Multiply the polynomials (3x−1)(2x+4) .(2 points)

Question

()x^2+()x+()

Answer 1

To multiply the polynomials $(3x-1)(2x+4)$, we can use the distributive property (also known as the FOIL method for binomials):

1. First: Multiply the first terms: $$3x\cdot 2x=6x^2$$

2. Outer: Multiply the outer terms: $$3x\cdot 4=12x$$

3. Inner: Multiply the inner terms: $$-1\cdot 2x=-2x$$

4. Last: Multiply the last terms: $$-1\cdot 4=-4$$

Now, combine all these results: $$6x^2+12x-2x-4$$

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

So the final answer should be: $$6x^2+10x-4$$

Thus, the polynomial can be expressed as: $$(6)x^2+(10)x+(-4)$$

So, the coefficients are $6$, $10$, and $-4$.