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2 years ago

Is 36z^2 - 9 a difference of squares?

Mathematics

1 answer:

Dvinal [7]2 years ago

4 0

Answer:

yes

Step-by-step explanation:

A difference of squares has the form a² - b² = (a - b)(a + b)

note that 36z² = (6z)² ⇒ a = 6z and 9 = 3² ⇒ b = 3

36z² - 9 is a difference of squares and factors as (6z - 3)(6z + 3)

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You were given the polynomial f(x)=3x^3+13x^2+19x+k and you know that f(-2)=0find k

eduard

Answer:

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Explanation:

The initial polynomial is:

$f(x)=3x^3+13x^2+19x+k$

If f(-2) = 0, then when we replace x by -2, the result will be 0. It means that we can write the following equation:

$\begin{gathered} f(-2)=3(-2)^3+13(-2)^2+19(-2)+k=0 \\ 3(-2)^3+13(-2)^2+19(-2)+k=0 \end{gathered}$

Therefore, we can solve for k as follows:

$\begin{gathered} 3(-8)+13(4)+19(-2)+k=0 \\ -24+52-38+k=0 \\ -10+k=0 \\ -10+k+10=0+10 \\ k=10 \end{gathered}$

So, the value of k is 10

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