( 1)x^4-7x^2+6
=(x^2- 1)(x^2-6)
= (x+1) (x-1) (x+√ 6) (x-√ 6) (cross multiplication)
(2)x^4-5x？ -36
=(x^2-9)(x^2+4)
= (x-3) (x+3) (x 2+4) (cross multiplication)
(3)4x^4-65x？ y？ + 16y^4
=(4x^2-y^2)(x^2- 16y^2)
=(2x-y)(2x+y)(x-4y)(x+4y) (cross multiplication)
(4)4a？ -B? +6a-3b
=(2a+b)(2a-b)+3(2a-b)
=(2a-b)(2a+b+3) (group decomposition method)
(5)(x？ -3)? -4x？
=x^4-6x^2+9-4x^2
=x^4- 10x^2+9
=(x^2- 1)(x^2-9)
= (x+1) (x-1) (x+3) (x-3) (cross multiplication)
(6)x？ (x-2)？ -9
=[x(x-2)-3][x(x-2)+3]
=(x^2-2x-3)(x^2-2x+3)
= (x-3) (x+ 1) (x 2-2x+3) (inverse application of square difference formula)
(7)(3x？ +2x+ 1)？ -(2x？ +3x+3)？ Did you miss a "-"in this question? If so, please refer to the following solution.
=(3x？ +2x+ 1+2x？ +3x+3)(3x？ +2x+ 1-2x？ -3x-3)
=(5x？ +5x+4)(x？ -x-2)
=(5x？ +5x+4)(x+ 1)(x-2) (inverse application of square difference formula)
(8)(x？ +x)？ - 17(x？ +x)+60
=(x^2+x- 12)(x^2+x-5)
= (x-3) (x+4) (x 2+x-5) (cross multiplication as a whole)
(9)(x？ +2 times)? -7(x？ +2x)-8
=(x^2+2x-8)(x^2+2x+ 1)
= (x+4) (x-2) (x+ 1) 2 (cross multiplication as a whole)
( 10)-7x？ y- 14xy？ +49x？ y？
=-7xy(x+2y+7xy) (common factor extraction method)
(Simplify before evaluating)
1/(a？ +3a) (a？ +3a+2) divided by (a+3) (a+ 1)-(2) (a+2), where a=√3.
Solution: The original formula = [(a+1) (a+2)] [a (a+3)] * [(a+3)/(a+1)] = (a+2)/2.
When a=√3, the original formula ①=√3/6.
The value is √3/6.
2/? Given |a-4|+(√b-9)=0, calculate (a? +ab) (b？ )*(a？ -ab) (a？ -B? The value of).
Solution: So a-4=0 and √b-9=0,
∴? A=4，b=8 1。
∴? The original formula = B2/A2 = 656116 = 410.0625.
That is, the value is 4 10.0625 (or 656116).
3/? If 4x-3 is a polynomial 4x? A factor of +5x+a, and find the value of a.
Solution: Let 4x-3 = 0,
X=3/4，
Substitute 4x 2+5x+a = 0,
9/4+ 15/4+a=0。
Solution: a=-6.
That is, a=-6.
4/? It is known that x-x is 1=? -? 3? , find the value of the fourth power of x+65438+0 of the fourth power of x.
Solution: ∵? x- 1/x=-3，
∴? x^2-2+ 1/x^2=9，
∴? x^2+ 1/x^2= 1 1，
∴? x^4+2+ 1/x^4= 12 1，
∴? x^4+ 1/x^4= 1 19.
The value is 1 19.
Just use your hands! ! ! ! ! ? Hope to adopt! ! ! ! ! ! ? TAT is very tired.