Answer to Question #193684 in Algebra for chris

Question #193684

1.Divide the polynomials using the division method of your choice (long or synthetic)

3x3 - 4x2 - + 2x -1 / x - 3


2.Perform the indicated operation for the following:

a. (3x2 - 8x + 4) - (6x2 + 7x -1)

b. (4x7 - 3x5 - + 2x + 4) + (12x5 - 3x + 2x2 + 3)

c. (3x + 4)(5x2 - 2x + 3)

d. (3 + 4i) + (1-2i)

e. (2-i) (5-6i)

f. (3-7i) ( 1-2i)


3.Solve x2 + 81= 0


4.Solve 3 square root of 7x = 3


1
Expert's answer
2021-05-17T16:53:07-0400

Calculations


1)

  • For this question refer to the figure attached in which both synthetic & long divisions are performed.


  • The final answer is gained the same in both ways as

"\\qquad\\qquad\n\\begin{aligned}\n\\small \\frac{3x^3-4x^2+2x-1}{(x-3)}&=\\small (3x^2 +5x+17)+\\frac{50}{(x-3)}\n\\end{aligned}"


2)

a."\\qquad\\qquad\n\\begin{aligned}\n\\small &=\\small 3x^2-8x+4-(6x^2+7x-1)\\\\\n&=\\small 3x^2-8x+4-6x^2-7x+1\\\\\n&=\\small -3x^2-15x+5\n\\end{aligned}"


b."\\qquad\\qquad\n\\begin{aligned}\n&=\\small 4x^7-3x^5+2x+4+(12x^5-3x+2x^2+3)\\\\\n&=\\small 4x^7-3x^5+2x+4+12x^5-3x+2x^2+3\\\\\n&=\\small 4x^7+9x^5+2x^2-x+7\n\\end{aligned}"


c."\\qquad\\qquad\n\\begin{aligned}\n\\small &=\\small 3x(5x^2-2x+3)+4(5x^2-2x+3)\\\\\n&=\\small 15x^3-6x^2+9x+20x^2-8x+12\\\\\n&=\\small 15x^3+14x^2+x+12\n\\end{aligned}"


d."\\qquad\\qquad\n\\begin{aligned}\n&=\\small 3+4i+(1-2i)\\\\\n&=\\small 3+4i+1-2i\\\\\n&=\\small 4+2i\n\\end{aligned}"


e."\\qquad\\qquad\n\\begin{aligned}\n &=\\small (2-i)(5-6i)\\\\\n&=\\small 10-12i-5i+6i^2\\\\\n&=\\small 10-17i-6\\\\\n&=\\small 4-17i\n\\end{aligned}"


f."\\qquad\\qquad\n\\begin{aligned}\n&=\\small (3-7i)(1-2i)\\\\\n&=\\small 3-6i-7i+14(-1)\\\\\n&=\\small -11-13i\n\\end{aligned}"


3)

"\\qquad\\qquad\n\\begin{aligned}\n\\small x^2-(-81)&=\\small 0\\\\\n\\small x^2-81i^2&=\\small 0\\\\\n\\small (x+9i)(x-9i)&=\\small 0\\\\\n\\small x&=\\small \\pm9i\n\\end{aligned}"


4)

"\\qquad\\qquad\n\\begin{aligned}\n\\small \\sqrt[3]{7x}&=\\small 3\\\\\n\\small (\\sqrt[3]{7x})^3&=\\small 3^3\\\\\n\\small 7x&=\\small 27\\\\\n\\small x&=\\small \\frac{27}{7}\n\\end{aligned}"


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