Problem to solve
Factor the expression \[x^4-4x^2+4\]
Solution
STEP 1
Factor the following: x^4 - 4 x^2 + 4
STEP 2
Hint: | Try to identify x^4 - 4 x^2 + 4 as a binomial power by factoring the constant coefficient 4 = (-2)^2. Using x^4 - 4 x^2 + 4 = (x^2)^2 + 2 (x^2) (-2) + (-2)^2, the absolute value of the coefficients match the 3^rd row of Pascal's triangle. Since they are alternating in sign and the leading coefficient is positive, the polynomial factors into (x^2 - 2)^2: Answer: | | (x^2 - 2)^2
More problems
Number
001Factor the expression \(3x^4-17x^3+9x^2+41x+12\)
002Factor the expression \(4x^3+20x^2+13x-12\)
003Factor the expression \(x^4-4x^2+4\)
004Factor the expression \(6x^4+27x^3+27x^2-24x-36\)
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Edited by tododemate® - 2021