An expression with three terms where the power of the first term is twice that of the second and the third term is a constant is called a quadratic type expression. They factor in the same way as quadratic polynomials. The power on x in the factorization will be the power on x in the middle term. To see the effect of changing the exponents, let us look at x2 – 2x – 3 = (x – 3) (x + 1):
x4 – 2x2 – 3 = (x2 – 3)(x2 + 1)
x6 – 2x3
– 3 = (x3 – 3)(x3 + 1)
x10 – 2x5 – 3 = (x5 –
3)(x5 + 1)
x–4 – 2x–2
– 3 = (x–2 – 3)(x–2 + 1)
x2/3 – 2x1/3
– 3 = (x1/3 – 3)(x1/3
+ 1)
x1 – 2x1/2
– 3 = (x1/2 – 3)(x1/2 + 1)
Practice
1.
x4 – 3x2
+ 2 =
2.
x– 6 – 3x–
3 + 2 =
3.
x + 6√x + 9 =
Solutions
1.
x4 – 3x2
+ 2 = (x2 – 2) (x2
– 1)
2.
x– 6 – 3x–
3 + 2 = (x–
3 – 2) (x– 3 – 1)
3.
x + 6√x + 9 = x
+ 6x1/2 + 9
= (x1/2 + 3) (x1/2 + 3)
= (x1/2 + 3)2
= (√x + 3)2
Sumber
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