Please help!!!!!!!!!!!!!

Mathematics

1 answer:

Setler79 [48]3 years ago

4 0

<h3>GCF for given expression is:</h3>

$GCF = 5(x+7)^2$

Solution:

Given that,

We have to find the greatest common factor

$5(x+7)^4\\\\35(x+7)^2\\\\15(x+7)^3$

First find the GCF of numbers 5, 35 and 15

Find the GCF of 5, 35 and 15

The factors of 5 are: 1, 5

The factors of 15 are: 1, 3, 5, 15

The factors of 35 are: 1, 5, 7, 35

Then the greatest common factor is 5

Now find the GCF of variables

$(x+7)^4\\\\(x+7)^2\\\\(x+7)^3$

Here, the common factor is $(x+7)^2$

Thus, GCF for given expression is:

$GCF = 5(x+7)^2$

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Using division, what is the quotient (2x3 − 2x − 12) ÷ (x − 2)?

topjm [15]

Answer:

2x^2 + 4x + 6

Step-by-step explanation:

First, we need to write the polynomial in descending order, since we have a missing term (x^2) we need to fill with zero:

2X^3+0x^2-2x-12

Then, grab the term with the highest power from the polynomial and divide it by the term with highest power from the polynomial located at the other side of the division symbol (this polynomial would be x-2)

The result (2x^3 / x) = 2x^2

This term will be part of the solution, and will be use to start the process of division.

This process start with the previous obtained term (2x^2), which will be multiplied by the polynomial from the other side of the division symbol (x-2).

The result another is another polynomial

This new polynomial will be multiply by negative 1

The new polynomial is then added to the poly (2X^3+0x^2-2x-12)

The result will constitute a new poly, that will be use as the remaining of the division.

Since, our remaining differs from zero, and we still have member to simplify, we repeat the step 1 using the remaining as the new poly that needs to be divided by (x-2).

The attached picture explains the whole procedure.