Question

[Chau, Bao Pham]

b1. Phân tích đthức -> nhân tử.

a) x^3 - 3x^2 - 4x +13

b) x^4 - 5x^2 +4

c) (x+y+z)^3 -x^3 - y^3 - z^3

d) 45+ x^3 -5x^2 - 9x

e) x^4 - 2x^3 - 3x^3 - 2x -3

b2. tìm GTLN hoặc GLNN

a) A = 2x^2 - 8x - 10 -> GTNN

b) B = 9x - 3x^2 -> GTLN

Answer 1

[Khánh Ngọc]

2. a. \(A=2x^2-8x-10=2\left(x^2-4x+4\right)-18\)

\(=2\left(x-2\right)^2-18\)

Vì \(\left(x-2\right)^2\ge0\forall x\)\(\Rightarrow2\left(x-2\right)^2-18\ge-18\)

Dấu "=" xảy ra \(\Leftrightarrow2\left(x-2\right)^2=0\Leftrightarrow x-2=0\Leftrightarrow x=2\)

Vậy minA = - 18 <=> x = 2

b. \(B=9x-3x^2=-3\left(x^2-3x+\frac{9}{4}\right)+\frac{27}{4}\)

\(=-3\left(x-\frac{3}{2}\right)^2+\frac{27}{4}\)

Vì \(\left(x-\frac{3}{2}\right)^2\ge0\forall x\)\(\Rightarrow-3\left(x-\frac{3}{2}\right)^2+\frac{27}{4}\le\frac{27}{4}\)

Dấu "=" xảy ra \(\Leftrightarrow-3\left(x-\frac{3}{2}\right)^2=0\Leftrightarrow x-\frac{3}{2}=0\Leftrightarrow x=\frac{3}{2}\)

Vậy maxB = 27/4 <=> x = 3/2

Answer 2

[FL.Han_]

Sửa đề:x³-3x²-4x+12

a,x³-3x²-4x+12

=(x³-3x²)-(4x+12)

=x²(x-3)-4(x-3)

=(x²-4)(x-3)

b,x⁴- 5x² +4

x⁴-4x²-x²+4

(x⁴-x²)-(4x²+4)

x²(x²-1)-4(x²-1)

(x²-4)(x²-1)