Question

Câu 1: Phân tích đa thức thành nhân tử:

a) (x² + y² - 36)² - 4x²y²

b) (x² + x)² - 5(x² + x) + 6

Câu 2: Tìm a để:

a) (2x² - 5x + a) chia hết cho (x+5)

b) (3x³ - x² + ax – 4) chia hết cho (x+2)

c) (ax⁴ - 4x³ + 3x² - 2x + 5) chia hết cho (x-1)

 

Answer 1

Câu 1:

a) \(\left(x^2+y^2-36\right)^2-4x^2y^2\)

\(=\left(x^2+y^2-36\right)^2-\left(2xy\right)^2\)

\(=\left(x^2+y^2+2xy-36\right)\left(x^2+y^2-2xy-36\right)\)

\(=\left[\left(x+y\right)^2-36\right]\left[\left(x-y\right)^2-36\right]\)

\(=\left(x+y+6\right)\left(x+y-6\right)\left(x-y+6\right)\left(x-y-6\right)\)

b) \(\left(x^2+x\right)^2-5\left(x^2+x\right)+6\)

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

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

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

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

Answer 2

1) a) (x² + y² - 36)² - 4x²y² 

= (x² + y² - 36 - 2xy)(x² + y² - 36 + 2xy)

= [(x - y)² - 36][(x + y)² - 36]

= (x - y - 6)(x - y  + 6)(x + y + 6)(x + y - 6)

b) (x² + x)² - 5(x² + x) + 6

= (x² + x)² - 2(x² + x) - 3(x² + x) + 6

= (x²  + x)(x² + x - 2) - 3(x² + x - 2)

= (x² + x - 3)(x² + 2x - x - 2)

=  (x² + x - 3)(x - 1)(x + 2)

2) Đặt tính là đc

Answer 3

Câu 2;

Áp dụng định lý Bezout,ta được:

a) \(f\left(-5\right)=2.\left(-5\right)^2-5.\left(-5\right)+a=0\)

\(\Leftrightarrow50+25+a=0\Leftrightarrow a=-75\)

b) \(f\left(-2\right)=3.\left(-2\right)^3-\left(-2\right)^2+a.\left(-2\right)-4=0\)

\(\Leftrightarrow-24-4-2a-4=0\Leftrightarrow a=-16\)

c) \(f\left(1\right)=a.1^4-4.1^3+3.1^2-2.1+5=0\)

\(\Leftrightarrow a-4+3-2+5=0\Leftrightarrow a=-2\)

Answer 4

Câu 1:

a) =(x²  + y² - 36 - 2xy) (x² +y²-36+ 2xy)

= [(x-y)²-6² ] [(x+y)²-6² ]

=(x-y+6)(x-y-6)(x+y-6)(x+y+6)

b) Đặt x² +x=t. => t² - 5t + 6 = (t-3)(t-2). Thay vào ta được : (x² +x -3)(x² +x-2)

Answer 5

câu 1: \(\left(x^2+y^2-36\right)^2-4x^2y^2=\left(x^2+y^2-36\right)^2-\left(2xy\right)^2\)

=\(\left[\left(x^2+y^2-36\right)-2xy\right].\left[\left(x^2+y^2-36\right)+2xy\right]\)

=\(\left[\left(x^2+y^2-2xy\right)-36\right].\left[\left(x^2+y^2+2xy\right)-36\right]\)

=\(\left[\left(x-y\right)^2-6^2\right].\left[\left(x+y\right)^2-6^2\right]\)

=\(\left[\left(x-y-6\right).\left(x-y+6\right)\right].\left[\left(x+y-6\right)\left(x+y+6\right)\right]\)

b) A= (x²+x)²- 5 (x²+x)+6 

ĐẶt (x²+x) = m

khi đó A= m²-5m+6 = m²-2m - 3m +6 = m.(m-2) - 3.(m-2)=(m-2).(m-3)

A= (x²+x - 2) . ( x²+x -3) = (x-1).(x+2).( x²+x -3)