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Ganezh [65]
2 years ago
12

Show that 2x +1 is a factor of 2x3 +5x2+4x+1 and factories completely

Mathematics
1 answer:
larisa [96]2 years ago
3 0

\text{According to the factor theorem, if f(b) = 0, then x-b is a factor of f(x).}\\\\\text{Given that,}\\\\f(x) = 2x^3 +5x^2 +4x +1 \\\\f\left(-\dfrac 12 \right) = 2\left( - \dfrac 12 \right)^3 +5 \left( - \dfrac 12 \right)^2 +4 \left( - \dfrac 12 \right) +1 \\\\\\~~~~~~~~~~~~=-2 \cdot \dfrac 18 + 5 \cdot \dfrac 14 -2 +1 \\\\\\~~~~~~~~~~~=\dfrac 54 -\dfrac14 -1\\\\\\~~~~~~~~~~~=\dfrac 44 -1 \\\\\\~~~~~~~~~~~=1-1\\\\\\~~~~~~~~~~~=0\\\\\text{So,}~ 2x +1 ~ \text{is a factor of f(x).}

\text{Now,}\\\\f(x) = 2x^3 +5x^2 +4x +1 \\\\~~~~~~=2x^3+x^2 +2x^2 +2x +2x+1\\\\~~~~~~=x^2(2x+1)  +2x(2x+1) +  (2x+1)\\\\~~~~~~=(2x+1)(x^2 +2x +1)\\\\~~~~~~=(2x+1)(x+1)^2

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Anyone who could do these 8 listed questions I will give a generous amount of points. Please make sure to list all the angles th
k0ka [10]

Answer:

1) 0, 180

2) 90

3) 3pi/2

4) pi/2, -3pi/2

5) 90, 270

6) 0

7) pi

8) -2pi, 0, 2pi

Step-by-step explanation:

1) sinx = 0

x = 0, 180, 360

2) sinx = 1

x = 90

3) sinx = -1

x = 270 or 3pi/2

4) sinx = 1

x = pi/2, pi/2 - 2pi = -3pi/2

5) cosx = 0

x = 90, 360

6) cosx = 1

x = 0, 360

7) cosx = -1

x = pi

8) cosx = 1

-2pi, 0 , 2pi

5 0
3 years ago
Can you add and subtract integers and surds together?
Ne4ueva [31]

Answer:

Both of these examples are wrong. You cannot add/subtract integers and square roots together, however, you could add square roots together if they have the same number under the square root. For example, 2 - 2√6 will stay as 2 - 2√6 because they aren't like terms. 25 + 5√5 + 5√5 + 5 = 30 + 10√5 because 25 + 5 = 30 and 5√5 + 5√5 = 10√5. We can add 5√5 and 5√5 together because they have the same number under the square root. If we were to compute √2 + √3, we would just leave it as is because they don't have the same number under the square root.

4 0
3 years ago
7x^2+66xy+80y^2 Please help me out i need this answer
lilavasa [31]
<span>There are no like terms.

If that's what your question is...

Not sure but hope I helped a bit.</span>
4 0
3 years ago
-4x+2(x-3)&gt;4x-(3+5x)-7
Archy [21]
I hope this helps you

5 0
3 years ago
A landscaper wants to create a 12-foot-long diagonal path through a rectangular garden. The width of the garden is x feet and th
dolphi86 [110]

Answer:

Width of the rectangle =  6.7 ft

length of the rectangle = 10.7 ft

Step-by-step explanation:

ABCD is the rectangle.

AB = length of the rectangle = 4 + x ft

BC = width of the rectangle = x ft

AC = Diagonal of the rectangular field = 12 ft

Since ΔABC is the Right angle triangle. So

AC^{2} = AB^{2} + BC^{2}

12^{2} = (4 + x)^{2} + x^{2}

144 = x^{2} + 16 + x^{2} + 8 x

144 = 2x^{2} + 8x + 16

x^{2} + 4x -72 = 0

By solving above equation we get

x = 6.7 ft

Thus is the width of the rectangle.

And length of the rectangle = 4 + x

⇒ 4 + 6.7

⇒ 10.7 ft

5 0
3 years ago
Read 2 more answers
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