Question

Hi someone help with these two questions. Thanks

Answer 1

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.