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Akimi4 [234]
3 years ago
5

Factor completely 2x3 + 8x2 + 3x + 12.

Mathematics
1 answer:
goblinko [34]3 years ago
8 0

Answer:

(2x^2+3)(x+4).

Step-by-step explanation:

2x^3+8x^2+3x+12

We need to find the factors of given equation;

Solution:

On Solving the above equation we get;

Now First we will take common factor from first 2 terms which is 2x^2 we get;

2x^2(x+4) + 3x+12

Now we will take the common factor from the last 2 terms which is 3 we get;

2x^2(x+4) + 3(x+4)

Here we get 2 terms in which (x+4) is common factor.

(x+4)(2x^2+3)

Hence After factorizing the given equation we get (2x^2+3)(x+4).

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your answer is 12 units

Step-by-step explanation:

I hope it helps

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3 years ago
Tisha and her academic team are working to go to state finals. They must have a certain number of points to advance. They have h
kolbaska11 [484]

Answer:

b=\frac{T-a-c-d}{3}

b = (T - a - c - d) / 3

Step-by-step explanation:

Let T be the total number of points required to advance.

a, c and d are points scored in the local matches, and b is the number of points scored in the district match. If b is worth 3 times as much as the other matches, the total number of points is given by:

T=a+c+d+3b

Isolate b in order to find out how many points they need in the district match:

T=a+c+d+3b\\3b=T-a-c-d\\b=\frac{T-a-c-d}{3}

They need to score (T - a - c - d)/3, in the district match in order to win.

4 0
3 years ago
If a polynomial has one root in the form a+√b , it has a second root in the form of a_√b
gulaghasi [49]
When roots of polynomials occur in radical form, they occur as two conjugates.
That is,
The conjugate of (a + √b) is (a - √b) and vice versa.
To show that the given conjugates come from a polynomial, we should create the polynomial from the given factors.

The first factor is x - (a + √b).
The second factor is x - (a - √b).

The polynomial is
f(x) = [x - (a + √b)]*[x - (a - √b)]
      = x² - x(a - √b) - x(a + √b) + (a + √b)(a - √b)
      = x² - 2ax + x√b - x√b + a² - b
      = x² - 2ax + a² - b

This is a quadratic polynomial, as expected.

If you solve the quadratic equation x² - 2ax + a² - b = 0 with the quadratic formula, it should yield the pair of conjugate radical roots.
x = (1/2) [ 2a +/- √(4a² - 4(a² - b)]
   = a +/- (1/2)*√(4b)
   = a +/- √b
x = a + √b, or x = a - √b, as expected.
3 0
3 years ago
Read 2 more answers
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