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2 years ago

Is (x+5) a factor of f(x)=x^3 - 4x^2 + 3x + 7? use either the remainder theorem or the factor theorem to explain your reasoning.

Mathematics

1 answer:

Rufina [12.5K]2 years ago

3 0

Answer:

Step-by-step explanation:

Use synthetic division

-5 | 1 -4 3 7

____-5 45 -240

1 -9 48 | -233

Since the remainder is not 0, then x+5 is not a factor of the polynomial

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Set up a proportion and solve: Marlon spent $18 for 12 gallons of

Airida [17]

18/12=22.50/n
he could buy 15 gallons

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3 years ago

10| x – 4| - 3 > 47

Andrew [12]

Answer:

x < -1 or x > 9

Step-by-step explanation:

$10|x-4|-3>47$

Add 3 to both sides.

$10|x-4|-3+3>47+3$

Simplify.

$10|x-4|>50$

Divide both sides by 10.

$\frac{10|x-4|}{10} >\frac{50}{10}$

Simplify.

$|x-4|>5$

Apply absolute value rule: If $|u|>a,a>0$ then $u < -a$ or $u>a$

$x-4$ or $x-4 >5$

$x-4$

Add 4 to both sides.

$x-4+4$

Simplify.

$x$

$x-4>5$

Add 4 to both sides.

$x-4+4>5+4$

Simplify.

$x>9$

Combine the intervals.

$x$ or $x>9$

8 0

3 years ago

What is the word phrase for 5x+2

Alex Ar [27]

Two plus the product of 5 and x
or
the product of 5 and x plus 2
or
5 times x plus two

5 0

3 years ago

When the sum of 5 and three times a positive number is subtracted from the square of the number, 0 results. Find the number.

Juliette [100K]

$x-the\ number\\\\x^2-(5+3x)=0\\\\x^2-5-3x=0\\\\x^2-3x-5=0$

$Use\ the\ quadratic\ formula:\\a^2x+bx+c=0\\\\\Delta=b^2-4ac\\\\if\ \Delta > 0\ then\ x_1=\dfrac{-b-\sqrt\Delta}{2a}\ and\ x_2=\dfrac{-b+\sqrt\Delta}{2a}\\\\if\ \Delta=0\ then\ x_0=\dfrac{-b}{2a}\\\\if\ \Delta < 0\ then\ no\ solution$

$x^2-3x-5=0\\\\a=1;\ b=-3;\ c=-5\\\\\Delta=(-3)^2-4\cdot1\cdot(-5)+3+20=29 \ \textgreater \ 0\\\\\sqrt\Delta=\sqrt{29}\\\\x_1=\dfrac{3-\sqrt{29}}{2\cdot1}=\dfrac{3-\sqrt{29}}{2} \ \textless \ 0\\\\x_2=\dfrac{3+\sqrt{29}}{2\cdot1}=\dfrac{3+\sqrt{29}}{2} \ \textgreater \ 0$

$Answer:\ \boxed{x=\dfrac{3+\sqrt{29}}{2}}$

6 0

3 years ago

Multiplying polynomials find the product . 2x(-2x-3)

skad [1K]

2x(-2x-3)=

=2x*(-2x)+2x*(-3)=

=-4x²-6x

7 0

3 years ago