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3 years ago

Factor the following polynomial completely. 6x^5-30x^4-84x^3

Mathematics

1 answer:

Lerok [7]3 years ago

6 0

6x^5 - 30x^4 - 84x^3

we can factor out 6x^3

6x^3(x^2 - 5x - 14)

Also, we can factor x - 7 and x + 2 out of x^2 - 5x - 14

The final answer = 6x^3(x - 7)(x + 2)

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(a) Expanded form:

$((X_1 + X_1Y_1) - X_1Z_1) + ((X_2 + X_2Y_2) - X_2Z_2) + ((X_3 + X_3Y_3) - X_3Z_3) + ((X_4 + X_4Y_4) - X_4Z_4)$

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Step-by-step explanation:

Given

$\sum \limit^4_{i=1}\ ((X_i+X_iY_i) - X_iZ_i)$

Solving (a): The expanded form:

This means that we substitute the values of i from 1 to 4 in the above expression.

So, the expression becomes:

$((X_1 + X_1Y_1) - X_1Z_1) + ((X_2 + X_2Y_2) - X_2Z_2) + ((X_3 + X_3Y_3) - X_3Z_3) + ((X_4 + X_4Y_4) - X_4Z_4)$

Solving (b): The value of the expression

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So, the expression becomes:

$((0 + 0*5) - 0*0) + ((1 + 1*26) - 1*-2) + ((12 + 12*-2) - 12*3) + ((-1 + -1*25) - -1*24)$

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$((0 + 0) - 0) + ((1 + 26) +2) + ((12 -24) - 36) + ((-1 -25) +24)$

$0 + 29 -48 -2$

$-21$

<em>Hence, the result of the expression is -21</em>

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