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Answer :
To find the product of the two linear factors, we multiply the expressions:
$$ (2x + 5)(7 - 4x) $$
Step 1: Distribute each term in the first factor over the second factor:
- Multiply $2x$ by $7$:
$$ 2x \cdot 7 = 14x $$
- Multiply $2x$ by $-4x$:
$$ 2x \cdot (-4x) = -8x^2 $$
- Multiply $5$ by $7$:
$$ 5 \cdot 7 = 35 $$
- Multiply $5$ by $-4x$:
$$ 5 \cdot (-4x) = -20x $$
Step 2: Combine the like terms from the multiplication:
Write out all the terms:
$$ -8x^2 + 14x - 20x + 35 $$
Combine the $x$ terms:
$$ 14x - 20x = -6x $$
So, the expression simplifies to:
$$ -8x^2 - 6x + 35 $$
Step 3: Compare with the answer options:
A. $$-8x^2 + 34x - 35$$
B. $$-8x^2 + 6x - 35$$
C. $$-8x^2 - 6x + 35$$
D. $$-8x^2 - 34x + 35$$
The expression we computed matches option C.
Hence, the correct answer corresponds to option C.
$$ (2x + 5)(7 - 4x) $$
Step 1: Distribute each term in the first factor over the second factor:
- Multiply $2x$ by $7$:
$$ 2x \cdot 7 = 14x $$
- Multiply $2x$ by $-4x$:
$$ 2x \cdot (-4x) = -8x^2 $$
- Multiply $5$ by $7$:
$$ 5 \cdot 7 = 35 $$
- Multiply $5$ by $-4x$:
$$ 5 \cdot (-4x) = -20x $$
Step 2: Combine the like terms from the multiplication:
Write out all the terms:
$$ -8x^2 + 14x - 20x + 35 $$
Combine the $x$ terms:
$$ 14x - 20x = -6x $$
So, the expression simplifies to:
$$ -8x^2 - 6x + 35 $$
Step 3: Compare with the answer options:
A. $$-8x^2 + 34x - 35$$
B. $$-8x^2 + 6x - 35$$
C. $$-8x^2 - 6x + 35$$
D. $$-8x^2 - 34x + 35$$
The expression we computed matches option C.
Hence, the correct answer corresponds to option C.
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