All categories

3 years ago

Find the GCF of the first two terms and the GCF of the last two terms of the polynomial. 5h^3+20h^2+4h+16

1 answer:

6 0

The GCF of the first two terms: 5h²
The GCF of the last two terms: 4

5h³ and 20h²

Both of these terms are divisible by 5. (constant)
Both of these terms also have at least 2 h's. (variable)

4h and 16

Both of these terms are divisible by 4.
Only one term has a variable, so that has to be left out.

You might be interested in

A kilometer is 3,280.8 feet. How many feet long is a meter?

love history [14]

There is 3.28084 feet in a meter

7 0

3 years ago

Consider the expansion of (5p + 2q)^6. Determine the coefficients for the terms with the powers of p and q shown.

Step2247 [10]

Answer:

Remember, the expansion of $(x+y)^n$ is $(x+y)^n=\sum_{k=0}^n \binom{n}{k}x^{n-k}y^k$ , where $\binom{n}{k}=\frac{n!}{(n-k)!k!}$ .

Then,

$(5p+2q)^6=\sum_{k=0}^6\binom{6}{k}(5p)^{6-k}(2q)^k=\sum_{k=0}^6\binom{6}{k}5^{6-k}2^k p^{6-k}q^k$

Then, the coefficient of the term $p^{6-k}q^k$ is $\binom{6}{k}5^{6-k}2^k$

a) since 6-k=2, then k=4. So the coefficient of $p^2q^4$ is

$\binom{6}{4}5^{6-4}2^4=15*5^2*2^4=15*25*16=6000$

b) since 6-k=5, then k=1. So, the coefficient of $p^5q$ is

$\binom{6}{1}5^{6-1}2^1=6*5^5*2=37500$

c) since 6-k=3, then k=3. So, the coefficient of $p^3q^3$ is

$\binom{6}{3}5^{6-3}2^3=20*5^3*8=20000$

6 0

3 years ago

Mr. rodriquez was on the telephone for 182 minutes. She called 7 friends to invite them to a luncheon. If she spoke to each frie

vitfil [10]

He spoke to each friends for 26 minutes

How I found out : how I found out is that all you have to do it get the total amount which in this question it is going to be 182. And you would need to dive 182 by 7 to find the unit rate (182/7) which is going to equal 26.which means he called each friend for 26 minutes

5 0

3 years ago

Read 2 more answers

A motorboat maintained a constant speed of 28 miles per hour relative to the water in going 45 miles upstream and then returning

Sveta_85 [38]

The speed of the current is 7 miles per
hour.
Step-by-step explanation:
Let × represent speed of the current.
We have been given that a motorboat
maintained a constant speed of 11 miles per
hour relative to the water in going 18 miles
upstream and then returning.
The speed of motorboat while going
upstream would be 11
The speed of motorboat while going
downstream would be 11 + 2
Time
Distance
Speed

3 0

2 years ago

Write an expression equivalent to 8(3/4x-1/4)-6(12-x) using the fewest possible terms.

Harrizon [31]

Use distributive property: (24/4x-8/4)-(72-6x)
Simplify: 6x-2-72+6x
Simplify: 12x-74

12x-74

3 0

3 years ago