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2 years ago

F. determine if (x + 3) is a factor of (x) = 2x3 + x2 –8x + 21 by using synthetic division. if so, find the other factors.

1 answer:

4 0

Since its x + 3 we use -3

-3| 2 1 -8 21 (these are the # without the x)
___________________

-6 15 -21
-------------------------------
2 -5 7 0

Drag the 2 down, multiple it by -3 to get -6
1+(-6) = -5. -5 * -3 =15 . 15+(-8) = 7
7*-3 = -21. -21 +21 = 0
Since last # is 0 we have a factor.

factor is 2x^2 -5x -7 (we start with a power 1 less the original.)

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2(x 4) = 35 − (7 − 4x)

Rus_ich [418]

2(x4) = 35 - (7-4x)
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2 years ago

3q+4+9=-14 <br> what is Q

BlackZzzverrR [31]

Hi! Your answer is q = -9

Please see an explanation for a better and clear understanding to your problem.

Any questions about my answer and explanation can be asked through comments! :)

Step-by-step explanation:

Since we want to solve for q-term. That means we are going to isolate q-term.

$\huge{3q+4+9=-14}$

We can add 4 and 9 together.

$\huge{3q+13=-14}$

Because we want to know the value of q. That means we have to isolate q-term by subtracting both sides by 13.

$\huge{3q+13-13=-14-13}\\\huge{3q=-27}$

We are reaching to the final step where we divide the whole equation by 3.

$\huge{\frac{3q}{3}=-\frac{27}{3}}\\\huge{q=-9}$

Finally, the solution for this equation is q = -9. But what if you are not certain or sure about the answer? Let's check it out!

To check the answer, simply substitute q = -9 in the equation.

$\huge{3q+4+9=-14}\\\huge{3(-9)+13=-14}\\\huge{-27+13=-14}\\\huge{-14=-14}$

Notice that the equation is true for q = -9. Hence, we can conclude that the solution for this equation is q = -9.

Hope this helps!

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2 years ago

Solve the following inequality. 21<_-3(x - 4) < 30 A. 28<_x < 37 B. -3 <_ x < 6 C. -6 < x <_ -3 D. -10 &

Aloiza [94]

Answer:

Option C $-6$

Step-by-step explanation:

we have

$21\leq -3(x-4)$

The compound inequality can be divided into two inequality

$21\leq -3(x-4)$ -----> inequality A

$-3(x-4)$ ----> inequality B

Solve inequality A

$21\leq -3x+12$

$9\leq -3x$

Divide by -3 both sides

when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality symbol

$-3\geq x$

Rewrite

$x\leq -3$

The solution of the inequality A is the interval (-∞,-3]

Solve the inequality B

$-3x+12$

$-3x$

Divide by -3 both sides

when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality symbol

$x>-6$

The solution of the inequality B is the interval [-6,∞)

The solution of the compound inequality is

[-6,∞) ∩ (-∞,-3]=(-6,-3]

$-6$

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