Question
Factorise:
4x4 + 7x2 - 2
4x4 + 7x2 - 2
✓
Answer
Let x2 = y
Then, 4x4 + 7x2 - 2
= 4y2 + 7y - 2
= 4y2 + 8y - y - 2
= 4y(y + 2) - 1(y + 2)
= (y + 2)(4y - 1)
Now replacing y by x2, we get
4x4 + 7x2 - 2
= (x2 + 2)(4x2 - 1) Since a2 - b2 = (a - b)(a + b)
= (x2 + 2)(2x + 1)(2x - 1)
Then, 4x4 + 7x2 - 2
= 4y2 + 7y - 2
= 4y2 + 8y - y - 2
= 4y(y + 2) - 1(y + 2)
= (y + 2)(4y - 1)
Now replacing y by x2, we get
4x4 + 7x2 - 2
= (x2 + 2)(4x2 - 1) Since a2 - b2 = (a - b)(a + b)
= (x2 + 2)(2x + 1)(2x - 1)
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