Week 11 in Math 10

What we learned Week 11 in Math 10 is to factor when the degree of a polynomial is more than 2. (for examples 4, 6, et cetera.) The bases of factoring polynomials are C, D, P, E, and U.

C has used the polynomial which can be divided into common factors.

3x2 + 6x = 3x(x + 2)

D is differences of squares, it is used when the polynomials are perfect squares.

16 – x2y2 = (4 – xy)(4 + xy)

P is to find the pattern of the polynomial.

x2 + 6x – 7 = (x + 7)(x – 1)

E is used by easy polynomials which can be used the easiest pattern.

x2 + 4x + 4 = (x + 2)2

U is used by ugly polynomials. (We usually use a square to factor.)

6x2 + 13x + 6 = (2x + 3)(3x + 2)

We can use the bases and solve the polynomials which degree is bigger than 2. We also learned the pattern about a degree. When the degree is bigger than 2, other exponents of x must be half of the degree if there are not any common factors, and it cannot be factored if it is not.

For an example, 32x4 – 2 can be divided by 2 (Greatest common factor) and it becomes 2(16x4 – 1). 16x4 and -1 are perfect squares, we can use D. 2(16x4 – 1) = 2(42 + 1)(42 – 1). 42 – 1 is even perfect square which can be used D, but 42 + 1 is not because the binomial must have ONE minus sign. 2(42 + 1)(42 – 1) = 2(42 + 1)(2x + 1)(2x – 1). So, the answer is 2(42 + 1)(2x + 1)(2x – 1).

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