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3 years ago

Which of the following is the correct factorization of the polynomial below? x3 + 14x2 + 49x

Mathematics

2 answers:

Naddika [18.5K]3 years ago

7 0

For this case we must factor the following polynomial:

$x ^ 3 + 14x ^ 2 + 49x\\$

We can take common factor x:

$x(x ^ 2+ 14x + 49)$

To factor the expression within the parenthesis, we must find two numbers that when multiplied give 49 and when added together, 14 are obtained. These are: 7 and 7.

$7*7=49,7+7=14$

Thus, the expression is factored as:

$x(x + 7)(x +7)$

Answer:

$x (x + 7) ^ 2$

loris [4]3 years ago

4 0

The answer is x(x+7)^2

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zaharov [31]

Hope this helps. Look at attachment

6 0

3 years ago

Read 2 more answers

Suppose M is the midpoint

AysviL [449]

x = 9

Since M is the midpoint of XY:

XM = MY

XM = 2x + 11

MY = 5x - 16

2x + 11 = 5x - 16

5x - 2x = 11 + 16

3x = 27

x = 27/3

x = 8

Learn more here: brainly.com/question/18315903

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2 years ago

If x^2+1/x^2=3 find the value of x^2/(x^2+1)^2<br> Express answer as a common fraction.<br> Thanks!!

timama [110]

$x^2+\dfrac1{x^2}=3\implies x^4+1=3x^2\implies x^4-3x^2+1=0$

By the quadratic formula,

$x^2=\dfrac{3\pm\sqrt5}2\implies x^2+1=\dfrac{5\pm\sqrt5}2$

Then

$(x^2+1)^2=\dfrac{25\pm10\sqrt5+5}4=\dfrac{15\pm5\sqrt5}2$

$\implies\dfrac{x^2}{(x^2+1)^2}=\dfrac{\frac{3\pm\sqrt5}2}{\frac{15\pm5\sqrt5}2}=\dfrac{3\pm\sqrt5}{15\pm5\sqrt5}$

Multiply numerator and denominator by the denominator's conjugate:

$\dfrac{3\pm\sqrt5}{15\pm5\sqrt5}\cdot\dfrac{15\mp5\sqrt5}{15\mp5\sqrt5}=\dfrac{45\pm15\sqrt5\mp15\sqrt5-25}{15^2-(5\sqrt5)^2}=\dfrac{20}{100}=\dfrac15$