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Alexandra [31]
3 years ago
6

By using the remainder theorem, determine the remainder when

Mathematics
2 answers:
lora16 [44]3 years ago
4 0

Answer:

C) -123

Step-by-step explanation:

x + 4 = 0

x = -4

3(-4)³ − (-4)2 − 20(-4) + 5

-123

Greeley [361]3 years ago
3 0

Answer:

-123

Step-by-step explanation:

The remainder theorem says that when a polynomial is divided by a linear factor x - c (note the minus sign), the remainder is the value of the polynomial at x = c.

When a polynomial P(x) is divided by x - c, the remainder is P(c).  In other words, to find the remainder, plug in c for x.

You're dividing by x + 4 which is the same thing as x - (-4) -- the role of c is being played by -4.

3(–4)^3 – (–4)^2 – 20(–4) + 5 = –123

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Answer:

(4, 1)

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

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  • Left to Right  

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Step-by-step explanation:

<u>Step 1: Define Systems</u>

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<u>Step 2: Solve for </u><em><u>x</u></em>

<em>Substitution</em>

  1. Substitute in <em>y</em>:                                                                                                2x - 7 = -x + 5
  2. [Addition Property of Equality] Isolate <em>x</em> terms:                                            3x - 7 = 5
  3. [Addition Property of Equality] Isolate <em>x</em> term:                                              3x = 12
  4. [Division Property of Equality] Isolate <em>x</em>:                                                       x = 4

<u>Step 3: Solve for </u><em><u>y</u></em>

  1. Define original equation:                                                                               y = -x + 5
  2. Substitute in <em>x</em>:                                                                                                y = -4 + 5
  3. Add:                                                                                                                 y = 1
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