Find the product of the polynomials (2x+1)(x−4).
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Find the product of the polynomials (2x+1)(x−4)
.(2 points)
To find the product of the polynomials (2x+1)(x−4), we can use the FOIL method. FOIL stands for First, Outer, Inner, Last.
First, we multiply the first terms of each polynomial:
(2x) * (x) = 2x^2
Next, we multiply the outer terms of each polynomial:
(2x) * (-4) = -8x
Then, we multiply the inner terms of each polynomial:
(1) * (x) = x
Finally, we multiply the last terms of each polynomial:
(1) * (-4) = -4
Now, we can combine the products we calculated to get the final result:
(2x^2) - (8x) + (x) - (4) = 2x^2 - 7x - 4
Therefore, the product of the polynomials (2x+1)(x−4) is 2x^2 - 7x - 4.
To find the product of the polynomials (2x+1)(x-4), we can use the distributive property.
First, we multiply the first term of the first polynomial (2x) by both terms of the second polynomial (x and -4):
(2x)(x) = 2x^2
(2x)(-4) = -8x
Next, we multiply the second term of the first polynomial (1) by both terms of the second polynomial (x and -4):
(1)(x) = x
(1)(-4) = -4
Finally, we add up all the intermediate products to get the final product of the polynomials:
2x^2 + (-8x) + x + (-4)
Simplifying this expression, we combine like terms:
2x^2 - 7x - 4
So the product of the polynomials (2x+1)(x-4) is 2x^2 - 7x - 4.