*s**4 - 5*s**3 - 7*s**2 - 5*s - 5. Let m(v) = 6*v**3 + 2*v**4 - 3*v**3 + 3*v + 4*v**2 - 4 + 7. Let b(r) = 6*c(r) + 10*m(r). Factor b(o).
2*o**2*(o - 1)*(o + 1)
Let o be -1 + (6/(-12))/(1/(-18)). Suppose 2*k = o*k. Factor -2/7*d**2 + 2/7 + k*d.
-2*(d - 1)*(d + 1)/7
Suppose -d = 3*j + d - 28, 0 = d - 2. Suppose -j + 5 = 2*a - 3*q, -9 = a - 4*q. Factor -9/2*g + 3 + 9/4*g**2 - 3/8*g**a.
-3*(g - 2)**3/8
Suppose 4*i - 650 + 57 = -3*p, 4*p + 20 = 0. Factor -2 - 151*s**2 + 2 - s**3 + i*s**2.
-s**2*(s - 1)
Let f be 8/36 - (-3)/27. Let s(o) be the first derivative of -f*o**6 - 4/3*o**2 - 3 + 8/3*o - 2*o**3 + 2/3*o**5 + 7/6*o**4. Suppose s(t) = 0. What is t?
-1, 2/3, 1, 2
Let d = -136 - -141. Factor -12 - 28*y**2 - 6*y**3 + 5*y**3 - d*y**3 + 46*y.
-2*(y - 1)*(y + 6)*(3*y - 1)
Suppose 3*h + h = 216. Let v = 56 - h. Factor 0 - 1/2*f**v + 1/2*f**4 + 0*f**3 + 0*f.
f**2*(f - 1)*(f + 1)/2
Let u(m) be the third derivative of -5*m**8/1344 + m**7/24 - 5*m**6/48 - 3*m**5/8 + 45*m**4/32 + 45*m**3/8 + 11*m**2 + 2*m. Factor u(o).
-5*(o - 3)**3*(o + 1)**2/4
Let s(k) = k**5 - k**4 + k**3 + k**2. Let x(r) = 5*r**5 + 15*r**3 - 4*r - 20*r**4 - 12*r + r**3 + 3*r**5 + 20*r**2. Let g(a) = -4*s(a) + x(a). Factor g(l).
4*l*(l - 2)**2*(l - 1)*(l + 1)
Let b(c) = c**3 - 5*c**2 + 9*c - 4. Let t be b(2). Suppose -3*n - n - 2*r + 10 = 0, t*n - 3 = r. Factor -2*z - 4/5 - 8/5*z**n - 2/5*z**3.
-2*(z + 1)**2*(z + 2)/5
Let s(q) be the first derivative of -q**6/27 - 14*q**5/45 - 4*q**4/9 + 32*q**3/27 - 97. Factor s(m).
-2*m**2*(m - 1)*(m + 4)**2/9
Let p be 1463/(-210) + 1 - -6. Let g(d) be the third derivative of 1/6*d**4 + 0*d + 0*d**3 + 5*d**2 + 0 + p*d**5. Factor g(w).
2*w*(w + 2)
Let z(u) be the third derivative of -2*u**7/105 - u**6/30 + u**5/3 - u**4/2 - u**2 - 196*u. Factor z(t).
-4*t*(t - 1)**2*(t + 3)
Let f(t) be the third derivative of 1/56*t**8 + 36*t**2 + 0 - 2/3*t**3 + 2/5*t**5 - 1/12*t**4 - 2/105*t**7 - 1/6*t**6 + 0*t. Factor f(a).
2*(a - 1)**3*(a + 2)*(3*a + 1)
Let r be ((-14)/(-35))/((-40)/(-25)). Let v(z) be the third derivative of 1/80*z**5 + 0 + r*z**3 + 0*z - 9*z**2 - 3/32*z**4. Factor v(i).
3*(i - 2)*(i - 1)/4
Let t(p) = -p**4 + 6*p - p**5 - 7*p - p**3 + 0*p**3 + p**2. Let y(w) = 9*w**5 - 11*w**4 - 6*w**3 + 56*w**2 - 36*w. Let x(h) = 4*t(h) + y(h). Factor x(z).
5*z*(z - 2)**2*(z - 1)*(z + 2)
Factor 2/5*f**4 + 6*f + 0 - 27/5*f**3 - 47/5*f**2.
f*(f - 15)*(f + 2)*(2*f - 1)/5
Suppose 0 = -6*o + 2*d + 12, 4*d = -22*o + 17*o + 10. Let 5/2*s**3 - 5/2*s**o + 0 + 0*s = 0. What is s?
0, 1
Let d(r) be the first derivative of 2*r**5/65 - 16*r**3/39 + 32*r/13 - 49. Solve d(c) = 0.
-2, 2
Let p(d) be the third derivative of d**7/630 - 11*d**6/720 + d**5/20 - d**4/36 - 2*d**3/9 + 172*d**2. What is n in p(n) = 0?
-1/2, 2
Let a = -41 + 49. Suppose 0 = -4*n + 4*p - 16, 0 = -2*p - 0*p + a. Factor 0 + 3/4*f**3 + n*f**4 + 1/2*f**2 - 1/4*f**5 + 0*f.
-f**2*(f - 2)*(f + 1)**2/4
Let x = 21968 - 21964. Let -8/5 - 6/5*n**x + 14/5*n**2 - 2/5*n**5 + 2/5*n**3 + 0*n = 0. What is n?
-2, -1, 1
Let d(i) be the first derivative of -i**3/6 - 9*i**2/4 - 7*i - 464. Find s, given that d(s) = 0.
-7, -2
Let t = 29 - 29. Find x, given that -7*x**3 - x**3 + 9*x**3 + t*x**2 - x**2 = 0.
0, 1
Let f = 25807 - 51581/2. Suppose -f*d - 3/2*d**2 + 0 = 0. Calculate d.
-11, 0
Let t be (-6)/(-15) + 173/5. Suppose -2*b = c, 4*c - 29*b - 20 = -33*b. Find i, given that 25*i**3 + 12*i**4 + 45*i**2 + t*i + 3*i**4 + 10 - c*i**4 = 0.
-2, -1
Let d(u) be the third derivative of u**5/30 - 9*u**4/2 + 169*u**2. What is x in d(x) = 0?
0, 54
Find k, given that k**5 + 104*k**3 - 195*k**4 - 675 - 378*k**2 - 1215*k - 41*k**3 + 224*k**4 + 127*k**3 = 0.
-15, -1, 3
Let z be (2*32/(-20))/(10/25). Let m be (z/36)/((-4)/6). Find x such that 2/3 - 1/3*x**2 - m*x = 0.
-2, 1
Let i = -1/23339 + 233393/70017. Factor 0 - 1/3*o**4 - i*o**3 + 0*o - 25/3*o**2.
-o**2*(o + 5)**2/3
Let h = 122 - 81. Let y = 43 - h. Let -3/5*l**4 + 9/5*l**3 + 6/5 - 9/5*l - 3/5*l**y = 0. What is l?
-1, 1, 2
Let p(y) be the first derivative of 0*y - y**2 - y**4 + 24 + 1/5*y**5 + 5/3*y**3. Suppose p(g) = 0. What is g?
0, 1, 2
Let w(h) = -13*h**5 - h**4 + 31*h**3 - 17*h**2 + 9*h. Let z(q) = -6*q**5 + 14*q**3 - 8*q**2 + 4*q. Let v(a) = 4*w(a) - 9*z(a). What is y in v(y) = 0?
-1, 0, 1, 2
Let r = -1/2646 - -3025/2646. Let r*h - 8/7 - 2/7*h**2 = 0. Calculate h.
2
Suppose g - 11 + 9 = 0. Suppose 0 = 3*p + g*p - 95. Find h such that -10*h**2 - 15*h**2 + p*h**2 - 8*h - 4*h**3 - 6*h**2 = 0.
-2, -1, 0
Let y(p) be the first derivative of 3*p**5/20 + 3*p**4/4 + p**3 + 8*p - 18. Let u(i) be the first derivative of y(i). Determine q, given that u(q) = 0.
-2, -1, 0
Factor 5*r**3 - 93*r - 85*r + 178*r.
5*r**3
Let n be 7/140*-7 + (-6)/(-10). Factor -1/2*j**4 - n*j**3 + 1/2*j**2 + 1/4*j**5 + 0 + 0*j.
j**2*(j - 2)*(j - 1)*(j + 1)/4
Let a = 1/111 - -73/111. Let s be ((-4)/5)/(-9*(-4)/(-30)). Find y such that 2/9 - 2/9*y**3 - a*y + s*y**2 = 0.
1
Let p(u) = -u**2 + 36*u - 151. Let j be p(31). Let f(r) be the first derivative of -1/7*r**2 + 0*r - 1/28*r**j - 9 + 1/7*r**3. Factor f(z).
-z*(z - 2)*(z - 1)/7
Let q = 23105/7 + -3293. Factor -q*a + 54/7 - 2/7*a**3 + 18/7*a**2.
-2*(a - 3)**3/7
Find s such that 4/3*s**4 + 0*s - 20/3*s**3 + 0 + 0*s**2 = 0.
0, 5
Let v(f) = f**3 + 2*f**2 + f + 22. Let m be v(0). Let a = m + -19. Factor 2*r**5 + 437*r**3 + 2*r**4 - 437*r**a.
2*r**4*(r + 1)
Let u(o) be the first derivative of -o**6/180 + o**5/90 + o**2/2 - 45*o + 5. Let f(c) be the second derivative of u(c). Factor f(t).
-2*t**2*(t - 1)/3
Let a = -2/1089 - -43/1452. Let v(n) be the second derivative of -2*n - a*n**4 - 1/6*n**2 + 0 + 1/9*n**3. Solve v(u) = 0 for u.
1
Determine a so that 212*a**3 + 35*a**5 - 10*a**2 - 413*a**3 + 216*a**3 + 60*a**4 = 0.
-1, 0, 2/7
Let v(x) be the third derivative of x**6/120 - x**4/6 + 124*x**2. Factor v(p).
p*(p - 2)*(p + 2)
Let h(y) be the first derivative of y**6/24 + y**5/2 + 5*y**4/2 + 20*y**3/3 + 10*y**2 + 8*y + 206. Determine x, given that h(x) = 0.
-2
Let a(x) be the second derivative of x**5/4 + 15*x**4/4 - 5*x**3/6 - 45*x**2/2 + 2*x. Determine s, given that a(s) = 0.
-9, -1, 1
Suppose 9*p = 4*p - 5. Let o(z) = z - 2*z**2 + 0*z + 4*z**2. Let h(x) = x**3. Let s(u) = p*o(u) + 3*h(u). Factor s(d).
d*(d - 1)*(3*d + 1)
Let w(i) be the second derivative of 6*i - 1/300*i**5 + 0*i**4 + 0 - 1/1800*i**6 + i**3 + 0*i**2. Let d(q) be the second derivative of w(q). Factor d(b).
-b*(b + 2)/5
Let w(n) = -n**3 - 7*n**2 - 8*n - 9. Let u be w(-6). Suppose -u = -x - 2*j + 2, -j = -x - 1. Factor 0 - 14*i**2 + 1 + x - 24*i + 6.
-2*(i + 2)*(7*i - 2)
Let f(t) = 4*t**2 + 16*t + 20. Let b(c) = 4*c**2 + 15*c + 21. Suppose -7*k = -12*k - 25. Let z(x) = k*f(x) + 4*b(x). Suppose z(u) = 0. Calculate u.
-4, -1
Let y(h) = -h**2 - 3*h - 9. Let r be y(-3). Let g(i) = 2*i**2 + 18*i. Let p be g(r). Suppose 2/7*a + p + 2/7*a**2 = 0. What is a?
-1, 0
Suppose -4*r + 3*r = -14. Let z = r + -12. Factor 4*p**2 - 2*p**4 + 5*p**4 + z*p**3 - 2*p**2 - 5*p**4 - 2*p.
-2*p*(p - 1)**2*(p + 1)
Let i be ((-18)/12)/((-3)/8). Let r be (-3)/(-1)*i/36. Factor -r*z - 4/9 + 1/9*z**2.
(z - 4)*(z + 1)/9
Find l, given that 43/3*l**2 - 29/3*l**3 - l**4 - 11/3*l + 0 = 0.
-11, 0, 1/3, 1
Let t(f) be the third derivative of f**8/672 + f**7/60 - 3*f**6/80 - 7*f**5/120 + f**4/6 + 145*f**2. Determine j, given that t(j) = 0.
-8, -1, 0, 1
Factor 0 - 30*g**2 - 18*g - 1/2*g**5 - 13/2*g**3 + 5*g**4.
-g*(g - 6)**2*(g + 1)**2/2
Determine x, given that -4/17 - 18/17*x**2 + 14/17*x - 2/17*x**4 + 10/17*x**3 = 0.
1, 2
Factor -2/11*a**5 + 12/11*a**3 + 0 + 6/11*a + 0*a**4 - 16/11*a**2.
-2*a*(a - 1)**3*(a + 3)/11
Suppose 3*b + 36 = -6. Let v = b - -17. Factor 1/2*s**2 + 0 + 0*s - 1/4*s**v.
-s**2*(s - 2)/4
Let q(s) be the second derivative of 5*s**5/22 + 5*s**4/33 + s**3/33 + 33*s + 3. Solve q(g) = 0 for g.
-1/5, 0
Let b(n) be the first derivative of -n**4/18 + 5*n**3/9 + 2*n - 10. Let c(j) be the first derivative of b(j). Factor c(o).
-2*o*(o - 5)/3
Suppose -3*t + 2*t + 4 = 0. Suppose 2*y + 7 = v, -11 + 3 = t*y. Solve -8*z**4 + 2*z**2 + 5*z**v - 2*z - 2*z**3 + 6*z**4 - z**3 = 0 for z.
-1, 0, 1
Suppose -1897*d - 37 = -1923*d + 67. Factor 243/5 + 324/5*a + 162/5*a**2 + 3/5*a**d + 36/5*a**3.
3*(a + 3)**4/5
Solve -87*b**4 + 3*b**2 + 25*b**3 - 10*b**3 -