Answer:
1). Option (d)
2). Options (a), (b) and (d)
Step-by-step explanation:
Question 1
a). [tex]3x^5-6x^3+9x-12x^{-1}[/tex]
Any expression with negative exponent is not a polynomial.
b). [tex]4\sqrt{x}+5[/tex]
Any expression having variable with square root is not a polynomial.
c). [tex]\frac{4x+5}{3x-1}[/tex]
Any expression having variables in the form of a fraction is not a polynomial.
d). [tex]-\frac{3}{2}x^{12}-7x^5+\frac{2}{3}x-10[/tex]
It's a polynomial.
e). [tex]-5x^{\frac{3}{2}}-7x^2+6[/tex]
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.
