c: \(x^3-8x^2+x+42\)

\(=x^3+2x^2-10x^2-20x+21x+42\)

\(=\left(x+2\right)\left(x^2-10x+21\right)\)

\(=\left(x+2\right)\left(x-3\right)\left(x-7\right)\)

a: \(x^3+6x^2+11x+6\)

\(=x^3+3x^2+3x^2+9x+2x+6\)

\(=\left(x+3\right)\left(x^2+3x+2\right)\)

\(=\left(x+3\right)\left(x+1\right)\left(x+2\right)\)

g) (x+2)(x+3)(x+4)(x+5)-24 = \(\left[\left(x+2\right)\left(x+5\right)\right]\left[\left(x+3\right)\left(x+4\right)\right]-24\)

                                       =\(\left[x^2+7x+10\right]\left[x^2+7x+12\right]\)

đặt \(x^2+7x+10=a\)

ta có \(a\left(a+2\right)-24=a^2+2a-24\)

                                      \(=a^2+2a+1-25\)

                                      \(=\left(a+1\right)^2-5^2\)

                                      \(=\left(a+1-5\right)\left(a+1+5\right)\)

                                     \(=\left(a-4\right)\left(a+6\right)\)

\(\Rightarrow\) \(\left(x^2+7x+10-4\right)\left(x^2+7x+10+6\right)=\left(x^2+7x+6\right)\left(x^2+7x+16\right)\)

a) = (x +5)² - 2² = (x+5 -2)(x+5 +2) = (x+3)(x+7)

b) = x(x² -1) -6(x-1)= x(x+1)(x-1) -6(x-1) = (x-1)(x(x+1)-6)

a)\(\left(x+1\right)\left(x+2\right)\left(x+3\right)\)

b)\(\left(x-3\right)\left(x-7\right)\left(x+2\right)\)

c)\(\left(x-3\right)\left(x+3\right)\left(x+2\right)\left(x+1\right)\)

d)\(\left(x+5\right)\left(x-3\right)\left(x+1\right)\left(x+2\right)\)

a) x³ + 6x² + 11x + 6

= (x³ + x²) + (5x² + 5x) + (6x + 6)

= x²(x + 1) + 5x(x + 1) + 6(x + 1)

= (x² + 5x + 6)(x + 1)

= (x² + 2x + 3x + 6)(x + 1)

= [x(x + 2) + 3(x + 2)](x + 1)

= (x + 3)(x + 2)(x + 1)

b) x³ - 8x² + x + 42

= x³ + 2x² - 10x² - 20x + 21x + 42

= x²(x + 2) - 10x(x + 2) + 21(x + 2)

= (x² - 10x + 21)(x + 2)

= (x² - 3x - 7x + 21)(x + 2)

=[x(x - 3) - 7(x - 3)](x + 2)

=(x - 7)(x - 3)(x + 2)

c) x⁴ + 3x³ - 7x² - 27x - 18

= x⁴ + x³ + 2x³ + 2x² - 9x² - 9x - 18x - 18

= x³(x + 1) + 2x²(x + 1) - 9x(x + 1) - 18(x + 1)

= (x³ + 2x² - 9x - 18)(x + 1)

= [x²(x + 2) - 9(x + 2)](x + 1)

=(x² - 9)(x + 2)(x + 1)

= (x - 3)(x + 3)(x + 2)(x + 1)

d) x⁴ + 5x³ - 7x² - 41x - 30

= x⁴ + x³ + 4x³ + 4x² - 11x² - 11x - 30x - 30

= x³(x + 1) + 4x²(x + 1) - 11x(x + 1) -30(x + 1)

= (x³ + 4x² - 11x - 30)(x + 1)

= (x³ + 2x² + 2x² + 4x - 15x - 30)(x + 1)

= [x²(x + 2) + 2x(x + 2) - 15(x +2)](x + 1)

=(x² + 2x - 15)(x + 2)(x + 1)

= (x² - 3x + 5x - 15)(x + 2)(x +1)

= [x(x - 3) + 5(x - 3)](x + 2)(x + 1)

= (x - 3)(x + 5)(x + 2)(x + 1)

NHỚ TIK CHO MIK NHA, đừng có mà đọc suông xong bỏ đi đấy. mik là đầy đủ hơn cái bn ở dưới nên cho mik nhiều tik hơn nhé

một đòn bẫy dài một mét .đặt ở đâu để có thể dùng 3600n có thể nâng tảng đá nặng 120kg?

$\textbf{5)}$

$(4x-5)(x+2)-(x+5)(x-3)-3x^2-x$

$=(4x^2+3x-10)-(x^2+2x-15)-3x^2-x$

$=4x^2+3x-10-x^2-2x+15-3x^2-x$

$=5.$

Dài 166

b) 2x²+3x-27=2x²-6x+9x-27=2x(x-3)+9(x-3)=(x-3)(2x+9)

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