Question

Guys help me with the following question attached below, these questions are from chapter POLYNOMIALS

Answer 1

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i)1-64a³-12a+48a²

1³-64a³-12a+48a²

Using (x-y)³=x³-y³-3xy²+3x²y

Here, x=1 & y=4a

1³-64a³-12a+48a²:-

=(1-4a)³

=(1-4a)(1-4a)1-4a)

ii) x³-8x²+17x-10

Using Factor theorem, Let's take x=1

1³-8×1²+17×1-10

1-8+17-10

18-18

0

x=1 gives 0

=(x-1)

iii) a³-b³+1+3ab

a³-b³+1³+3ab

Using x³+y³+z³-3xyz=(x+y+z) (x²+y²+z²-xy-yz-zx)

x=a, y=b & z=1

a³-b³+1+3ab:-

=(a+b+1) (a²+b²+1-ab-b-a)

iv) (a+2b)²+101(a+2b) +100

Let (a+2b) =x

x²+101x+100

x²+100x+x+100

x(x+1) +100(x+1)

=(x+100) (x+1)

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