(i) Factorise: x3−3x2+x−3 1. Identify the polynomial: Let f(x)=x3−3x2+x−3.2. Check for rational roots: Use the Rational Root Theorem. We can test x=1 and x=3. - For x=1: f(1)=13−3(12)+1−3=1−3+1−3=−4(not a root) - For x=3: f(3)=33...
例如,对于$x^3 + 3x^2 + 3x + 1$,可以将其分组为$(x^3 + 3x^2) + (3x + 1)$,然后利用公式法和提取公因式进行分解。 因式分解在解决数学问题中的应用 因式分解在解决数学问题中具有广泛应用。在代数方程中,通过因式分解可以将方程转化为更简单的形式,便于求解。在不等式证明中,...
Factorise 12x^2-7x+1 00:56 Factorise : - 12x^(2)-7x+1 01:17 Factorise : - 2x^(2)+7x+3 01:09 Factorise (Using factor theorem ) : 3x^(3)-7x^(2)+8x-12 02:16 Factorise: x^(2) -7x+12 03:49 Factorise: x ^(2) - 7x- 30 01:28 Factorise the following algebraic expressi...
Considering theways of obtaining –3 gives:2x²-x-3 = (2x )(x )-1 +3+1-3 Note that these will+3-1 be multiplied by the-3+1 2 in the 2x termFrom the last of these we can obtain the middle middle term,(-3×x)+(1×2x) =-3x+2x=-xso2x²-x-3 = (2x-3)(x+1)....
(2)a^3-a^2+a-1=(3)x^3+x^2-x-1=(4)x^3+x^2+xy^2+y^2=(5)x^3-2x^2+3x-6= 相关知识点: 试题来源: 解析 (1)=(x^2+1)(x+1)(2)=(a^2+1)(a-1)(3)=(x+1)^2(x-1)(4)=(x^2+y^2)(x+1)(5)=(x^2+3)(x-2) (1)N/A.(2)N/A.(3)N/A...
(x+1)-1(x+1) again, regrouping the terms as the factors. (x 2 -1) (x+1) therefore, the factorisation of x 3 + x 2 –x – 1 gives (x 2 -1) (x+1) solved examples question 1: check whether x+3 is a factor of x 3 + 3x 2 + 5x +15. solution: let x + 3= 0 ...
x3+x−2. 因式分解x3+x−2. 相关知识点: 试题来源: 解析 (x−2)(x+1)2. 结果一 题目 Factorise x3+x−2.因式分解x3+x−2. 答案 (x−2)(x+1)2.x3−3x−2=x2−8−3(x−2)=(x−2)(x2+2x+4)−3(x−2)=(x−2)(x+1)2.相关推荐 1Factorise x3+x−2....
4(x+3)(x-3)(8+a)(8-a)(6(y+x)(y-x)3x(x+3)(x-3)8(2y+x)(2y-x)(4x+7y^2)(4x-7y^2) 10 2y(x-y) 结果一 题目 II. Fill in the blanks4 Factorise: x2-9 =Factorise:64-a^2=6F Factorise_2-x^2+y^2=Factorise: 3x^3-27x=3 Factorise: -x^2+4y^2=8Factorise: 16...
(1)Solution:x2 xy 8x 8y = x × x x × y 8 × x 8 × y=x(x y) 8(x y)=(x y)(x 8) (2)15xy - 6x 5y - 2 = 3×5×x×y-3×2×x×5xy-2= 3x (5y - 2) 1(5y - 2)= (5y - 2) (3x 1) (3)ax bx- ay - by = a × x b × x - a ...
x=-1 [Let find the factors of 3 which will make 4 (coefficient of x)]3=3* 1 [3+1=4]. Hence 3x+x=4x, then(split)x^2+4x+3&=x^2+3x+x+3 &=x(x+3)+1(x+3) &=(x+3)(x+1)(split)Solving (x+3)(x+1)=0, either(x+3)=0, then x=-3 or (x+1)=0, then x=...