Question

Consider the following polynomial functions. f(a) = (2a - 7 + a?) and g(a) = (5 – a).

Answer 1

Answer:

1 false

2 true

3 true

4 false

5 true

Step-by-step explanation:

f(a) = (2a - 7 + a^2) and g(a) = (5 – a).

1 false f(a) is a second degree polynomial and g(a) is a first degree polynomial

When added together, they will be a second degree polynomial

2. true  When we add and subtract polynomials, we still get a polynomial, so it is closed under addition and subtraction

3.  true  f(a) + g(a) = (2a - 7 + a^2) + (5 – a)

Combining like terms = a^2 +a -2

4.  false   f(a) - g(a) = (2a - 7 + a^2) - (5 – a)

Distributing the minus sign (2a - 7 + a^2) - 5 + a

Combining like terms  a^2 +3a -12

5.  true  f(a)* g(a)  = (2a - 7 + a^2)  (5 – a).

Distribute

                       (2a - 7 + a^2)  (5)  – (2a - 7 + a^2)  (a)

                        10a -35a +5a^2 -2a^2 -7a +a^3

Combining like term

-a^3 + 3 a^2 + 17 a - 35

Answer 2

Answer:

Statement 2,3 and 5

Step-by-step explanation:

The sum, difference and product of two (or more) polynomials is also a polynomial.

Statement 2 is correct

Sum:

(a² - 7 + 2a) + (5 - a)

a² + 2a - a - 7 + 5

a² + a - 2

Statement 3 is correct

This is a degree 2 polynomial so

Statement 1 is incorrect

Difference:

(a² - 7 + 2a) - (5 - a)

a² + 2a + a - 7 - 5

a² + 3a - 12

Statement 4 is incorrect

Product:

(a² + 2a - 7) × (-a + 5)

-a³ + 5a² - 2a² + 10a + 7a - 35

-a³ + 3a² + 17a - 35

Statement 5 is correct