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lozanna [386]
2 years ago
5

Factor the polynomial, x2 + 5x + 6

Mathematics
1 answer:
patriot [66]2 years ago
4 0

Answer:

Choice b.

x^{2} + 5\, x + 6 = (x + 3)\, (x + 2).

Step-by-step explanation:

The highest power of the variable x in this polynomial is 2. In other words, this polynomial is quadratic.

It is thus possible to apply the quadratic formula to find the "roots" of this polynomial. (A root of a polynomial is a value of the variable that would set the polynomial to 0.)

After finding these roots, it would be possible to factorize this polynomial using the Factor Theorem.

Apply the quadratic formula to find the two roots that would set this quadratic polynomial to 0. The discriminant of this polynomial is (5^{2} - 4 \times 1 \times 6) = 1.

\begin{aligned}x_{1} &= \frac{-5 + \sqrt{1}}{2\times 1} \\ &= \frac{-5 + 1}{2} \\ &= -2\end{aligned}.

Similarly:

\begin{aligned}x_{2} &= \frac{-5 - \sqrt{1}}{2\times 1} \\ &= \frac{-5 - 1}{2} \\ &= -3\end{aligned}.

By the Factor Theorem, if x = x_{0} is a root of a polynomial, then (x - x_0) would be a factor of that polynomial. Note the minus sign between x and x_{0}.

  • The root x = -2 corresponds to the factor (x - (-2)), which simplifies to (x + 2).
  • The root x = -3 corresponds to the factor (x - (-3)), which simplifies to (x + 3).

Verify that (x + 2)\, (x + 3) indeed expands to the original polynomial:

\begin{aligned}& (x + 2)\, (x + 3) \\ =\; & x^{2} + 2\, x + 3\, x + 6 \\ =\; & x^{2} + 5\, x + 6\end{aligned}.

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On saturday, you bowl at mar vista bowl, where renting shoes costs $2 and each game bowled is $3.50. on sunday, you bowl at pinz
ExtremeBDS [4]

Given, at Mar Vista bowl the cost of renting shoes = $2.

The cost for each game bowled = $3.50

There are g games given. So the cost for g games bowled = $(3.50)(g) = $(3.50g)

The total amount soent at Mar Vista Bowl = $(2+3.50g)

At Pinz, the cost for shoe rental = $5.

The cost for each game bowled = $3.25.

So the cost for g game bowled = $(3.25)(g) = $(3.25g)

Total amount spent at Pinz = $(5+3.25g)

Given, the amount spent ateach of the places is same.

so we can write the equation as,

2+3.50g = 5+3.25g

We will move 3.25 to the left side by subtracting it from both sides. we will get,

2+3.50g-3.25g = 5+3.25g-3.25g

2+0.25g = 5

Now we will move 2 to the right side by subtracting 2 from both sides. We will get,

2+0.25g-2 = 5-2

0.25g = 3

Now to get g we will divide 0.25 to both sides. We will get,

\frac{0.25g}{0.25}= \frac{3}{0.25}

g =\frac{3}{0.25}

g = 12

So we have got the required answer.

The number of games bowled = 12.

6 0
3 years ago
11) A building casts a shadow of 100 feet. The angle of elevation from the end of the shadow to the top of the
svp [43]

Answer:

≈ 27 ft

Step-by-step explanation:

using the tangent ratio in the right triangle formed by the building and the ground.

tan15° = \frac{opposite}{adjacent} = \frac{?}{100} ( multiply both sides by 100 )

100 × tan15° = ? , then

? ≈ 27 ft ( to the nearest whole number )

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1 year ago
An airplane has a wingspan of 20 feet and a length of 15 feet. If the model of this airplane has a wingspan of 8 inches, what is
Katen [24]

Answer:

The length of the model is 6 inches.

Step-by-step explanation:

The wingspan of the airplane and length of the airplane are a ratio of 4:3

The model is also supposed to be 4:3.

4:3 x 2 = 8:6

Or, 20x12=240

240/8=30

15x12=180

180/30=6.

8 0
2 years ago
Read 2 more answers
Solve 1/p+1/s=1 for p
jekas [21]

Answer:

Step-by-step explanation:

Multiply through by the L. C. M which is PS.

1/p*ps+1/s*ps=1*ps

P+p=ps

2p=ps

Divide both sides by 2

2p/2=ps/2

P=ps/2

3 0
3 years ago
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