10 Factoring Cross Method Exercise 5

2.(x+1)(x+2)-x-10

5.(x -x) -18 (x -x) + 72 Answer: 1(2x+y)(3a-b)

2.(x+4)(x-2)

3.(y+1)(y-1)(x+1)(x-1)4.(3+a-2b)(3-a+2b)

5.(x+3)(x-4)(x+2)(x-3)6.(a-b-5)(a-b+2)

7.(5x-1)²

8.(ab+4)(ab-5)

9.(x+10y)(x+15y)

10.(3x-y+10) (3x-y-10) These are all things I have done, don't worry, the answer is definitely right, not enough! ~~o(∩_o~

。2. 5xn+1－15xn＋60xn--1。

3.4. (a+b)2x2-2(a2-b2)xy+(a-b)2y25. x4-1

6.2 2ab defactoring.

12．3x2+5x-2

13. (x+1)(x+2)(x+3)(x+4)+114. (x2+3x+2)(x2+7x+12)-120.

15 Factor the polynomial 3x2+11x+10.

16.Factor the polynomial 5x2 6xy 8y2.

40.Factorization (x 2) (x 3) (x 2) (x 4).

41.Factoring 2ax2 3x 2ax 3.

42.Factorization 9x2 66x 121.

43.Factoring 8 2x2.

44.Factoring x2 x 14

45.Factorization 9x2 30x25.

46.Factoring 20x2 9x 20.

47.Factoring 12x2 29x 15.

48.Factoring 36x2 39x9.

49.Factoring 21x2 31x 22.

50.Factoring 9x4 35x2 4.

51.Factorization (2x 1) (x 1) (2x 1) (x 3).

52.Factoring 2ax2 3x 2ax 3.

53.Factoring x(y 2) x y 1.

54.Factoring (x2, 3x) (x3)2.

55.Factorization 9x2 66x 121.

56.Factoring 8 2x2.

57.Factorization x4 1.

58.Factoring x2 4x xy 2y 4.

59.Factoring 4x2 12x5.

60.Factoring 21x2 31x 22.

61.Factoring 4x2 4xy y2 4x 2y 3.

62.Factorization 9x5 35x3 4x.

Cross decomposition formula: The left side of the Fenghe cross is multiplied equal to the quadratic term coefficient, the right side multiplied is equal to the constant term, and the cross multiplication and then added is equal to the primary term coefficient.

In fact, it is to use the inverse operation of the multiplication formula (x+a)(x+b)=x + (a+b)x+ab to factorize.

For an integer like ax +bx+c=(a1x+c1)(a2x+c2), the key to this method is to decompose the quadratic coefficient a into the product of the two factors a1 and a2, and the constant term c into the product of the two factors c1 and c2, so that a1c2+a2c1 is exactly equal to the coefficient b of the primary term. Then you can write the result directly: ax +bx+c=(a1x+c1)(a2x+c2).

When using this method to decompose factors, it is important to observe, try, and realize that it is essentially the inverse process of binomial multiplication. When the first coefficient is not 1, it often takes several tests, and it is important to pay attention to the symbols of each coefficient. Basic formula:

x²+(p+q）x+pq=(x+p）(x+q）。

Cross multiplicationIt is an applicationPerfectly squared formulaNo, you can'tFactorizationAnother basic approach that needs to be prioritizedIt is based on the formula x 2 + (a + b) x + ab = x 2 + (a + b) x + ab = (x + a) (x + a) (x + b) (x + b) from the multiplicative identity (x+a) (x+b).

In a sense, the cross multiplication method is also the use of the macro laughter formula method.

It is for quadratic coefficients.

is a quadratic trinomial of 1.

x 2 + px + q is the third basic method of decomposition.

The idea of using this method is to find two numbers a and b so that their product ab is equal to the constant term.

q, and the sum is equal to the coefficient p. Once you have found these two numbers, you can decompose the polynomial x 2+px+q to (x+a)(x+b).

Precautions when using cross multiplication factoring1. The above method is aimed at the quadratic trinomial formula with a quadratic term coefficient of 1, and if the quadratic term coefficient is not 1, the decomposition idea is the same.

2. When the quadratic term has a negative sign "", the negative sign "" is extracted first and then decomposed.

3. If the polynomial has a common factor, it still needs to be extracted first.

4. Don't forget the perfect square formula.

5. The quadratic trinomial formula of the double letter can still be multiplied by cross.

6. After decomposition, the factor should be calculated, simplified and organized, and those that can continue to be decomposed should continue to be decomposed.

After presenting x, 1

After presenting x, 3

Decompose after two beats.

Decompose after two times.

Think of 2x-3 as a number.

Think of x 2+8x as a base argument orange number.

Let's try it out on your own.