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3 years ago

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

Mathematics

2 answers:

Dmitrij [34]3 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]3 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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madreJ [45]

Answer:

2. n = 11

4. g = -2

6. t = 21

8. n = 4

10. y = -1

Step-by-step explanation:

2. 63 = -3(1 - 2n)

Dividing both the side by negative 3 we get

$-21=1-2n\\2n=1+21\\2n=22\\n=\frac{22}{2} \\\therefore n=11$

4. -g + 2(3 + g) = -4(g + 1)

First we will open the bracket by distributive property A( B +C) = AB + AC

$-g+2\times 3 + 2\times g = -4\times g + -4\times 1\\-g+6+ 2g=-4g-4\\\textrm{we will take all the g term the left side and the constant to the right side}\\4g-g+2g=-6-4\\5g=-10\\g=\frac{-10}{5}\\\therefore g=-2$

6.-3(t +5 ) + (4t + 2) = 8

Using distributive property A( B +C) = AB + AC we get

$-3\times t + -3\times 5 + 4t + 2=8\\-3t-15+ 4t + 2=8\\t=8+15-2\\t=21\\\therefore t=21\\$

8. -8 - n = -3(2n -4)

Using distributive property A( B +C) = AB + AC we get

$-8 - n = -3\times 2n - -3\times4\\-8-n=-6n+12\\\textrm{all the n terms to the left inside and the constant of the right-hand side}\\6n-n=8+12\\5n=20\\n=\frac{20}{5}\\ \therefore n= 4$

10. -4( 2 - y) + 3y = 3(y - 4)

Using distributive property A( B +C) = AB + AC we get

$-4\times 2 --4\times y + 3y = 3\times y -3\times 4\\-8+4y+3y =3y-12\\\textrm{all the y terms to the left side and the constant to the right side}\\4y+3y-3y=-12+8\\4y=-4\\y=\frac{-4}{4}\\ \therefore y=-1$