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Aleks04 [339]
2 years ago
7

100 points

Mathematics
1 answer:
Pavlova-9 [17]2 years ago
3 0
STEP
1
:

y
Simplify —
3
Equation at the end of step
1
:

y
(((18•(x5))•(y3))+((6•(x2))•(y4)))+((((24•(x6))•—)•x)•y)
3
STEP
2
:

Equation at the end of step
2
:

y
(((18•(x5))•(y3))+((6•(x2))•(y4)))+((((23•3x6)•—)•x)•y)
3
STEP
3
:

Canceling Out:

3.1 Canceling out 3 as it appears on both sides of the fraction line


Equation at the end of step
3
:

(((18•(x5))•(y3))+((6•(x2))•(y4)))+((8x6y•x)•y)
STEP
4
:

Equation at the end of step
4
:

(((18•(x5))•(y3))+((2•3x2)•y4))+8x7y2
STEP
5
:

Equation at the end of step
5
:

(((2•32x5) • y3) + (2•3x2y4)) + 8x7y2
STEP
6
:

STEP
7
:
Pulling out like terms

7.1 Pull out like factors :

8x7y2 + 18x5y3 + 6x2y4 = 2x2y2 • (4x5 + 9x3y + 3y2)

Trying to factor a multi variable polynomial :

7.2 Factoring 4x5 + 9x3y + 3y2

Try to factor this multi-variable trinomial using trial and error

Factorization fails

Final result :
2x2y2 • (4x5 + 9x3y + 3y2)
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3 years ago
algebraically determine the values of h and k to correctly complete the identity stated below : 2 x cubed - 10x squared + 11x -
11Alexandr11 [23.1K]

Answer:

The values for expression is h = - 2 and k = 5

Step-by-step explanation:

Given algebraic expression can be written as :

2 x³ - 10 x² + 11 x - 7 = ( x - 4 ) × ( 2 x² + h x + 3 ) + k

Now opening the bracket

Or, 2 x³ - 10 x² + 11 x - 7 = x × ( 2 x² + h x + 3 ) - 4 × ( 2 x² + h x + 3  ) + k

Or, 2 x³ - 10 x² + 11 x - 7 = 2 x³ + h x² + 3 x - 2 x² - 4 h x - 12  +k

Or , 2 x³ - 10 x² + 11 x - 7 = 2 x³ + ( h - 2 ) x² + ( 3 - 4 h ) x - 12  + k

Now, equating the equation both sides

I.e  - 10 =  ( h - 2 )

Or , h - 2 = - 10

I.e , h = - 10 + 2

∴ h = - 2

Again , 11  = ( 3 - 4 h )

or, 11 = 3 - 4 h

or, 11 - 3 = - 4 h

or, 8 = - 4 h

∴ h = \frac{-8}{4}

I.e h = - 2

Again

- 7 = - 12 + k

Or, k = - 7 + 12

∴  k = 5

Hence The values for expression is h = - 2 and k = 5    . Answer

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