To rewrite the expression [tex]\((2x + 5)(x - 4)\)[/tex] in standard form [tex]\(ax^2 + bx + c\)[/tex]:
Start by expanding the expression step-by-step:
[tex]\((2x + 5)(x - 4)\)[/tex]
First, distribute [tex]\(2x\)[/tex] to both terms inside the parentheses [tex]\((x - 4)\)[/tex]:
[tex]\[2x \cdot x = 2x^2\][/tex]
[tex]\[2x \cdot (-4) = -8x\][/tex]
Next, distribute [tex]\(5\)[/tex] to both terms inside the parentheses [tex]\((x - 4)\)[/tex]:
[tex]\[5 \cdot x = 5x\][/tex]
[tex]\[5 \cdot (-4) = -20\][/tex]
Now, combine all the results:
[tex]\[2x^2 - 8x + 5x - 20\][/tex]
Combine the like terms [tex]\(-8x\)[/tex] and [tex]\(5x\)[/tex]:
[tex]\[2x^2 - 3x - 20\][/tex]
So, the standard form [tex]\(ax^2 + bx + c\)[/tex] is:
[tex]\[2x^2 - 3x - 20\][/tex]
Therefore,
Standard form: [tex]\(ax^2 + bx + c\)[/tex] is:
[tex]\[2x^2 - 3x - 20\][/tex]
Hence, the coefficients are [tex]\(a = 2\)[/tex], [tex]\(b = -3\)[/tex], and [tex]\(c = -20\)[/tex].
Now you can fill in the blanks from the rewritten form:
[tex]\[
\begin{array}{l}
(2 x + 5)(x - 4) \\
\text { Rewrite in standard form: } \\
2x^2 - 3x - 20 \\
\end{array}
\][/tex]
So,
[tex]\[
ax^2 = 2x^2, \quad bx = -3x, \quad c = -20
\][/tex]
