Answer:

In the picture attached, we have two questions.

⇒ Q1)

Now, the graph shows both the polynomials.

→ When h(x) is divided by (x - 3), the remainder is k.

→ When g(x) is divided by (x - 3), let the remainder be m

We know the remainder theorem: when a polynomial p(x) is divided by a linear polynomial (x - a), then the remainder is equal to p(a).

Since h(x) is divided by (x-3), the remainder is h(3) = k.

Since g(x) is divided by (x-3) remainder is g(x) = m

Looking at the graph, at x = 3, we can conclude:

⇒ h(3) > g(3)

⇒ k > m.

So, the remainder of g(x) when divided by (x-3) is less than k.

Option 1 is correct.

⇒ Q2)

Again, the remainder theorem can be used.

Since the desired remainder is 0, h(x) = 0,

Referring to the graph, h(x) is 0 only when x = -2.

Therefore (x+2) is a factor of the polynomial because (x+2=0), x= -2.

Therefore, Option ii is correct.