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3 years ago

Steps in how to solve

Mathematics

1 answer:

Alexxandr [17]3 years ago

6 0

First, you replace x with -3.
It will look like -3/3.
Then you divide and get -1.

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Factorize x^3-10x^2-53x-42

pochemuha

Answer:

(x+1)(x-14)(x+3)

Step-by-step explanation:

The first step in factorising polynomials is to find the smallest factor first. The way to do this is with trial and error. Lets see if x+1 is a factor.

According to the factor theorem, (x-a) is a factor of P(x) if and only when P(a) = 0

In this case we will use f(x) = ((x)^3)-((10x)^2)-53x-42

f(-1) = 0

Therefore (x+1) is a factor of the polynomial.

Now we divide the polynomial with (x+1) via long division to get (x^2)-11x-42.

We now factorise (x^2)-11x-42 using whatever method you would like. I'm going to use the AC method, where we find a number that multiplies to AC and adds to B, In this case AC = -42, and B = -11.

Therefore (x^2)-11x-42 factosied is (x-14)(x+3)

Now merge (x+1) with (x-14)(x+3)

The final answer is (x+1)(x-14)(x+3)

If this has helped, please consider making this the Brainliest answer!

7 0

3 years ago

Read 2 more answers

What is the solution to the following system of equations?

Fed [463]

Do it on a scientific calculator

3 0

3 years ago

Read 2 more answers

Solve v pls 3|v - 3|=9

Ganezh [65]

The answer is 0

Let's solve your equation step-by-step.

3(|v−3|)=9

Step 1: Divide both sides by 3.

3(|v−3|)3=93

|v−3|=3

Step 2: Solve Absolute Value.

|v−3|=3

We know either v−3=3orv−3=−3

v−3=3(Possibility 1)

v−3+3=3+3(Add 3 to both sides)

v=6

v−3=−3(Possibility 2)

v−3+3=−3+3(Add 3 to both sides)

v=0

Answer:

v=6 or v=0

7 0

3 years ago

Which equation is equivalent to

STALIN [3.7K]

Answer:

Step-by-step explanation:

y + 2x + 10 = 4x + 5

y = 4x - 2x + 5 - 10

y = 2x - 5

Answer- C

8 0

3 years ago

Jeremy wants to construct an open box from an 18-inch square piece of aluminum. He plans to cut equal squares, with sides of x i

serious [3.7K]

The volume of the box V = 4x³ - 72x² + 324x

Since the dimensions of the square piece of paper are 18 inches each, and we cut out a length x from each side to give a total length of 2x cut from each side. So, each dimension is L = 18 - 2x.

Since the height of the open box is x and its base is a square, the volume of the open box ix V = L²x

= (18 - 2x)²x

= (324 - 72x + 4x²)x

= 324x - 72x² + 4x³

The volume of the box V = 4x³ - 72x² + 324x

The minimum value of length of the sides of the squares cut from each corner is x = 3 inches.

the length of the box, L = 12 inches,
the width of the box = 12 inches
and the height of the box, x = 3 inches.

Since the volume of the box is 432 cubic inches,

V = 324x - 72x² + 4x³

324x - 72x² + 4x³ = 432

4x³ - 72x² + 324x - 432 = 0

x³ - 18x² + 81x - 108 = 0

A factor of the expression is x - 3

So, x³ - 18x² + 81x - 108 ÷ x - 3 = x² - 15x + 36

So, x³ - 18x² + 81x - 108 = (x² - 15x + 36)(x - 3) = 0

Factorizing the expression x² - 15x + 36 = 0

x² - 3x - 12x + 36 = 0

x(x - 3) - 12(x - 3) = 0

(x - 3)(x - 12) = 0

So, x³ - 18x² + 81x - 108 = (x - 3)(x - 3)(x - 12) = 0

So, (x - 3)²(x - 12) = 0

(x - 3)² = 0 and (x - 12) = 0

x - 3 = √0 and x - 12 = 0

x - 3 = 0 and x - 12 = 0

x = 3 twice and x = 12

Since x = 3 is the minimum value, the minimum value of x = 3.

Since the length of the box, L = 18 - 2x

= 18 - 2(3)

= 18 - 6

= 12 inches

The width of the box = L = 12 inches

The height of the box = x = 3 inches.

So,

The minimum value of length of the sides of the squares cut from each corner is x = 3 inches.

the length of the box, L = 12 inches,
the width of the box = 12 inches
and the height of the box, x = 3 inches.

Learn more about volume of a box here:

brainly.com/question/13309609

6 0

2 years ago