Question

4x^4 - 18x^3 - 10x^2

solve using box method pls
a =
b =
c =

gcf = 2

Answer 1

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To solve the quadratic expression \(4x^4 - 18x^3 - 10x^2\) using the box method, first, factor out the greatest common factor (GCF), which is 2:

\[2(2x^4 - 9x^3 - 5x^2)\]

Now, set up a box with two rows and three columns to distribute the terms:

\[
\begin{array}{|c|c|c|}
\hline
2x^4 & -9x^3 & -5x^2 \\
\hline
& & \\
\hline
& & \\
\hline
\end{array}
\]

Next, fill in the boxes by distributing the terms \(2x^4\), \(-9x^3\), and \(-5x^2\):

\[
\begin{array}{|c|c|c|}
\hline
2x^4 & -9x^3 & -5x^2 \\
\hline
2x^3 & -9x^2 & -5x \\
\hline
\end{array}
\]

Now, factor out the common terms from each row and each column:

From the first row: \(2x^3\)
From the second row: \(-x^2\)
From the first column: \(x^2\)
From the second column: \(x\)

So, the factored expression is:

\[2x^2(x^2 - 9x - 5)\]

To solve the quadratic expression \(x^2 - 9x - 5\), use the quadratic formula:

\[x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}\]

For \(x^2 - 9x - 5\), \(a = 1\), \(b = -9\), and \(c = -5\).

\[x = \frac{{9 \pm \sqrt{{101}}}}{{2}}\]

So, the factored expression is:

\[2x^2(x - \frac{{9 + \sqrt{{101}}}}{{2}})(x - \frac{{9 - \sqrt{{101}}}}{{2}})\]

Thus, in the box method:
- \(a = 2x^2\)
- \(b = \frac{{9 + \sqrt{{101}}}}{{2}}\)
- \(c = \frac{{9 - \sqrt{{101}}}}{{2}}\)

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Answer 2

Answer:

$\huge\boxed{2x^2(2x+1)(x-5)}$

Step-by-step explanation:

We are factoring the given expression:

$4x^4 - 18x^3 - 10x^2$

First, we can undistribute (factor out) the GCF between all the terms, which is 2x²:

$2x^2(2x^2 - 9x - 5)$

Next, we can factor the resulting quadratic by grouping:

    1) Multiply the $x^2$ term's coefficient by the constant term.

    $2\cdot (-5) = -10$

    2) List the product's factor pairs.

    (1, -10)     ← 3) Select the pair whose factors add to the $x$ term's coefficient.

    (2, -5)

    (10, -1)

    3) Split the $x$ term using these factors.

    $2x^2 +1x - 10x - 5$

    4) Group terms using the distributive property.

    $x(2x +1) - 5(2x + 1)$

    5) Rewrite again using the distributive property.

    $(2x+1)(x-5)$

Finally, we can put that factored quadratic back into the original expression:

$\huge\boxed{2x^2(2x+1)(x-5)}$