(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...
(i) x ^ 3 −2x ^ 2 −x+2 =x ^ 2 (x−2)−1(x−2) =(x−2)(x ^ 2 −1) =(x−2)(x+1)(x−1) (ii) x ^ 3 −3x ^ 2 −9x−5 =x ^ 3 −5x ^ 2 +2x ^ 2 −10x+x−5 =x ^ 2 (x−5)+2x(x−5)+1(x−5) =(x
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,...
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 ...
2(b)(i)( 5 x - 4)(3 x + 2 )oe final answer 2(b)(i)4/5oeand-2/3oe 2(b)(i) B1 for (ax +b)(cx +d) where either ac = 15 and bd =-8 or ad + bc =-2 or 5x(3x+ 2)-4(3x+2) or 3x(5x-4)+ 2(5x-4) or correct factors seen and spoiled FT a fac...
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....
5. Factorise:(a) x^3+1/(x^3) (b) a^3-1/(b^3) () (a^3)/(27)+(b^3)/(64) (d) (x^3)/(27)-(125)/(y^3) () (27x^3)/(64)+1 相关知识点: 试题来源: 解析 c)( (C (a/3+a/4)((a^2)/9-(ab)/(12)+(b^2)/(16)) e) (-(3x)/4+1...
【题目】Questions that require solutions(1)Factorise:3ax+4by+4ay+3bx .(2)Factorise:x^2-2xy-a^2+y^2 (3)Factorise:7x^2-3y+xy-21x .(4)Factorise:4a^2-4(ab+4)+b^2 .(5)Factorise:x^2-4xy+4y^2-2x+4y-3 .(6)Factorise:a^2-a^2b+ab^2-a+b-b^2. ...