Question

Розкладіть на множники: 1) ab+ac+ad+bx+cx+dx2) 7p − 7k − px + kx + k − p3)x²+8x+124) x²− 4 − 325) x³+ 2x²− 36x − 726) x³y²− x³− xy²+ x

Answer 1

1) ab+ac+ad+bx+cx+dx = a(b+c+d) + x(b+c+d) = (b+c+d)(a+x)

2) 7p − 7k − px + kx + k − p = 7(p-k) - x(p-k) - (p-k) = (p-k)(7-x-1) = (p-k)(6-x)

3)x²+8x+12 = x² + 6x + 2x + 12 = x(x+6) + 2(x+6) = (x+2)(x+6)

4) x²− 4 − 32 = x² - 36 = (x-6)(x+6)

5) x³+ 2x²− 36x − 72 = x²(x+2) - 36(x+2) = (x²-36)(x+2) = (x-6)(x+6)(x+2)

6) x³y²− x³− xy²+ x = x³(y²-1) -x(y²-1) = (x³-x)(y²-1) = x(x²-1)(y-1)(y+1) = x(x-1)(x+1)(y-1)(y+1)

Answer 2

1. ab + ac + ad + bx + cx + dx can be factored as follows:

ab + ac + ad + bx + cx + dx = a(b + c + d) + x(b + c + d) = (a + x)(b + c + d)

2. 7p - 7k - px + kx + k - p can be factored as follows:

7p - 7k - px + kx + k - p = 7(p - k) - x(p - k) + (k - p) = (7 - x)(p - k) + (k - p) = -(x - 7)(p - k) + (k - p)

3. x² + 8x + 12 can be factored as follows:

x² + 8x + 12 = (x + 6)(x + 2)

4. x² - 4 - 32 can be factored as follows:

x² - 4 - 32 = (x - 6)(x + 6)

5. x³ + 2x² - 36x - 72 can be factored as follows:

x³ + 2x² - 36x - 72 = (x - 6)(x + 6)(x + 2)

6. x³y² - x³ - xy² + x can be factored as follows:

x³y² - x³ - xy² + x = x(x²y² - x² - y² + 1)