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Hi someone help with these two questions. Thanks

Hi someone help with these two questions. Thanks-example-1
User Foibs
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1 Answer

2 votes

Answer:

1). Option (d)

2). Options (a), (b) and (d)

Explanation:

Question 1

a).
3x^5-6x^3+9x-12x^(-1)

Any expression with negative exponent is not a polynomial.

b).
4√(x)+5

Any expression having variable with square root is not a polynomial.

c).
(4x+5)/(3x-1)

Any expression having variables in the form of a fraction is not a polynomial.

d).
-(3)/(2)x^(12)-7x^5+(2)/(3)x-10

It's a polynomial.

e).
-5x^{(3)/(2)}-7x^2+6

Expressions having variables with square root are not the polynomial.

Therefore, Option (d) is a polynomial.

Question 2.

P(x) = (2x + 1)(5x³ - 8x + 4)

= 2x(5x³ - 8x + 4) + 1(5x³ - 8x + 4)

= 10x⁴ - 16x² + 8x + 5x³ - 8x + 4

= 10x⁴ - 5x³ - 16x²+ 4

a). Degree of polynomial = 4

True

b). P(0) = 10(0) - 5(0) - 16(0) + 4

= 4

True

c). P(-1) = 10(-1)⁴ - 5(-1)³ - 16(-1)² + 4

= 10 + 5 - 16 + 4

= 3

False

d). Coefficient of x₂ is -16.

True

e). Coefficient of x is -16

False

Therefore, Options (a), (b) and (d) are correct.

User Dongx
by
7.1k points

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