b. -3x^3+30x^2-76x-5
c. -3x^3-76x-5
d. -3x^3+30x^2+74x-5
The given expression can be simplified to obtain -3x³ + 74x - 5. The correct option is (a).
An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.
The variable part of an algebraic expression can never be added or subtracted from the constant part.
The given algebraic expression is (x + 5)(-3x² + 15x - 1).
It can be evaluated as follows,
(x + 5)(-3x² + 15x - 1)
⇒ x(-3x² + 15x - 1) + 5(-3x² + 15x - 1)
⇒ -3x³ + 15x² - x - 15x² + 75x - 5
⇒ -3x³ + 74x - 5
Hence, the product of the given expression is -3x³ + 74x - 5.
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Answer:
-3x^3+74x-5
Step-by-step explanation:
(x+5)(-3x^2+15x-1)
-3x^3+15x^2-x-15x^2+75x-5
-3x^3+15x^2-15x^2+75x-x-5
-3x^3+74x-5
d.
Given : p(x) = x⁵
p(-x) = (-x)⁵
p(-x) = (-1)⁵(x)⁵
p(-x) = -(x)⁵
0.5p(-x) = -0.5(x)⁵
0.5p(-x) + 4 = -0.5(x)⁵ + 4
m(x) = -0.5(x)⁵ + 4
e.
Given : p(x) = x⁴
p(0.5x) = (0.5x)⁴
p(0.5x) = (0.5)⁴(x)⁴
-p(0.5x) = -(0.5)⁴(x)⁴
-p(0.5x) + 2 = -(0.5)⁴(x)⁴ + 2
m(x) = -(0.5)⁴(x)⁴ + 2
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