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Anton [14]
2 years ago
12

(x+5)(x+4)(x-2)-(x^2+11x-9)(x+1)+5x^2

Mathematics
2 answers:
alina1380 [7]2 years ago
8 0

Answer:

(x+5)•(x+4)•(x-2)•(x2+11x-9)•(x+26)

STEP

2

:

Equation at the end of step 2

(((x+5)•(x+4)•(x-2))•(x2+11x-9))•(x+26)

STEP

3

:

Equation at the end of step 3

((x+5)•(x+4)•(x-2)•(x2+11x-9))•(x+26)

STEP

4

:

Trying to factor by splitting the middle term

4.1 Factoring x2+11x-9

The first term is, x2 its coefficient is 1 .

The middle term is, +11x its coefficient is 11 .

The last term, "the constant", is -9

Step-1 : Multiply the coefficient of the first term by the constant 1 • -9 = -9

Step-2 : Find two factors of -9 whose sum equals the coefficient of the middle term, which is 11 .

-9 + 1 = -8

-3 + 3 = 0

-1 + 9 = 8

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step

4

:

(x+5)•(x+4)•(x-2)•(x2+11x-9)•(x+26)

Step-by-step explanation:

Luda [366]2 years ago
6 0
(x+5)•(x+4)•(x-2)•(x2+11x-9)•(x+26)
STEP
2
:
Equation at the end of step 2

(((x+5)•(x+4)•(x-2))•(x2+11x-9))•(x+26)
STEP
3
:
Equation at the end of step 3

((x+5)•(x+4)•(x-2)•(x2+11x-9))•(x+26)
STEP
4
:
Trying to factor by splitting the middle term

4.1 Factoring x2+11x-9

The first term is, x2 its coefficient is 1 .
The middle term is, +11x its coefficient is 11 .
The last term, "the constant", is -9

Step-1 : Multiply the coefficient of the first term by the constant 1 • -9 = -9

Step-2 : Find two factors of -9 whose sum equals the coefficient of the middle term, which is 11 .

-9 + 1 = -8
-3 + 3 = 0
-1 + 9 = 8

Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored

Equation at the end of step
4
:

(x+5)•(x+4)•(x-2)•(x2+11x-9)•(x+26)
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If (x^2 - 1) is a factor of ax^4 + bx^3 + cx^2 + dx + e, show that a + c + e = b + d = 0
alisha [4.7K]
x^2-1=x^2-1^2=(x-1)(x+1)

If x²-1 is a factor of the polynomial, both x-1 and x+1 are factors of it.

According to the remainder theorem, if a binomial x-a is a factor of a polynomial p(x), then p(a)=0.

If x-1 and x+1 are factors of the polynomial p(x)=ax⁴+bx³+cx²+dx+e, then p(1)=0 and p(-1)=0.

p(1)=a \times 1^4+b \times 1^3 + c \times 1^2+ d \times 1+e \\
p(-1)=a \times (-1)^4 + b \times (-1)^3 + c \times (-1)^2 + d \times (-1)+e \\ \\
p(1)=a+b+c+d+e \\
p(-1)=a-b+c-d+e \\ \\
p(1)=0 \\
p(-1)=0 \\ \\ \hbox{add both equations:} \\
a+b+c+d+e=0 \\
\underline{a-b+c-d+e=0} \\
2a+2c+2e=0 \\
2(a+c+e)=0 \\
a+c+e=0 \\ \\
\hbox{substitute 0 for a+c+e in the first equation:} \\
a+b+c+d+e=0 \\
(a+c+e)+b+d=0 \\
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\hbox{proved } \checkmark
8 0
3 years ago
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lys-0071 [83]

Answer:

8x+8y

Step-by-step explanation:

y + 3x + 4y + 2x + 3y +3x

<em>With</em><em> </em><em>this</em><em> </em><em>we</em><em> </em><em>group</em><em> </em><em>x</em><em> </em><em>with</em><em> </em><em>x</em><em> </em><em>and</em><em> </em><em>y</em><em> </em><em>with</em><em> </em><em>y</em><em> </em><em>and </em><em>in</em><em> </em><em>ascending</em><em> </em><em>order</em><em> </em><em>so</em><em> </em><em>x</em><em> </em><em>comes</em><em> </em><em>before</em><em> </em><em>y</em>

3x+2x+3x

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Which is;

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8 0
2 years ago
Question that i dont know
lutik1710 [3]

Answer:

A translation of 3 units to the right and a translation of one unit upwards.

Step-by-step explanation:

When we analyze translations of whole figures, all the points in the figure suffer the same translation, then we only need to analyze the translation of one of the points.

This means that we can only see the translation from A to A'

First, let's find the coordinates of each point:

A (2, 3)

A' (5, 4)

The translation is given if we calculate the difference between these coordinates:

A' - A =  (5, 4) - (2, 3) = (5 - 2, 4 - 3) = (3, 1)

The change in the x-value is 3.

The change in the y-value is 1.

Then we can conclude that:

A' is 3 units at the right of A

A' is 1 unit above A.

Then the translation is:

A translation of 3 units to the right and a translation of one unit upwards.

5 0
3 years ago
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2 3/8 - 1 7/8
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6 0
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2a−3+3=7+3

2a=10

Divide both sides by 2.

2a / 2 = 10 / 2

a=5

5 0
3 years ago
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