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bekas [8.4K]
3 years ago
15

Why would the polynomial, "

lign="absmiddle" class="latex-formula">" factor out to (x-3)(x+8)?
Mathematics
1 answer:
UkoKoshka [18]3 years ago
4 0

Step-by-step explanation:

5x can also be written as " -3x + 8x " so:

x^2+5x-24 = x^2-3x+8x-24

Using the distributive property:

x(x-3)+8(x-3)

Then again, using the distributive property (but in reverse):

(x-3)(x+8)

The two numbers that the middle term should be split into in order to factor can be found by listing out pairs of factors for the product of the last term and the coefficient of the first term, and using the two factors whose sum is the middle term.

For eg (because that was a bit text heavy):

The product of the last term and the first coefficient (1 * (-24)) is -24

the factors of -24 include (and their sum)

-1, 24 (23)

1, -24 (-23)

-2, 12 (10)

2, -12 (-10)

-3, 8 (5)

3, -8 (-5)

-4, 6 (2)

4, -6 (-2)

The middle coefficient is 5 and the sum of the factors -3 and 8 are 5, so split 5x into -3x + 8x to be able to factor how I showed before.

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Natasha_Volkova [10]

Answer:

C

Step-by-step explanation:

3 0
3 years ago
^Answer needed ASAP! <br> Solve x2-6x=-5 by completing the square. show ALL work
ankoles [38]

Have a nice day, be safe and healthy :)

Hope this helped

<u>formula: </u>

(a+b)^2

= a^2+2ab+b^2

Here, we have x^2  (as in a^2)

and -6x (as in 2ab), which, we're missing the b^2

(I'm not really sure how to describe this but bare with me)

-6/2 (-6 is from the -6x) = -3 (the b)

-3^2 = -3*-3 which is equal to 9 (positive 9)

Writing it out -

x^2-6x+9 = -5

- Addition of inequality -

Since we add 9 to the left side, we have to add 9 to the right side; which gives us:

x^2-6x+9=4

Next, lets put the x^2-6x+9 as in (a+b)^2:

(x-3)^2 = 4

<em>Then let's do the square root of equality (square rooting both sides) :</em>

<u>x-3 = 2</u>

<em>Finally lets add 3 to both sides</em>

<u>x = 5</u>

THE ANSWER IS <u><em>x=5</em></u>

<u><em></em></u>

Have a nice day, be safe + healthy - Hope this helped

8 0
4 years ago
Consider f (x) = StartRoot x squared minus 1 EndRoot and g (x) = StartRoot x squared + 1 EndRoot. What value(s) of x would make
dalvyx [7]

Answer:

Any value of x

<em></em>

Step-by-step explanation:

Given

f(x) = \sqrt{x^2 - 1}

g(x) = \sqrt{x^2 + 1}

Required

What value of x is  f(g(x)) = g(f(x))

Solving for f(g(x))

f(x) = \sqrt{x^2 - 1}

f(g(x)) = \sqrt{(\sqrt{x^2 + 1})^2 - 1}

Solve the inner square

f(g(x)) = \sqrt{(x^2 + 1 - 1}

f(g(x)) = \sqrt{x^2 } }

f(g(x)) = x

Solving g(f(x))

g(x) = \sqrt{x^2 + 1}

g(f(x)) = \sqrt{(\sqrt{x^2 - 1})^2 + 1}

g(f(x)) = \sqrt{x^2 - 1 + 1}

g(f(x)) = \sqrt{x^2 }

g(f(x)) = x

Equate f(g(x)) and g(f(x))

f(g(x)) = g(f(x))

x = x

<em>This implies that </em>f(g(x)) = g(f(x))<em> at any value of x</em>

8 0
4 years ago
Five years ago, Tom was one third as old as his father was then.In 5 years, Tom will be half as old as his father will be then.
sleet_krkn [62]

Answer:

The father is 35years old and the son Tom is 15years old

Step-by-step explanation:

Let the father's be y

Let Tom's age be T

5 years ago:

The father's age is: y — 5

Tom's age:

T— 5.

But Tom's age was one third the father's age. This is written as:

T — 5 = 1/3(y — 5)

3(T — 5) = y — 5

3T — 15 = y — 5

3T — y = — 5 + 15

3T — y = 10 (1)

In 5years time:

The father's age is:

y + 5

Tom's age:

T + 5

But in 5years time, Tom will be half as old as his father. This is written as:

T + 5 = 1/2(y + 5)

2(T + 5) = y + 5

2T + 10 = y + 5

2T — y = 5 — 10

2T — y = — 5 (2)

Therefore, the equations are

3T — y = 10 (1)

2T — y = — 5. (2)

Solving by elimination method:

Subtract equation (2) from (1)

3T — y = 10

— (2T — y = — 5)

T = 15

Substituting the value of T into equation (1)

3T — y = 10

3(15) — y = 10

45 — y = 10

45 — 10 = y

y = 35

Therefore,

The father is 35years old and the son Tom is 15years old

5 0
4 years ago
Penn has a board that is 8 feet long. He cuts a piece off of the board that is
Arisa [49]
8-3 = 5 feet long.
The remaining will be 5 feet long

6 0
3 years ago
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