MATHEMATICS HIGH SCHOOL

Consider the polynomial P(x)=x⁴+3x³-28x²-36x+144. Write the equation of P in factored form.

Answers

Answer 1

Answer:

Answer:

P(x)=(x-2)(x-4)(x+3)(x+6)

Step-by-step explanation:

Given: P(x)=x⁴+3x³-28x²-36x+144

It is a polynomial with degree 4.

It should maximum four factor.

Hit and trial error method.

Put x = 2 into P(x)

P(2)=2⁴+3×2³-28×2²-36×2+144

P(2) = 0

So, x-2 would be factor of P(x)

Now divide x⁴+3x³-28x²-36x+144 by x-2 to get another factors

$(x^4+3x^3-28x^2-36x+144)/ (x-2) = x^3+5x^2-18x-72$

$P(x)=(x-2)(x^3+5x^2-18x-72)$

Put x = 4

$P(4) = 0$

now divide $x^3+5x^2-18x-72$ by x-4

$(x^3+5x^2-18x-72)/ (x-4) = x^2+9x+18$

$P(x)=(x-2)(x-4)(x^2+9x+18)$

Now factor $x^2+9x+18$

$\Rightarrow x^2+9x+18$

$\Rightarrow (x+6)(x+3)$

Complete factor of P(x)

P(x)=(x-2)(x-4)(x+3)(x+6)

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If (x + 2 ) is a factor of x3 − 6x2 + kx + 10, k =

Answers

If a binomial x-a is a factor of a polynomial p(x), then p(a)=0.

x+2 is a factor of p(x)=x³-6x²+kx+10, so p(-2)=0.

$p(-2)=0 \n(-2)^3 - 6 * (-2)^2 + k * (-2) + 10=0 \n-8-6 * 4-2k+10=0 \n-8-24-2k+10=0 \n-2k-22=0 \n-2k=22 \nk=(22)/(-2) \n\boxed{k=-11}$

Answer:

-11

Step-by-step explanation:

What is the value of x?

Answers

Answer:

Step-by-step explanation:

X+y=X so the answers x

The value of x using the two rectangles is 8.

We have,

A rectangle is a 2-D shape with length and width.

The length and width are different.

If the length and width are not different then it is a square.

The area of a rectangle is given as:

Area = Length x width

Rectangle A:

Area

= length x width

= 6 x 4

=24 cm²

Rectangle B:

Area

= length x width

= 3x cm²

Now,

The area of both triangles is the same.

This means,

Area of first rectangle = Area of the second rectangle

24 = 3x

x = 24/3

x = 8

Thus,

The value of x using the two rectangles is 8.

Learn more about rectangles here:

brainly.com/question/15019502

#SPJ4

Write a compound inequality that represents the situation. On a road in the city of Rochester, the maximum speed is 50 miles per hour, and the minimum speed is 20 miles per hour.A. 20 > x > 50

B. 20 ≤ x ≤ 50

C. 20 ≥ x ≥ 50

D. 20 < x < 50

Answers

Answer:

B. 20 ≤ x ≤ 50

Step-by-step explanation:

If the maximum speed is 50 miles per hour, that means it cannot go above 50 miles per hour, it has to be 50 miles per hour or less, which is expressed like this

$x\leq 50$

Now, if the minimum speed is 20 miles per hour, that means the speed can only be 20 miles per hour or more, that's represented as

$x\geq 20$

If we unit both expression, we would have the following compound inequality

$20\leq x\leq 50$

This means that the speed has to be 20 miles per hour or more, but 50 miles per hour or less.

Therefore, the right answer is

The correct answer is b. Hope that helps!

Select the correct difference. -3z 7 - (-5z 7) 2z7 8z14 -2z7 2z

Answers

Answer:

$2z^(7))$ .

Step-by-step explanation:

Given : $-3 z^(7) - ( -5 z^(7))$

To find : Select the correct difference.

Solution : we have given

$-3 z^(7) - ( -5 z^(7))$ .

Open the parenthesis

$-3 z^(7) + 5 z^(7))$ .

By the rule ( + - = -) .

$2z^(7))$ .

Therefore, $2z^(7))$ .

-3z^7 - (-5z^7) = -3z^7 + 5z^7 = 2z^7

What is the elapsed time between 10:50 a.m. and 3:45 p.m.?4 hours and 5 minutes
4 hours and 55 minutes
3 hours and 55 minutes
4 hours

Answers

4 hours and 55 minutes

Please i need help with this 3 questions (#5,6,7)

Thank you

Answers

5. 15' x 15' x 9' = 2025 Cubic Feet. so its 15

6. 1.5 * 2.5 = 3.75; 3.75 * 3 = 11.25 so it 3.75*3

7.Really the only thing that can help you is plunging in the formula

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