The first step in factorising the given polynomial is to identify the highest common factor.

The highest common factor in the coefficients (24, 42, 48, 24) is 6.

The highest common factor in the powers of a (a^10, a^8, a^7, a^5) is a^5.

So, the highest common factor of the entire polynomial is 6a^5.

Now, we divide each term of the polynomial by the highest common factor:

24a^10 ÷ 6a^5 = 4a^5
42a^8 ÷ 6a^5 = 7a^3
48a^7 ÷ 6a^5 = 8a^2
24a^5 ÷ 6a^5 = 4

So, the factorised form of the polynomial is:

6a^5(4a^5 + 7a^3 + 8a^2 + 4)

Question

The first step in factorising the given polynomial is to identify the highest common factor.

The highest common factor in the coefficients (24, 42, 48, 24) is 6.

The highest common factor in the powers of a (a^10, a^8, a^7, a^5) is a^5.

So, the highest common factor of the entire polynomial is 6a^5.

Now, we divide each term of the polynomial by the highest common factor:

24a^10 ÷ 6a^5 = 4a^5
42a^8 ÷ 6a^5 = 7a^3
48a^7 ÷ 6a^5 = 8a^2
24a^5 ÷ 6a^5 = 4

So, the factorised form of the polynomial is:

6a^5(4a^5 + 7a^3 + 8a^2 + 4)

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