Multiply the polynomial expressions (2x^2−3)(x+5).
2x2−3x−15
2 x squared minus 3 x minus 15
2x3+10x2−3x−15
2 x cubed plus 10 x squared minus 3 x minus 15
3x3+10x2−3x−15
3 x cubed plus 10 x squared minus 3 x minus 15
3x2+7x−15
3 x squared plus 7 x minus 15
The correct answer is 2x^3+7x^2-3x-15
Which of the following responses shows that polynomials form a closed system under multiplication?
13)(x4−2)
left parenthesis Start Fraction 1 over 3 End Fraction right parenthesis left parenthesis Start Fraction x over 4 End Fraction minus 2 right parenthesis
5x⋅2
5 x times 2
2x3+x2
2 x cubed plus x squared
5⋅3
5 times 3
The correct answer is: 2x^3 + x^2
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To multiply the polynomial expressions (2x^2 − 3)(x + 5), you can use the distributive property or the FOIL method.
Using the distributive property:
1. Take each term from the first polynomial, 2x^2 - 3, and multiply it by each term from the second polynomial, (x + 5).
2. Start by multiplying 2x^2 by x and 2x^2 by 5:
2x^2 * x = 2x^3
2x^2 * 5 = 10x^2
3. Next, multiply -3 by x and -3 by 5:
-3 * x = -3x
-3 * 5 = -15
4. Combine all the resulting terms:
2x^3 + 10x^2 - 3x - 15
Using the FOIL method:
1. Multiply the first terms of each polynomial: 2x^2 * x = 2x^3
2. Multiply the outer terms: 2x^2 * 5 = 10x^2
3. Multiply the inner terms: -3 * x = -3x
4. Multiply the last terms: -3 * 5 = -15
5. Combine all the resulting terms:
2x^3 + 10x^2 - 3x - 15
So, the product of (2x^2 − 3)(x + 5) is 2x^3 + 10x^2 - 3x - 15.