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2 years ago

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The polynomial 24x3 − 54x2 + 44x − 99 is factored by grouping. 24x3 − 54x2 + 44x − 99 24x3 + 44x − 54x2 − 99 4x() − 9()

What is the common factor that is missing from both sets of parentheses?

1 answer:

Alenkasestr [34]2 years ago

3 0

Answer: $6x^2+11$

Step-by-step explanation:

Given the polynomial of degree 3:

$24x^3 - 54x^2 + 44x -99$

You can observe make two groups or two terms each:

$(24x^3 + 44x) - (54x^2 + 99)$

The Greatest Common Factor (GCF), is the highest number that divides into two or more numbers without leaving remainder.

You can observe that the GCF of both set are factored out ( $4x$ and $9$ ), then, you can find the common factor that is missing from both sets of parentheses with this procedure:

$(\frac{24x^3}{4x}+\frac{44x}{4x})-(\frac{54x^2}{9}+\frac{99}{9})=(6x^2+11)-(6x^2+11)$

You can observe that the common factor that is missing from both sets of parentheses is:

$6x^2+11$

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What is the binomial expansion of (x + 2)4? x4 + 4x3 + 6x2 + 4x + 1 8x3 + 24x2 + 32x x4 + 8x3 + 24x2 + 32x + 16 2x4 + 8x3 + 12x2

Margaret [11]

<u>Answer-</u>

$\boxed{\boxed{(x+2)^4=x^4+8x^3+24x^2+32x+16}}$

<u>Solution-</u>

Given expression is $(x+2)^4$

Applying Binomial Theorem

$\left(a+b\right)^n=\sum _{i=0}^n\binom{n}{i}a^{\left(n-i\right)}b^i$

Here,

a = x, b = 2 and n = 4

So,

$\left(x+2\right)^4=\sum _{i=0}^4\binom{4}{i}x^{\left(4-i\right)}\cdot \:2^i$

Expanding the summation

$=\dfrac{4!}{0!\left(4-0\right)!}x^4\cdot \:2^0+\dfrac{4!}{1!\left(4-1\right)!}x^3\cdot \:2^1+\dfrac{4!}{2!\left(4-2\right)!}x^2\cdot \:2^2+\dfrac{4!}{3!\left(4-3\right)!}x^1\cdot \:2^3+\dfrac{4!}{4!\left(4-4\right)!}x^0\cdot \:2^4$

$=\dfrac{4!}{0!\left(4\right)!}x^4\cdot \:2^0+\dfrac{4!}{1!\left(3\right)!}x^3\cdot \:2^1+\dfrac{4!}{2!\left(2\right)!}x^2\cdot \:2^2+\dfrac{4!}{3!\left(1\right)!}x^1\cdot \:2^3+\dfrac{4!}{4!\left(0\right)!}x^0\cdot \:2^4$

$=1\cdot x^4\cdot \:1+4\cdot x^3\cdot \:2+6x^2\cdot \:4+4\cdot x\cdot \:8+1\cdot 1\cdot \:16$

$=x^4+8x^3+24x^2+32x+16$

4 0

2 years ago

Read 2 more answers

You launch a water balloon. The function h=-0.08t^2+1.6t+2 models the height h (in feet) of the water balloon after t seconds. W

stellarik [79]

Answer:

The initial height of the balloon is 2 feet.

Step-by-step explanation:

The height of the balloon in feet after t seconds is given by the following equation:

$h(t) = -0.08t^{2} + 1.6t + 2$

What is the initial height of the balloon?

This is h when t = 0, that is, h(0). So

$h(0) = -0.08*0^{2} + 1.6*0 + 2 = 2$

The initial height of the balloon is 2 feet.

4 0

2 years ago

Mai spends 7 and 3/5 hours in school each day. Her lunch period is 30 minutes long, and she spends a total of 42 minutes switchi

Sonja [21]

First, we solve for the number of minutes in 7 and 3/5 hours by multiplying the number by 60 giving us,
(7 + 3/5) x (60) = 456 minutes
Spending 30 minutes for lunch will leave her with 426 minutes. Then, spending 42 minutes for switching of classes will finally give her 414 minutes.

We then divide this value by 6 (for her 6 classes) giving us 69 minutes. Thus, each class is 69 minutes long.

8 0

2 years ago

Isabella filled her pool with water at a constant rate.

Anon25 [30]

Answer:

The size of Isabella's pool is 220 liters.

Step-by-step explanation:

Let the size of Isabella's pool be $x$ liters, $R$ be the rate of fill, $t$ be the time of fill and $V$ be the volume of water filled in the pool.

As the rate of fill is constant,

Therefore, volume of water filled in the pool can be given as,

$V= Rt$

Volume of water left is given as $x-V=x-Rt$

From the table,

Volume of water left after $t=2$ minutes is 184 liters.

So, $x-R(2)=184\\x-2R=184$ -------- 1

Volume of water left after $t=12$ minutes is 4 liters.

So, $x-R(12)=4\\x-12R=4$ ------------2

Multiply equation 1 by 6 and equation 2 by -1, we get

$6x-12R=1104\\-x+12R=-4$

Now, we add the above equations, we get

$(6x-x)+(12R-12R)=1104-4\\5x=1100\\x=\frac{1100}{5}=220$

Therefore, the size of Isabella's pool is 220 liters.

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2 years ago

Write and solve the inequality three times a number plus five is less than three-fourths of the number. Please help!

Schach [20]

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5 0

2 years ago