Multiply the polynomials (3x−1)(2x+4)

Question

(
3
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−
1
)
(
2
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+
4
)
.(2 points)
x2+
𝑥
2
+
x+
𝑥
+

Answer 1

To multiply the polynomials \((3x - 1)(2x + 4)\), we can use the distributive property (often referred to as the FOIL method for binomials).

Let's distribute each term in the first polynomial to each term in the second polynomial:

1. Multiply \(3x\) by \(2x\): \[ 3x \cdot 2x = 6x^2 \]

2. Multiply \(3x\) by \(4\): \[ 3x \cdot 4 = 12x \]

3. Multiply \(-1\) by \(2x\): \[ -1 \cdot 2x = -2x \]

4. Multiply \(-1\) by \(4\): \[ -1 \cdot 4 = -4 \]

Now we combine all the results: \[ 6x^2 + 12x - 2x - 4 \]

Combine like terms (the \(12x\) and \(-2x\)): \[ 6x^2 + (12x - 2x) - 4 = 6x^2 + 10x - 4 \]

So, the product of the polynomials \((3x - 1)(2x + 4)\) is: \[ \boxed{6x^2 + 10x - 4} \]