Question Simplify and factor the expression $-5(x^2 + 6/5 x + 5/2) - 40 + 5(5/2)$ .

Studdy Solution

STEP 1

Assumptions1. We are given the expression $-5\left(x^{}+\frac{6}{5} x+\frac{5}{}\right)-40+5\left(\frac{5}{}\right)$ . We need to simplify and factor this expression

STEP 2

First, distribute the $-5$ to each term inside the first parentheses.
$-5x^{2}-6x-\frac{25}{2} -40 + \frac{25}{2}$

STEP 3

Combine like terms.
$-5x^{2}-6x -40$

STEP 4

Now, we need to factor the expression. First, look for a common factor in all terms. In this case, the common factor is $-2$ .
$-2(2.x^{2}+3x +20)$

STEP 5

Next, we need to factor the quadratic expression inside the parentheses. This can be done by finding two numbers that add up to $3$ and multiply to $50$ (which is the product of $2.5$ and $20$ ). The numbers $5$ and $10$ satisfy these conditions.
$-2(2.5x^{2}+5x+10x +20)$

STEP 6

Now, group the terms and factor by grouping.
$-2[(2.5x^{2}+5x)+(10x +20)]$

STEP 7

Factor out the common factors in each group.
$-2[x(2.5x+5)+20(0.5x +1)]$

STEP 8

Notice that the expressions in the parentheses are the same. Factor out the common binomial.
$-2(2.5x+5)(x+4)$

STEP 9

Finally, simplify the expression.
$-5x(2x+5)(x+4)$ So, the simplified and factored form of the given expression is $-5x(2x+5)(x+4)$ .

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Question Simplify and factor the expression $-5(x^2 + 6/5 x + 5/2) - 40 + 5(5/2)$ .

Studdy Solution

STEP 1

Assumptions1. We are given the expression $-5\left(x^{}+\frac{6}{5} x+\frac{5}{}\right)-40+5\left(\frac{5}{}\right)$ . We need to simplify and factor this expression

STEP 2

First, distribute the $-5$ to each term inside the first parentheses.
$-5x^{2}-6x-\frac{25}{2} -40 + \frac{25}{2}$

STEP 3

Combine like terms.
$-5x^{2}-6x -40$

STEP 4

Now, we need to factor the expression. First, look for a common factor in all terms. In this case, the common factor is $-2$ .
$-2(2.x^{2}+3x +20)$

STEP 5

Next, we need to factor the quadratic expression inside the parentheses. This can be done by finding two numbers that add up to $3$ and multiply to $50$ (which is the product of $2.5$ and $20$ ). The numbers $5$ and $10$ satisfy these conditions.
$-2(2.5x^{2}+5x+10x +20)$

STEP 6

Now, group the terms and factor by grouping.
$-2[(2.5x^{2}+5x)+(10x +20)]$

STEP 7

Factor out the common factors in each group.
$-2[x(2.5x+5)+20(0.5x +1)]$

STEP 8

Notice that the expressions in the parentheses are the same. Factor out the common binomial.
$-2(2.5x+5)(x+4)$

STEP 9

Finally, simplify the expression.
$-5x(2x+5)(x+4)$ So, the simplified and factored form of the given expression is $-5x(2x+5)(x+4)$ .

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Question Simplify and factor the expression −5(x2+6/5x+5/2)−40+5(5/2)-5(x^2 + 6/5 x + 5/2) - 40 + 5(5/2)−5(x2+6/5x+5/2)−40+5(5/2).

Studdy Solution

STEP 1

Assumptions1. We are given the expression −5(x+65x+5)−40+5(5)-5\left(x^{}+\frac{6}{5} x+\frac{5}{}\right)-40+5\left(\frac{5}{}\right)−5(x+56​x+5​)−40+5(5​). We need to simplify and factor this expression

STEP 2

First, distribute the −5-5−5 to each term inside the first parentheses.−5x2−6x−252−40+252-5x^{2}-6x-\frac{25}{2} -40 + \frac{25}{2}−5x2−6x−225​−40+225​

STEP 3

Combine like terms.−5x2−6x−40-5x^{2}-6x -40−5x2−6x−40

STEP 4

Now, we need to factor the expression. First, look for a common factor in all terms. In this case, the common factor is −2-2−2.−2(2.x2+3x+20)-2(2.x^{2}+3x +20)−2(2.x2+3x+20)

STEP 5

STEP 6

Now, group the terms and factor by grouping.−2[(2.5x2+5x)+(10x+20)]-2[(2.5x^{2}+5x)+(10x +20)]−2[(2.5x2+5x)+(10x+20)]

STEP 7

Factor out the common factors in each group.−2[x(2.5x+5)+20(0.5x+1)]-2[x(2.5x+5)+20(0.5x +1)]−2[x(2.5x+5)+20(0.5x+1)]

STEP 8

Notice that the expressions in the parentheses are the same. Factor out the common binomial.−2(2.5x+5)(x+4)-2(2.5x+5)(x+4)−2(2.5x+5)(x+4)

STEP 9

Finally, simplify the expression.−5x(2x+5)(x+4)-5x(2x+5)(x+4)−5x(2x+5)(x+4)So, the simplified and factored form of the given expression is −5x(2x+5)(x+4)-5x(2x+5)(x+4)−5x(2x+5)(x+4).

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Question Simplify and factor the expression $-5(x^2 + 6/5 x + 5/2) - 40 + 5(5/2)$ .

Assumptions1. We are given the expression $-5\left(x^{}+\frac{6}{5} x+\frac{5}{}\right)-40+5\left(\frac{5}{}\right)$ . We need to simplify and factor this expression

First, distribute the $-5$ to each term inside the first parentheses.
$-5x^{2}-6x-\frac{25}{2} -40 + \frac{25}{2}$

Combine like terms.
$-5x^{2}-6x -40$

Now, we need to factor the expression. First, look for a common factor in all terms. In this case, the common factor is $-2$ .
$-2(2.x^{2}+3x +20)$

Now, group the terms and factor by grouping.
$-2[(2.5x^{2}+5x)+(10x +20)]$

Factor out the common factors in each group.
$-2[x(2.5x+5)+20(0.5x +1)]$

Notice that the expressions in the parentheses are the same. Factor out the common binomial.
$-2(2.5x+5)(x+4)$

Finally, simplify the expression.
$-5x(2x+5)(x+4)$ So, the simplified and factored form of the given expression is $-5x(2x+5)(x+4)$ .