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Lera25 [3.4K]
3 years ago
12

Add the polynomials. 1. (-4x^2+2x+6)+(5x^2-x+10) 2. (5x^2-9x+2)+(-3x^2+2x+4)

Mathematics
1 answer:
skelet666 [1.2K]3 years ago
4 0

Answer:

1. x^2+x+16

2. 2x^2-7x+6

Step-by-step explanation:

Hope this helps!!

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Step-by-step explanation:

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Describe the steps to dividing imaginary numbers and complex numbers with two terms in the denominator?
zlopas [31]

Answer:

Let be a rational complex number of the form z = \frac{a + i\,b}{c + i\,d}, we proceed to show the procedure of resolution by algebraic means:

1) \frac{a + i\,b}{c + i\,d}   Given.

2) \frac{a + i\,b}{c + i\,d} \cdot 1 Modulative property.

3) \left(\frac{a+i\,b}{c + i\,d} \right)\cdot \left(\frac{c-i\,d}{c-i\,d} \right)   Existence of additive inverse/Definition of division.

4) \frac{(a+i\,b)\cdot (c - i\,d)}{(c+i\,d)\cdot (c - i\,d)}   \frac{x}{y}\cdot \frac{w}{z} = \frac{x\cdot w}{y\cdot z}  

5) \frac{a\cdot (c-i\,d) + (i\,b)\cdot (c-i\,d)}{c\cdot (c-i\,d)+(i\,d)\cdot (c-i\,d)}  Distributive and commutative properties.

6) \frac{a\cdot c + a\cdot (-i\,d) + (i\,b)\cdot c +(i\,b) \cdot (-i\,d)}{c^{2}-c\cdot (i\,d)+(i\,d)\cdot c+(i\,d)\cdot (-i\,d)} Distributive property.

7) \frac{a\cdot c +i\,(-a\cdot d) + i\,(b\cdot c) +(-i^{2})\cdot (b\cdot d)}{c^{2}+i\,(c\cdot d)+[-i\,(c\cdot d)] +(-i^{2})\cdot d^{2}} Definition of power/Associative and commutative properties/x\cdot (-y) = -x\cdot y/Definition of subtraction.

8) \frac{(a\cdot c + b\cdot d) +i\cdot (b\cdot c -a\cdot d)}{c^{2}+d^{2}} Definition of imaginary number/x\cdot (-y) = -x\cdot y/Definition of subtraction/Distributive, commutative, modulative and associative properties/Existence of additive inverse/Result.

Step-by-step explanation:

Let be a rational complex number of the form z = \frac{a + i\,b}{c + i\,d}, we proceed to show the procedure of resolution by algebraic means:

1) \frac{a + i\,b}{c + i\,d}   Given.

2) \frac{a + i\,b}{c + i\,d} \cdot 1 Modulative property.

3) \left(\frac{a+i\,b}{c + i\,d} \right)\cdot \left(\frac{c-i\,d}{c-i\,d} \right)   Existence of additive inverse/Definition of division.

4) \frac{(a+i\,b)\cdot (c - i\,d)}{(c+i\,d)\cdot (c - i\,d)}   \frac{x}{y}\cdot \frac{w}{z} = \frac{x\cdot w}{y\cdot z}  

5) \frac{a\cdot (c-i\,d) + (i\,b)\cdot (c-i\,d)}{c\cdot (c-i\,d)+(i\,d)\cdot (c-i\,d)}  Distributive and commutative properties.

6) \frac{a\cdot c + a\cdot (-i\,d) + (i\,b)\cdot c +(i\,b) \cdot (-i\,d)}{c^{2}-c\cdot (i\,d)+(i\,d)\cdot c+(i\,d)\cdot (-i\,d)} Distributive property.

7) \frac{a\cdot c +i\,(-a\cdot d) + i\,(b\cdot c) +(-i^{2})\cdot (b\cdot d)}{c^{2}+i\,(c\cdot d)+[-i\,(c\cdot d)] +(-i^{2})\cdot d^{2}} Definition of power/Associative and commutative properties/x\cdot (-y) = -x\cdot y/Definition of subtraction.

8) \frac{(a\cdot c + b\cdot d) +i\cdot (b\cdot c -a\cdot d)}{c^{2}+d^{2}} Definition of imaginary number/x\cdot (-y) = -x\cdot y/Definition of subtraction/Distributive, commutative, modulative and associative properties/Existence of additive inverse/Result.

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