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4 years ago

Factor this trinomial completely. 2x^2 + 6x + 4

Mathematics

2 answers:

Dmitrij [34]4 years ago

5 0

Step-by-step explanation:

$2 {x}^{2} + 6x + 4 \\ \\ = 2 {x}^{2} + 2x + 4x + 4 \\ \\ = 2x(x + 1) + 4(x + 1) \\ \\ = (2x + 4)(x + 1) \\ \\ = 2(x + 2)(x + 1) \\ \\ = 2(x + 1)(x + 2) \\ are \: the \: required \: factors \: of \: the \: \\ given \: trinomial$

Sholpan [36]4 years ago

5 0

Answer: $(x+1)(2x+4)$

Step-by-step explanation:

Given :

$2x^{2}+6x+4$

in order to factorize , we will find two factors that when multiplied together gives $8x^{2}$ and when added gives $6x$ .

The factors are : $2x$ and $4x$

The next thing is to replace $6x$ in the trinomial by this two factors , that is

$2x^{2} +2x+4x+4$

Factorizing , we have

$2x(x+1)+4(x+1)$

which will give

$(x+1)(2x+4)$

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Read 2 more answers

A company is constructing an open-top, square-based, rectangular metal tank that will have a volume of 49 cubic feet. What dime

yawa3891 [41]

Answer:

b = 4.6 ft

h = 2.3 ft

Step-by-step explanation:

The volume of the tank is given by:

$b^2*h=49$

Where 'b' is the length of the each side of the square base, and 'h' is the height of the tank.

The surface area can be written as:

$A=b^2+4bh\\A=b^2+4b*({\frac{49}{b^2}})\\A=b^2+\frac{196}{b}$

The value of b for which the derivate of the expression above is zero is the value that yields the minimum surface area:

$\frac{dA}{db} =0=2b-\frac{196}{b^2}\\2b^3=196\\b=4.61\ ft$

The value of h is then:

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Rounded to the nearest tenth, the dimensions are b = 4.6 ft and h = 2.3 ft.

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3 years ago