3 years ago

Using the grouping method to factor the polynomial below completely. x^3+2x^2+4x+8

Mathematics

1 answer:

Ivenika [448]3 years ago

3 0

Answer: $(x+2)(x^2+4)$

Step-by-step explanation:

$x^3+2x^2+4x+8$

$(x^3+2x^2)+(4x+8)\\x^2(x+2)+4(x+2)$

$(x+2)(x^2+4)$

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What is the radius of a circle given by the equation x2 + y2 – 2x + 8y – 47= 0? radius = units

il63 [147K]

ANSWER

The radius is 8

EXPLANATION

We were given,

${x}^{2} + {y}^{2} - 2x + 8y - 47 = 0$

We rewrite the above equation to obtain,

${x}^{2} - 2x \: \: \: \: + {y}^{2} + 8y \: \: \: \: = 47$

We now add half the square of the coefficient of
$x \: and \: y$
to both sides of the equation to get,

${x}^{2} - 2x + ( - 1) ^{2} + {y}^{2} + 8y + {(4)}^{2} = 47 + ( - 1) ^{2} + {4}^{2}$

We now got two perfect squares on the left hand side of the equation,

$(x - 1)^{2} + {(y + 4)}^{2} = 47 + 1 + 16$

$(x - 1)^{2} + {(y + 4)}^{2} =64$

$(x - 1)^{2} + {(y + 4)}^{2} = {8}^{2}$

By comparing to the general formula of the circle,

${(x - a)}^{2} + {(y - b)}^{2} = {r}^{2}$

We can see that the radius is 8.

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