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stiks02 [169]
3 years ago
9

Given the polynomial 21x 4 + 3y - 6x 2 + 34 What polynomial must be subtracted from it to obtain 29x 2 - 7 ? What polynomial mus

t be added to it to obtain a first degree polynomial?
Mathematics
1 answer:
fredd [130]3 years ago
6 0

Answer:

1. 21x⁴+3y-35x² + 41

2. -21x⁴-3y+6x² + x

Step-by-step explanation:

When adding and subtracting polynomials , you can use the distributive property to add or subtract the coefficients of like terms.

1. The polynomial is 21x⁴ + 3y -6x² + 34

To obtain polynomial 29x² -7 , we must subtract some polynomial from it.

Let that polynomial be k.

So, 21x⁴ + 3y -6x² + 34 - k =  29x² -7

k = 21x⁴ + 3y - 6x² +34 - 29x² +7 = 21x⁴ + 3y - 35x² + 41

2. To obtain a first degree polynomial, let that polynomial be x +34

So, 21x⁴ + 3y - 6x² + 34 + K = x + 34

K = x + 34 - 21x⁴ -3y + 6x² - 34

  = -21x⁴ - 3y + 6x² + x

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<u>Step-by-step explanation:</u>

Let's compare the values of f(x) and g(x) when x = 0, 2, 8, and 4

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f(2) = 2(2) - 3                     g(2)=\dfrac{3}{2}(2)+1

     = 1                                      = 4                     f(2) < g(2)

f(8) = 2(8) - 3                     g(8)=\dfrac{3}{2}(8)+1

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      = 5                                   = 7                       f(4) < g(4)


The only statement provided that is true is f(8) = g(8)




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