Question: Factorise out the highest common factor. If the highest common factor is 1, just retype the polynomial.
2p³ + 8p² = ?
(1) 2p² (p + 2)
(2) 2p² (p * 4)
(3) 2p³ (p + 4)
(4) 2p² (p + 4)
Solution:
REMEMBER : To factorise a polynomial, first find the highest common factor (HCF) of each monomial. Then factor out the highest common factor using the distributive property.
First, factorise each monomial and find the common factors.
2p³ = 2*p*p*p
8p² = 2*2*2*p*p
The common factors are 2, p and p. Multiply them to find the highest common factor.
2*p*p = 2p²
The highest common factor is 2p².
Now factorise out 2p².
2p³ + 8p²
= 2p²*p + 2p²*4
= 2p²(p + 4)
The factorised form of the polynomial is 2p²(p + 4).
Then the option is (4).
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