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3 years ago

Can we conclude that x - 4 is a factor of the polynomial 4x^3-20x^2+18x-12? How do you know?

Mathematics

1 answer:

agasfer [191]3 years ago

6 0

Answer:

The answer to your question is: x - 4 is not a factor

Step-by-step explanation:

x - 4 is a factor of 4x³ - 20x² + 18x -12

We can do synthetic division to know if it is a factor

4 - 20 +18 -12 4

16 -16 8

4 -4 +2 -4

x -4 is not a factor because there was a residue of -4

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$\sf\implies \: - 15 - ( - 4) + 17$

$\sf \implies \: - 15 + 4 + 17$

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$\boxed{ \tt \: ans \dashrightarrow 6}$

<h3>Remember these laws of integers:</h3>

(+)(-)=(-)
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2 years ago

Read 2 more answers

What values of a and b make the equation true? StartRoot 648 EndRoot = StartRoot 2 Superscript a Baseline times 3 Superscript b

kramer

Option C: $a=3, b=4$ is the value of a and b

Explanation:

Given that the expression $\sqrt{648}=\sqrt{2^a\times3^b}$

We need to determine the value of a and b

Let us consider the term $\sqrt{648}$ and take the prime factorization of the term 648

Thus, we have,

648 divides by 2,

$648=2 \cdot 324$

324 divides by 2,

$648=2 \cdot 2 \cdot 162$

162 divides by 2,

$648=2 \cdot 2 \cdot 2 \cdot 81$

81 divides by 3,

$648=2 \cdot 2 \cdot 2 \cdot 3 \cdot 27$

27 divides by 3,

$648=2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 9$

9 divides by 3,

$648=2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3 \cdot 3$

Thus, we have,

$\sqrt{648}=\sqrt{2^{3} \cdot 3^{4}}$

Therefore, equating the powers of 2 and 3, we get,

$a=3, b=4$

Hence, the value of a and b is 3 and 4

Thus, Option C is the correct answer.

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Vsevolod [243]

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