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3 years ago

Factor completely 18x2 − 21x −15. 3(2x + 1)(3x − 5) 3(2x − 5)(3x + 1) 3(2x − 1)(3x + 5) 3(6x + 1)(x − 5)

Mathematics

2 answers:

solmaris [256]3 years ago

7 0

3(2x+1)(3x-5)
is the correct answer

r-ruslan [8.4K]3 years ago

4 0

Answer: The required factored form of the given expression is $3(3x-5)(2x+1).$

Step-by-step explanation: We are given to factor completely the following quadratic expression :

$E=18x^2-21x-15=3(6x^2-7x-5)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

To factor the expression within the bracket, we need two integers with sum is -7 and product -90.

From (i), we get

$E\\\\=3(6x^2-7x-5)\\\\=3(6x^2-10x+3x-5)\\\\=3(2x(3x-5)+1(3x-5))\\\\=3(3x-5)(2x+1).$

Thus, the required factored form of the given expression is $3(3x-5)(2x+1).$

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Step-by-step explanation:

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puteri [66]

Answer:

Width: 7

Length: 14

Step-by-step explanation:

The area of a rectangle can be found my multiplying the length by the width. We do not know neither the length nor the width. However, we do know that the length is 7 feet longer than the width. Because we do not know the value of either side, let's let $x$ represent the width.

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Now that we have our values for the length and the width we can multiply them together to find our area.

$(x)(x+7)=x^{2} +7x$

Now we have our equation, so we can address the changes made by the original question. The original question states that when 7 is added to both the length and width the area becomes 3 times larger. To do so simply increase each side by 7 by adding 7 to the original values.

$(x+7)(x+14)$

And multiply our area by 3.

$3(x^{2} +7x)$

set these equal to each other to find your new equation.

$(x+7)(x+14)=3(x^{2} +7x)$

Now you need to solve for $x$ . To do this first muliply $(x+7)$ and $(x+14)$ .

$(x+7)(x+14)=\\x^{2} +14x+7x+98=\\x^{2} +21x+98$

Then multiply $3(x^{2} +7x)$

$3(x^{2} +7x)=\\3x^{2} +21x$

Now you can begin solving for $x$ .

$x^{2} +21x+98=3x^{2} +21x$

Subtract $x^{2}$ from both sides.

$21x+98=2x^{2} +21x$

Subtract $21x$ from both sides.

$98=2x^{2}$

Divide by 2.

$49=x^{2}$

And finally take the sqaure root of both sides.

$\sqrt{x^{2} }=\sqrt{49}\\x=7$

Remember, because we are dealing with length, there cannot be negative. So while normally we would get both +7 <em>and</em> -7, in this case we <em>only </em>get +7.

Now that we have the value of $x$ , we can plug it into our original values.

For width we simply get 7.

For length we get 7+7=14

To check our answer we cna multiply 7 by 14 to get 98. Then we can add 7 to our length and width to get 14 and 21. Multiply these together and we get 294. 294 divided by 3 is 98, proving our answer correct.

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