a, Để f(x) có nghiệm thì f(x) = 0

Hay: 4x² - x = 0 ⇒ x(4x - 1) = 0 \(\Rightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{1}{4}\end{matrix}\right.\)

Vậy...

b, Để f(x) có nghiệm thì f(x) = 0

Hay: x² - 121 = 0 ⇒ x² = 121 ⇒ \(\left[{}\begin{matrix}x=11\\x=-11\end{matrix}\right.\)

Vậy...

c, Để f(x) có nghiệm thì f(x) = 0

Hay: 5x + 2 = 0 \(\Rightarrow x=-\dfrac{2}{5}\)

Vậy...

d, Để đa thức có nghiệm thì 5x² - 7x - 6 = 0

⇒ 5x² - 10x + 3x - 6 = 0

⇒ 5x(x - 2) + 3(x - 2) = 0

⇒ (x - 2)(5x + 3) = 0

\(\Rightarrow\left[{}\begin{matrix}x=2\\x=\dfrac{-3}{5}\end{matrix}\right.\)

Vậy...

a) \(4x^2-7x+5=\left(x+2\right)\left(2x-9\right)\)

\(\Leftrightarrow4x^2-7x+5=2x^2-5x-18\)

\(\Leftrightarrow2x^2-2x+23=0\)

\(\Rightarrow\Delta=b^2-4ac=\left(-2\right)^2-4\cdot1\cdot23=-732< 0\)

Vậy pt vô nghiệm

b) \(-x^2-12x+21=\left(3-x\right)\left(x+11\right)\)

\(\Leftrightarrow-x^2-12x+21=-x^2-8x+33\)

\(\Leftrightarrow4x+12=0\Leftrightarrow x=-3\)

c) \(9x+5x^2+1=5x^2-22+13x\)

\(\Leftrightarrow4x-23=0\Leftrightarrow x=\frac{23}{4}\)

a) P (x) =11+5x³+3x²-9x⁶-(6x²+5-9x⁶-4x⁴)

             =11+5x³+3x²-9x⁶-6x²-5+9x⁶+4x⁴

             =4x⁴+5x³-3x²+6                           

Q(x)=(3x⁴-5x²)-4x²+x⁴-4x-1

       =3x⁴-5x²-4x²+x⁴-4x-1

       =4x⁴-9x²-4x-1

b) M(x) = 4x⁴+5x³-3x²+6 + 4x⁴-9x²-4x-1

            = 8x⁴+5x³-12x²-4x+5

N(x)= 4x⁴+5x³-3x²+6 - 4x⁴+9x²+4x+1

       = 5x³+6x²+4x+7

a) \(2x\left(x^2-7x-3\right)=2x.x^2-2x.7x-2x.3=2x^3-14x^2-6x\)

b) \(\left(-2x^3+y^2-7xy\right)4xy^2=\left(-2x^3\right)4xy^2+y^24xy^2-7xy.4xy^2=-8x^4y^2+4xy^4-28x^2y^3\)

c) \(\left(-5x^3\right)\left(2x^2+3x-5\right)=-5x^32x^2-5x^33x-5x^3.-5=-10x^5-15x^4+25x^3\)

d) \(\left(2x^2-xy+y^2\right)\left(-3x^3\right)=-3x^32x^2-3x^3.-xy-3x^3y^2=-6x^5+3x^4y-3x^3y^2\)

e) \(\left(x^2-2x+3\right)\left(x-4\right)=x\left(x^2-2x+3\right)-4\left(x^2-2x+3\right)=x^3-2x^2+3x-4x^2+8x-12=x^3-6x^2+11x-12\)

f) \(\left(2x^3-3x-1\right)\left(5x+2\right)=5x\left(2x^3-3x-1\right)+2\left(2x^3-3x-1\right)=10x^4-15x^2-5x+4x^3-6x-2=10x^4+4x^3-15x^2-11x-2\)

g)

\(\left(25x^2+10xy+4y^2\right).\left((5x-2y\right)\)

\(=125x^3-50x^2y+20x^2y-20xy^2+20xy^2-8y^3\)

\(=125x^3-30x^2y+8y^3\)

h)

\(\left(5x^3-x^2+2x-3\right)\left(4x^2-x+2\right)\)

\(=20x^5-5x^4+10x^3-4x^4+x^3-2x^2+8x^3-2x^2+4x-12x^2+3x-6\)

\(=20x^5-9x^4+19x^3-16x^2+7x-6\)

a,\(4x^2-14x^2-6x=-10x^2-6x\)

các câu còn lại làm tg tuj

a) 2x.(x² - 7x - 3)

= 2xx² + 2x(-7x) + 2x(-3)

= 2x²x - 2.7xx - 2.3x

= 2x³ - 14x² - 6x

Bài 1: P+Q=(5xyz+2xy-3x^2-11)+(15-5x^2+xyz-xy)

=5xyz+2xy -3x^2-11+15-5x^2+xyz-xy

=6xyz+xy-8x^2+4

P-Q=(5xyz+2xy-3x^2-11)-(15-5x^2+xyz-xy)

=5xyz+2xy -3x^2-11-15+5x^2-xyz-xy

=4xyz+xy+2x^2-26

Mình lm bài 1 thôi cn bài 2 thì mình ko có thời gian,nếu sai thì thôi nha

Thu gọn Q(x) = x4 + 7x2 + 1

Khi đó R(x) = Q(x) - P(x) = 4x2 + 3x + 2. Chọn A

Bài 2:

a) \(3x^2-7x-10=\left(x+1\right)\left(3x-10\right)\)

b) \(x^2+6x+9-4y^2=\left(x+3\right)^2-\left(2y\right)^2=\left(x+3-2y\right)\left(x+3+2y\right)\)

c) \(x^2-2xy+y^2-5x+5y=\left(x-y\right)^2-5\left(x-y\right)=\left(x-y\right)\left(x-y-5\right)\)

d) \(4x^2-y^2-6x+3y=\left(2x-y\right)\left(2x+y\right)-3\left(2x-y\right)=\left(2x-y\right)\left(2x+y-3\right)\)

e) \(1-2a+2bc+a^2-b^2-c^2=\left(a-1\right)^2-\left(b-c\right)^2=\left(a-1-b+c\right)\left(a-1+b-c\right)\)

f) \(x^3-3x^2-4x+12=\left(x+2\right)\left(x-3\right)\left(x-2\right)\)

g) \(x^4+64=\left(x^2+8\right)^2-16x^2=\left(x^2+8-4x\right)\left(x^2+6+4x\right)\)h) \(x^4-5x^2+4=\left(x+2\right)\left(x+1\right)\left(x-1\right)\left(x-2\right)\)

i) \(\left(x+1\right)\left(x+3\right)\left(x+5\right)\left(x+7\right)+16=\left(x^2+8x+7\right)\left(x^2+8x+15\right)+16=\left(x^2+8x+7\right)^2+8\left(x^2+8x+7\right)+16=\left(x^2+8x+11\right)^2\)

a: \(3x^2-7x-10\)

\(=3x^2+3x-10x-10\)

\(=\left(x+1\right)\left(3x-10\right)\)

b: \(x^2+6x+9-4y^2\)

\(=\left(x+3\right)^2-4y^2\)

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

c: \(x^2-2xy+y^2-5x+5y\)

\(=\left(x-y\right)^2-5\left(x-y\right)\)

\(=\left(x-y\right)\left(x-y-5\right)\)

a) 

b) 

c) 

d) 

e) 

f) 

g) h) 

i) 

=>5x^3+4x^2+3x+3-4+x+4x^2-5x^3=5

=>8x^2+4x-1-5=0

=>8x^2+4x-6=0

=>4x^2+2x-3=0

=>\(x=\dfrac{-1\pm\sqrt{13}}{4}\)