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2 years ago

Use the grouping method to factor the polynomial below completely. x3 - 3x2 + 5x - 15

Mathematics

2 answers:

FromTheMoon [43]2 years ago

8 0

X^3 - 3x^2 + 5x - 15
x^2(x-3) +5(x-3)
(x^2 + 5)(x - 3) <==Answer

11Alexandr11 [23.1K]2 years ago

4 0

Answer:

$(x^2+5)*(x-3)$

Step-by-step explanation:

In grouping method factoring, you must have to split the middle term in a way that the product of two terms in middle must be equal to the product of two terms at the edges of equation. Remember you have to consider the resultant signs as well as the magnitude of both products.

Now in the case given above,

$x^3-3x^2+5x-15$

the result is $-15x^3$

Note that the magnitude is 15x^3 and sign is '-' for both products.

Now taking out the common terms, equation becomes;

$x^2(x-3)+5(x-3)$

Taking out (x-3) as common, now the factorized version we have is:

$(x-3)(x^2+5)$

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Allushta [10]

Answer and Step-by-step explanation:

First, we need to find out the circumference of the circle.

We know that the circle has a radius of 1, and that we are finding the circumference. We'll use the circumference equation of a circle.

2 $\pi$ r

Plug in 1 for r.

$2\pi (1)$ = $2\pi$ = circumference of circle

Now, multiply the answer (the circumference) by 4 to get the perimeter of the square.

$2\pi$ x 4 = $8\pi$ = perimeter of square

Now, divide the perimeter by 4 to get what the side of the square is.

$8\pi$ ÷ 4 = $2\pi$

Now, multiply $2\pi$ by $2\pi$ (side times side) to get the area.

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2 years ago

Henry has a bag containing 39 letter tiles, some consonants, and some vowels. He selects a tile without looking and then replace

adoni [48]

Answer:

21 consonant tiles

Step-by-step explanation:

Henry has a bag containing 39 letter tiles, some consonants, and some vowels.

He selects a tile without looking and then replaces it. If he pulls 7 consonant tiles and 6 vowel tiles, which is the most likely number of consonant tiles in Henry's bag?

Step 1

We add up the number of tiles that he pulls out of the bag

= 7 consonant tiles + 6 vowel tiles

= 13 tiles

Step 2

We divide the total number of tiles in the bag by the total number of tiles that was pulled out of the bag

= 39 tiles ÷ 13 tiles

= 3

Step 3

The most likely number of consonant tiles in Henry's bag is calculated as:

3 × The number of consonant tiles that was pulled out of the bag.

Hence:

3 × 7 consonant tiles

= 21 consonant tiles.

Therefore, the most likely number of consonant tiles in Henry's bag is 21 consonant tiles.

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2 years ago

In how many ways can you seat 5 women and 5 men in a row if women must seat next to each other,men must seat next to each other,

makvit [3.9K]

Answer: 288ways

Step-by-step explanation:

There are 5men and 5women to be arranged, since the men must seat together, they will be arranged in 5! ways. For the women, since they must also seat together but with siamese twins between them, they can be arranged in 4! ways instead of 5! ways and this is due to presence of the twins among them.

Note that Siamese twins cannot be separated as such both are taken as one making it 4!.

Since the women and men are always sitting together, they can be arranged in 2! ways i.e 2 sexes

The final seating arrangement can be done in 2!×(5!+4!) ways

= 2× (120+24)

= 2×144

= 288ways.

Note that the arrangement of the men and women are added because they can only be arranged differently to ensure different sex are not sitting together.

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