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4 years ago

Factor x^3 +2x^2 -9x -18, given that -2 is a zero

Mathematics

2 answers:

natulia [17]4 years ago

4 0

Answer:

(x-2)(x-3)(x+3)are the factors of the given expression.

Step-by-step explanation:

We have given the expression:

x³ +2x² -9x -18

And we have given that -2 is the zero of the given expression.

We have to find the other factors of this expression.

Taking common from the given expression we get,

x³ +2x² -9x -18 = x²(x-2)-9(x-2)

Taking (x-2) common from x²(x-2)-9(x-2) we get,

x²(x-2)-9(x-2) = (x-2)(x²-9)

As we know that,

(x²-9) = (x-3)(x+3)

(x-2)(x²-9) = (x-2)(x-3)(x+3)

(x-2)(x-3)(x+3)are the factors of the given expression.

Mnenie [13.5K]4 years ago

3 0

Answer:

Step-by-step explanation:

Take out the common factor from the first and second terms and again from the 3rd and fourth terms.

x^2(x + 2) - 9(x + 2)

Take out x + 2 from around the minus sign.

(x + 2)(x^2 - 9)

Factor x^2 - 9 which will come out to the difference of squares.

(x + 2)(x + 3)(x - 3)

This is how it factors.

You could also use synthetic division if you know how it works.

-2 || 1 2 -9 -18

-2 0 18

====================

1 0 -9 0

This gives you (x + 2)(x^3 - 9) just as before.

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Find the rational roots of the following: \)3x^3-5x^2+15x-25=0\)

Ghella [55]

Answer:

possible: ±{1/3, 1, 5/3, 5, 25/3, 25}
actual: 5/3

Step-by-step explanation:

The rational root theorem tells you any rational roots of the expression will be found from the constant and the leading coefficient:

rational roots = ±{divisor of 25} / {divisor of 3}

<h3>Possible roots</h3>

The list of divisors in each case is pretty short, so this is ...

rational roots = ±{1, 5, 25) / {1, 3} = ±{1/3, 1, 5/3, 5, 25/3, 25}

<h3>Actual roots</h3>

We find the only actual rational root is x = 5/3 when we graph the function.

(Factoring out that root, we find the remaining roots are ±i√5, irrational imaginary values.)

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2 years ago

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Step-by-step explanation:

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3 years ago

Find the sequence of differences for the given sequence. Next, find a closed form solution for the following sequence. (Be sure

padilas [110]

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$\{a_n\}_{n\ge1}=\{1,5,11,19,29,41,\ldots\}$

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$2n+2=a_{n+1}-a_n\implies a_{n+1}=a_n+2n+2$

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and since $a_1=1$ we can write this as

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$a_n=-1+2+2(2+3+4+\cdots+n)$

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3 years ago

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Rina8888 [55]

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3 years ago

Read 2 more answers

Solve. 5(y - 10) = -5 Answer: Submit Answer att

enyata [817]

Solving an equation<h2>Step 1</h2>

We divide both sides by 5 so we can eliminate the parenthesis:

$\begin{gathered} 5(y-10)=-5 \\ \frac{5(y-10)}{5}=-\frac{5}{5} \\ y-10=-1 \end{gathered}$ <h2>Step 2</h2>

We rearrange the terms so the terms with the unkown variable y are on the left side and the other ones on the right side:

y - 10 = -1

↓ <em>adding 10 both sides</em>

y - 10 + 10 = -1 + 10

y + 0 = 9

y = 9

<h2>Answer: y = 9</h2>

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1 year ago