x^2-7+2x-2x^3 - Combine like terms

10x^3+9x^2-9

LekaFEV [45]2 years ago
3 0

Answer:

\boxed{\boxed{\sf 6x^3+9x^2+6x-9}}

Step-by-step explanation:

\sf \left(8x^3+3x-2\right)+\left(9x^2-7+3x-2x^3\right)

\sf 8x^3+3x-2+9x^2-7+3x-2x^3

Note: If there is a negative sign in front of  parentheses, each term within the expression changes sign.

\Longrightarrow \sf 8x^3+3x-2+9x^2-7+3x-2x^3

Now, we need to organize expression into groups like terms:

\Longrightarrow \sf (8x^3, -2x^3)\: (3x, 3x)\:(-2,-7)

\longmapsto\sf 8x^3-2x^3=6x^3

\longmapsto\sf 3x+3x=6x

\longmapsto\sf -2-7=-9

\boxed{\sf 6x^3+9x^2+6x-9}

_____________________________

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Consider the cubic function f(x) = x^3 + ax^2 + bx + 4 where (a) and (b) are constants. When f(x) is divided by x-3, the remaind
Debora [2.8K]

Answer:

see explanation

Step-by-step explanation:

Using the Remainder theorem

If f(x) is divided by (x - h) then f(h) = remainder, thus

f(3) = 3³ + a(3)² + b(3) + 4 = 10, that is

27 + 9a + 3b + 4 = 10

9a + 3b + 31 = 10 ( subtract 31 from both sides )

9a + 3b = - 21 → (1)

f(- 1) = (- 1)³ + a(- 1)² + b(- 1) + 4 = 6, that is

- 1 + a - b + 4 = 6

a - b + 3 = 6 ( subtract 3 from both sides )

a - b = 3 → (2)

Rearrange (2) expressing a in terms of b

a = 3 + b → (3)

Substitute a = 3 + b into (1)

9(3 + b) + 3b = - 21 ← distribute and simplify left side

27 + 9b + 3b = - 21

12b + 27 = - 21 ( subtract 27 from both sides )

12b = - 48 ( divide both sides by 12 )

b = - 4

Substitute b = - 4 into (3)

a = 3 - 4 = - 1

Hence a = - 1 and b = - 4

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2 years ago
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dimaraw [331]
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3 years ago
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45% of 20
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Step-by-step explanation:

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