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a) \(P=2x^2-7x+6\)
b) \(P=2x^2-7x+3\)
c) \(P=2x^2+9x-5\)
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10 tháng 11 2023
a: \(P=x^2-5x+6\)
\(=x^2-2x-3x+6\)
\(=x\left(x-2\right)-3\left(x-2\right)\)
\(=\left(x-2\right)\left(x-3\right)\)
b: \(P=3x^2+14x-5\)
\(=3x^2+15x-x-5\)
\(=3x\left(x+5\right)-\left(x+5\right)\)
\(=\left(x+5\right)\left(3x-1\right)\)
c: \(P=-2x^2-7x-5\)
\(=-\left(2x^2+7x+5\right)\)
\(=-\left(2x^2+2x+5x+5\right)\)
\(=-\left[2x\left(x+1\right)+5\left(x+1\right)\right]\)
\(=-\left(x+1\right)\left(2x+5\right)\)
7 tháng 7 2022
a) x2 - 7x + 5 = ( x2 - 2 . 7/2 . x + 49 / 4 ) + 5 - 49 / 4
= (x - 7/2)^2 - 29/4
= (x - 7/2)^2 - (√ 29 / 2 )^2
= ( x - ( 7 + √ 29 / 2 )). ( x + ( 7 - √ 29 / 2 ))
MH
25 tháng 10 2021
a) \(3x\left(2x-y\right)+5y\left(y-2x\right)\)
\(=3x\left(2x-y\right)-5y\left(2x-y\right)\)
\(=\left(3x-5y\right)\left(2x-y\right)\)
b) \(\left(x-5\right)^2-9\left(x+y\right)^2\)
\(=\left(x-5\right)^2-3^2\left(x+y\right)^2\)
\(=\left(x-5\right)^2-\left(3x+3y\right)^2\)
\(=\left(x-5+3x+3y\right)\left(x-5-3x-3y\right)\)
\(=\left(4x+3y-5\right)\left(-2x-3y-5\right)\)
25 tháng 10 2021
a: \(3x\left(2x-y\right)+5y\left(y-2x\right)=\left(2x-y\right)\left(3x-5y\right)\)
e: \(x^2-10x+24=\left(x-4\right)\left(x-6\right)\)
BA
19 tháng 6 2019
\(b,x^3-3x^2-4x+12\)
\(\Leftrightarrow x^2\left(x-3\right)-4\left(x-3\right)\)
\(\Leftrightarrow\left(x-3\right)\left(x^2-4\right)\)
\(\Leftrightarrow\left(x-3\right)\left(x-2\right)\left(x+2\right)\)
\(c,3x^3-7x^2+17x-5\)
\(\Leftrightarrow3x^3-x^2-6x^2+2x+15x-5\)
\(\Leftrightarrow x^2\left(3x-1\right)-2x\left(3x-1\right)+5\left(3x-1\right)\)
\(\Leftrightarrow\left(3x-1\right)\left(x^2-2x+5\right)\)
BA
19 tháng 6 2019
\(\text{d) 2x}^4- 7x^3 - 2x^2 + 13x + 6\)
\(\text{= (2x^4 + 2x^3) - (9x^3 + 9x^2) + (7x^2 + 7x) + (6x + 6)}\)
\(\text{= 2x^3(x + 1) - 9x^2(x + 1) + 7x(x + 1) + 6(x + 1)}\)
\(\text{= (x + 1)(2x^3 - 9x^2 + 7x + 6)}\)
\(\text{= (x + 1)(2x + 1)(x - 3)(x - 2)}\)
PQ
1
1 tháng 11 2015
a) x3 - 7x - 6 = x3 + x2 - x2 - x - 6x - 6
= x2(x + 1) - x(x + 1) - 6(x + 1)
= (x + 1)(x2 - x - 6)
= (x + 1)(x2 + 2x - 3x - 6)
= (x + 1)[x(x + 2) - 3(x + 2)]
= (x + 1)(x + 2)(x - 3)
KL
1
20 tháng 8 2018
\(2x^4+7x^3-2x^2-13x+6\)
\(=2x^4+6x^3+x^3+3x^2-5x^2-15x+2x+6\)
\(=2x^3\left(x+3\right)+x^2\left(x+3\right)-5x\left(x+3\right)+2\left(x+3\right)\)
\(=\left(2x^3+x^2-5x+2\right)\left(x+3\right)\)
\(=\left(2x^3+4x^2-3x^2-6x+x+2\right)\left(x+3\right)\)
\(=\left[2x^2\left(x+2\right)-3x\left(x+2\right)+\left(x+2\right)\right]\left(x+3\right)\)
\(=\left(2x^2-3x+1\right)\left(x+2\right)\left(x+3\right)\)
\(=\left(2x^2-2x-x+1\right)\left(x+2\right)\left(x+3\right)\)
\(=\left[2x\left(x-1\right)-\left(x-1\right)\right]\left(x+2\right)\left(x+3\right)\)
\(=\left(2x-1\right)\left(x-1\right)\left(x+2\right)\left(x+3\right)\)
DT
3
22 tháng 12 2021
\(a,=5x^2-5x+3x-3=\left(x-1\right)\left(5x+3\right)\\ b,=2x^2-5x+2x-5=\left(2x-5\right)\left(x+1\right)\\ c,=x^2+5x-3x-15=\left(x+5\right)\left(x-3\right)\\ d,=7x^2-7x+x-1=\left(x-1\right)\left(7x+1\right)\)
PA
1
30 tháng 9 2021
a) \(=\left(x^2-6\right)\left(x^2-1\right)=\left(x^2-6\right)\left(x-1\right)\left(x+1\right)\)
b) \(=\left(x^2-1\right)\left(x^2+3\right)=\left(x-1\right)\left(x+1\right)\left(x^2+3\right)\)
c) \(=x^2\left(x-1\right)-x\left(x-1\right)+4\left(x-1\right)=\left(x-1\right)\left(x^2-x+4\right)\)
a: \(P=2x^2-7x+6\)
\(=2x^2-4x-3x+6\)
\(=2x\left(x-2\right)-3\left(x-2\right)\)
\(=\left(x-2\right)\left(2x-3\right)\)
b: \(P=2x^2-7x+3\)
\(=2x^2-6x-x+3\)
\(=2x\left(x-3\right)-\left(x-3\right)\)
\(=\left(x-3\right)\left(2x-1\right)\)
c: \(P=2x^2+9x-5\)
\(=2x^2+10x-x-5\)
\(=2x\left(x+5\right)-\left(x+5\right)\)
\(=\left(x+5\right)\left(2x-1\right)\)