Question

when (x+2)^6 is written as a polynomial, what is the coefficient of the term containing x^4

a-15
b-60
c-120
d-6

Answer 1

Answer:

c-120

Step-by-step explanation:

Answer 2

When (x+2)⁶  is written as a polynomial, the coefficient of the term x⁴ is 60.

How to expand an expression to form a polynomial?

We have to expand (x+2)⁶ to form a polynomial.

A polynomial can have constants, variables and exponents, but never division by a variable.

Therefore, using pascal triangle, the appropriate row is 1 6 15 20 15 6 1.

Hence,

Substituting the appropriate powers of x and 2 gives 1x⁶2⁰ + 6x⁵2¹ + 15x⁴2² + 20x³2³ + 15x²2⁴ + 6x¹2⁵ + 1x⁰2⁶.

Finally,

x⁶ + 12x⁵ + 60x⁴ + 160x³ + 240x² + 192x + 64

Therefore, the coefficient of x⁴ is 60.

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