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Andrews [41]
2 years ago
13

Can someone help please?

Mathematics
1 answer:
Vlada [557]2 years ago
5 0

Answer:

Step-by-step explanation:

Vertex of the given parabola = (1, -4)

Since, vertex form of a parabola is given by,

y = (x - h)² + k

Here (h, k) is the vertex

Now substitute the coordinates (1, -4) in the equation.

y = (x - 1)²- 4 [Vertex Form]

Further solve this equation,

y = x² - 2x + 1 - 4

y = x² - 2x - 3 [Standard form]

Further write this equation in the factored form,

y = x² - 3x + x - 3

y = x(x - 3) + 1(x - 3)

y = (x + 1)(x - 3) [Factored form]

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Given the polynomial 2x3 18x2 − 18x − 162, what is the value of the constant 'k' in the factored form? 2x3 18x2 − 18x − 162 = 2(
oee [108]

The value of the constant 'k' in the factored form factorization the provided polynomial equation is 3.

<h3>What is polynomial equation?</h3>

Polynomial equations is the expression in which the highest power of the unknown variable is n (n is real number).

The factor of a polynomial is the terms in linear or equation form, which are when multiplied together, give the original polynomial equation as result.

The given polynomial equation in the problem is,

2x^3 +18x^2 - 18x - 162

The factor of the polynomial equation are given as,

2(x+ k)(x - k)(x +9)

First find out the factors to compare and find the value of k.The above equation has the unknown variable x and the highest power of this unknown variable is 3.

Take out the highest common factor 2, which can divide each term of the above equation (2, 18, -18, -162). Thus,

2(x+ k)(x - k)(x +9)=2(x^3 +9x^2 - 9x - 81)

Take out the highest common factor to make the groups as,

2(x+ k)(x - k)(x +9)=2(x^2( x+9) - 9(x + 9))\\2(x+ k)(x - k)(x +9)=2( x+9) (x^2 - 9)\\2(x+ k)(x - k)(x +9)=2( x+9) (x^2 - 3^2)

Use the property of difference of the square for the (x²-3²) term as,

2(x+ k)(x - k)(x +9)=2( x+9) (x+3)(x-3)\\2(x+ k)(x - k)(x +9)=2 (x+3)(x-3)( x+9)

On comparing the two equation, we get the value of k as 3. Thus, the value of the constant 'k' in the factored form factorization the provided polynomial equation is 3.

Learn more about factor of polynomial here;

brainly.com/question/24380382

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or,X°=165°

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Step-by-step explanation:

An interior angle and its exterior angle are supplementary (they add up to 180°).

I would really appreciate it if you would mark me brainliest!

<em>Have a blessed day!</em>

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