Multiply the polynomials (3x−1)(2x+4)
.
(3x-1)(2x+4) = 3x * 2x + 3x * 4 + (-1) * 2x + (-1) * 4
= 6x^2 + 12x - 2x + (-4)
= 6x^2 + 10x - 4
Which of the following responses shows that polynomials form a closed system under multiplication?(1 point)
Responses
3x24−1
Start Fraction 3 x squared over 4 minus 1 End Fraction
(x)(12x)
left parenthesis x right parenthesis left parenthesis Start Fraction 1 over 2 End Fraction x right parenthesis
6⋅−3
6 times negative 3
4x3⋅5
The correct response that shows that polynomials form a closed system under multiplication is:
4x3⋅5
To multiply the polynomials (3x-1)(2x+4), you can use the distributive property, which states that a(c + d) = ac + ad.
Here are the steps to multiply the polynomials:
1. Multiply the first terms in each polynomial:
(3x) * (2x) = 6x^2
2. Multiply the outer terms in each polynomial:
(3x) * (4) = 12x
3. Multiply the inner terms in each polynomial:
(-1) * (2x) = -2x
4. Multiply the last terms in each polynomial:
(-1) * (4) = -4
5. Simplify the results from steps 1-4:
6x^2 + 12x - 2x - 4
6. Combine like terms:
6x^2 + 10x - 4
Therefore, the result of multiplying the polynomials (3x-1)(2x+4) is 6x^2 + 10x - 4.