Divide 6x^6+5x^5+2x^4-9x^3+7x^2-10x+2 by 3x + 1 by using long division. Show all work and steps work. Then explain if 3x + 1 is
a factor of the dividend.
1 answer:
A) First, write all the terms of the polynomial separated; then follow these steps:
1) take the term of the highest degree of the dividend and divide it by the term of the highest degree of the divisor (6x⁶ ÷ 3x = 2x⁵) and write the result on the proper part of the division;
2) multiply the monomial obtained times the divisor (2x⁵ × 3x+1 = 6x⁶ + <span>2x</span>⁵), write the result under the polynomial, under the colum of the same degree;
3) subtract the result obtained from the polynomial (all the terms of the polynomial!!);
4) repeat step 1-3 with the new polynomial obtained.
Complete work is shown on the picture attached.
The result is: 6x⁶ + 5x⁵ + 2x⁴ - 9x³ + 7x² -10x + 2 = (3x + 1) · (2x⁵ + x⁴ + 1/3 x³ - 28/9 x² + 91/27 x - 361/81) + 523/81
B) (3x + 1) is not a factor of the dividend because the division has a remainder not equal to zero.
1) take the term of the highest degree of the dividend and divide it by the term of the highest degree of the divisor (6x⁶ ÷ 3x = 2x⁵) and write the result on the proper part of the division;
2) multiply the monomial obtained times the divisor (2x⁵ × 3x+1 = 6x⁶ + <span>2x</span>⁵), write the result under the polynomial, under the colum of the same degree;
3) subtract the result obtained from the polynomial (all the terms of the polynomial!!);
4) repeat step 1-3 with the new polynomial obtained.
Complete work is shown on the picture attached.
The result is: 6x⁶ + 5x⁵ + 2x⁴ - 9x³ + 7x² -10x + 2 = (3x + 1) · (2x⁵ + x⁴ + 1/3 x³ - 28/9 x² + 91/27 x - 361/81) + 523/81
B) (3x + 1) is not a factor of the dividend because the division has a remainder not equal to zero.
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Answer:
Hello! :) I hope I’m correct!!
Step-by-step explanation:
<em>I think the answer should be the second one.</em>
<u><em>the angle with the square at the corner is obviously a right angle, 90°. opposite angles have the same angle so opposite to it, angle 3 is also 90°. then add the angle 3 and the given angle (23°). 90°+23°=113° then subtract it to 180° (since a straight line is 180°). 180°-113°=67°</em></u>
<em />
<em>The steps:</em>
<em>To solve m< 2,</em>
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<h3><em>Therefore, I think the answer should be 67 (second choice)</em></h3><em>i’m not really sure if this is the answer, but I hope this was helpful!! :)</em>
<em>if you have any questions about these steps, feel free to ask!</em>
<em>by: BrainlyAnime! ^-^</em>
<em>~Thank you!! Have a great day! ~</em>
a ) The domain:
x^4 - 16 x² ≥ 0
x² ( x² - 16 ) ≥ 0
x² - 16 ≥ 0
x² ≥ 16
x ∈ ( - ∞, - 4 ] ∪ [ 4 , + ∞ )
b ) f ` ( x ) =
= ( 2 x³ - 16 x ) / √(x^4 - 16 x²)
c ) The slope of the tangent line at x = 5:
f ` ( 5 ) = ( 2 * 125 - 16 * 5 ) / √ ( 625 - 400 ) = 170 / 15 = 34 / 3
The slope of the line normal to the graph at x = 5:
m = - 3 / 34