All categories

4 years ago

The polynomial p(x)=2x^3-x^2-25x-12 has a known factor of (x+3). Rewrite p(x) as a product of linear factors.

Mathematics

1 answer:

katrin2010 [14]4 years ago

8 0

Answer:

p(x) = (x + 3) (2x + 1) (x − 4)

Step-by-step explanation:

One way to find the other factor is long division (see attached).

Another way is to multiply x + 3 by ax² + bx + c, then match the result to p(x).

(x + 3) (ax² + bx + c)

ax³ + bx² + cx + 3ax² + 3bx + 3c

ax³ + (b+3a)x² + (c+3b)x + 3c

a = 2, b = -7, c = -4

Therefore:

p(x) = (x + 3) (2x² − 7x − 4)

Factoring:

p(x) = (x + 3) (2x + 1) (x − 4)

You might be interested in

13 POINTS- please help me

allsm [11]

Answer:

See explanation

Step-by-step explanation:

16. Two parallel lines are cut by transversal. Angles with measures $(6x+20)^{\circ}$ and $(x+100)^{\circ}$ are alternate exterior angles. By alternate exterior angles, the measures of alternate exterior angles are the same:

$6x+20=x+100\\ \\6x-x=100-20\\ \\5x=80\\ \\x=16$

Then

$(6x+20)^{\circ}=(6\cdot 16+20)^{\circ}=116^{\circ}\\ \\(x+100)^{\circ}=(16+100)^{\circ}=116^{\circ}$

17. Two parallel lines are cut by transversal. Angles with measures $(2x+12)^{\circ}$ and $(3x-22)^{\circ}$ are alternate interior angles. By alternate interior angles, the measures of alternate interior angles are the same:

$2x+12=3x-22\\ \\2x-3x=-22-12\\ \\-x=-34\\ \\x=34$

Then

$(2x+12)^{\circ}=(2\cdot 34+12)^{\circ}=80^{\circ}\\ \\(3x-22)^{\circ}=(3\cdot 34-22)^{\circ}=80^{\circ}$

18. Two parallel lines are cut by transversal. Angles with measures $(6x-7)^{\circ}$ and $(5x+10)^{\circ}$ are alternate exterior angles. By alternate interior angles, the measures of alternate exterior angles are the same:

$6x-7=5x+10\\ \\6x-5x=10+7\\ \\x=17$

Then

$(6x-7)^{\circ}=(6\cdot 17-7)^{\circ}=95^{\circ}\\ \\(5x+10)^{\circ}=(5\cdot 17+10)^{\circ}=95^{\circ}$

19. The diagram shows two complementary angles with measures $2x^{\circ}$ and $56^{\circ}$ . The measures of complementary angles add up to $90^{\circ},$ then

$2x+56=90\\ \\2x=90-56\\ \\2x=34\\ \\x=17$

Hence,

$2x^{\circ}=2\cdot 17^{\circ}=34^{\circ}$

Check:

$34^{\circ}+56^{\circ}=90^{\circ}$

20. Angles $\angle 1$ and $\angle 2$ are vertical angles. By vertical angles theorem, vertical angles are congruent, so

$m\angle 1=m\angle 2\\ \\5x+7=3x+15\\ \\5x-3x=15-7\\ \\2x=8\\ \\x=4$

Hence,

$m\angle 1=(5x+7)^{\circ}=(5\cdot 4+7)^{\circ}=27^{\circ}\\ \\m\angle 2=(3x+15)^{\circ}=(3\cdot 4+15)^{\circ}=27^{\circ}$

21. $\angle 5$ and $\angle 8$ are supplementary. The measures of supplementary angles add up to $180^{\circ},$ so

$m\angle 5+m\angle 8=180^{\circ}\\ \\3x-40+7x-120=180\\ \\10x-160=180\\ \\10x=180+160\\ \\10x=340\\ \\x=34$

Therefore,

$m\angle 5=(3x-40)^{\circ}=(3\cdot 34-40)^{\circ}=62^{\circ}\\ \\m\angle 8=(7x-120)^{\circ}=(7\cdot 34-120)^{\circ}=118^{\circ}\\ \\62^{\circ}+118^{\circ}=180^{\circ}$

7 0

3 years ago

When you divide a whole number by a decimal less than 1, the quotient is greater than the whole number. Why?

Setler [38]

For this type of problem you would have to move the decimal as many places to the right as needed to make the divisor a whole number the you would move the dividend the same amount of times even if it is a whole number . Then you use what you have to divide normally. Hope this helps!

3 0

4 years ago

5x + 2 (x+7) =14x - 7

qaws [65]

The answer is x=-23/21

5 0

3 years ago

Rewrite the quadratic function below in standard form y=3(x+2)(x-3)

babunello [35]

X=3(x^2-x_6)
3x^2-x-6

8 0

3 years ago