10*o**2 - 10*o**2 + o**3 + 2*o**3 = 0. What is o?
0
Let i(g) = -g + 4. Let t be i(2). What is c in -c**3 + c**3 + 2*c**3 - 4*c**2 + t*c**3 = 0?
0, 1
Let a(s) be the third derivative of -s**7/945 + s**6/45 - s**5/9 + 7*s**4/27 - s**3/3 + 40*s**2. Determine k so that a(k) = 0.
1, 9
Let a(k) be the first derivative of k**6/12 - 3*k**5/5 + k**4/8 + 4*k**3 + 4*k**2 + 18. Factor a(f).
f*(f - 4)**2*(f + 1)**2/2
Let f(p) = -p + 7. Let s be f(-5). Factor -s*z - 11*z**2 + 8*z**3 - 3*z**2 + 8 + 2*z**2.
4*(z - 2)*(z + 1)*(2*z - 1)
Let s(c) = -6*c**5 - 11*c**4 + 23*c**3 + 11*c**2. Let g(b) = -b**5 - 2*b**4 + 4*b**3 + 2*b**2. Let x(w) = 34*g(w) - 6*s(w). Factor x(j).
2*j**2*(j - 1)**2*(j + 1)
Solve 25*b - 235*b**4 - 5 + 35*b**4 + 25*b**2 - 67*b**3 - 58*b**3 - 80*b**5 = 0 for b.
-1, 1/4
Let i(v) = -v**3 - 4*v**2 - 3*v. Let y be i(-2). Let f be 4/3 + y/3. Factor -2/3 + f*d**2 + 2/3*d - 2/3*d**3.
-2*(d - 1)**2*(d + 1)/3
Factor -6*u**4 - 8*u**2 - 2/9 + 20/9*u + 12*u**3.
-2*(u - 1)*(3*u - 1)**3/9
Let n(v) be the third derivative of -5*v**8/336 - v**7/14 - v**6/12 + v**5/6 + 5*v**4/8 + 5*v**3/6 - 16*v**2. Find o, given that n(o) = 0.
-1, 1
Let m(t) = t**2 - t. Let k be m(1). Suppose 2*s + s + 5*s**3 + k*s**4 + 8*s**2 + s + s**4 = 0. What is s?
-2, -1, 0
Determine s so that 0 - 3/4*s**2 - 15/4*s = 0.
-5, 0
Suppose -8/7*t**2 - 2/7*t + 0 = 0. What is t?
-1/4, 0
Suppose 2/3*j**2 - 4/3*j + 0 = 0. What is j?
0, 2
Let g(r) = -2*r - 8. Let q be g(-7). Let s be (10/q - 1)*-3. Let v(f) = f - 1. Let j(i) = -2*i**2 - 2*i + 4. Let u(m) = s*v(m) - j(m). Factor u(o).
2*(o - 1)*(o + 1)
Let p(j) be the third derivative of -j**9/30240 + j**8/6720 - j**7/5040 + j**4/24 + 5*j**2. Let d(c) be the second derivative of p(c). Factor d(v).
-v**2*(v - 1)**2/2
Let o(a) be the second derivative of 1/20*a**5 + 0 - 1/6*a**4 + 0*a**3 + 0*a**2 + 3*a. Solve o(j) = 0.
0, 2
Let z = 5 + -4. Suppose -9 = -2*c + z. Factor -4*v**4 - v**3 + v**4 + c*v**4 - 3*v**3.
2*v**3*(v - 2)
Suppose 2*w - 4 = 3*s, 5*w - 5*s - 2 - 8 = 0. Let a = -10/91 + 474/1001. Solve -2/11*z**w - a + 6/11*z = 0 for z.
1, 2
Let b = 21 - 21. Let u(f) be the third derivative of 1/240*f**6 + b + 0*f + 0*f**3 + 1/120*f**5 + 0*f**4 - f**2. Solve u(y) = 0.
-1, 0
Let z = -6 - -2. Let a be (3*z/(-48))/1. Let -1/4*b + a*b**2 + 1/4*b**3 - 1/4 = 0. What is b?
-1, 1
Factor -1/5*z**2 - 12/5*z**4 + 6/5*z**3 + 0*z + 8/5*z**5 + 0.
z**2*(2*z - 1)**3/5
Let j be (105/45)/(1*(-8)/(-6)). Let b(f) be the first derivative of -f**2 + 5/3*f**3 + 0*f + j*f**4 - 2. Factor b(t).
t*(t + 1)*(7*t - 2)
Factor -1/5*p**2 + 0 + 1/5*p.
-p*(p - 1)/5
Let b(m) = 5*m**3 - 9*m**2 + 6*m - 1. Let u(q) = q**2 + q - 1. Let h(k) = -b(k) + u(k). Solve h(s) = 0 for s.
0, 1
Suppose -4*x + 26 = -22. Suppose x = -0*y + 4*y. Solve 1/2*k**2 + 1/4*k + 0 + k**4 - 7/4*k**y = 0 for k.
-1/4, 0, 1
Let y(m) be the third derivative of 0 + 1/24*m**4 + 1/60*m**5 - 1/3*m**3 - 4*m**2 + 0*m. Factor y(f).
(f - 1)*(f + 2)
Factor 3/2*g**3 - 3 + 0*g**2 - 9/2*g.
3*(g - 2)*(g + 1)**2/2
Let j(g) = 3*g**3 - 3*g. Let y(k) = 9*k**3 - 9*k. Let p(q) = -17*j(q) + 6*y(q). Find v such that p(v) = 0.
-1, 0, 1
Let f(l) be the first derivative of l**3/6 + 4*l**2 + 32*l - 31. Determine n so that f(n) = 0.
-8
Let y(u) be the first derivative of -u**3/27 - 5*u**2/18 - 4*u/9 - 12. Factor y(t).
-(t + 1)*(t + 4)/9
Let q(n) be the first derivative of 16*n**4 + 48*n**3 + 54*n**2 + 27*n + 9. Factor q(m).
(4*m + 3)**3
Suppose 4*t = 2*s - 13 - 13, 2*t = -10. Suppose -2*n + 15 = s*q + 2*q, q - 3 = 4*n. Factor -4*x**3 + 0*x**2 + 2*x**4 - x**2 + q*x**2.
2*x**2*(x - 1)**2
Let n(u) = u**3 - 4*u**2 - 13*u + 6. Let f be n(6). Factor 1/3*p - 4/3*p**2 + f.
-p*(4*p - 1)/3
Let r be -2*(-6)/(-4) - -3. Let b(c) be the third derivative of 1/4*c**5 + 0*c + 1/6*c**3 + 7/24*c**4 + r + 2*c**2 + 3/40*c**6. Factor b(k).
(k + 1)*(3*k + 1)**2
Suppose 3*w - 2*v = -6*v + 26, w - 22 = -4*v. Factor -6/7*g - 2/7*g**w - 4/7.
-2*(g + 1)*(g + 2)/7
Suppose -s + 13 = 3*n, -40*n - 6 = -42*n. Factor 8/3 + s*h + 4/3*h**2.
4*(h + 1)*(h + 2)/3
Factor -w**4 + w**3 - 5/4*w + 1/2*w**2 + 1/2 + 1/4*w**5.
(w - 2)*(w - 1)**3*(w + 1)/4
Factor -32*d - 2*d**2 - 3*d**2 - 70 + 6 + d**2.
-4*(d + 4)**2
Let j = -30 + 33. Suppose 0*z + j*z = 0. Factor -1/6*b**4 + 0 + 1/6*b**3 + 0*b**2 + z*b.
-b**3*(b - 1)/6
Let n(y) = 3*y**4 + 11*y**3 - 19*y**2 - 37*y + 3. Let x(b) = b**4 + 3*b**3 - 5*b**2 - 9*b + 1. Let a(g) = -6*n(g) + 26*x(g). Solve a(l) = 0 for l.
-2, -1, 1/2, 1
Let d = 87/1414 + 1/101. Let i(p) be the first derivative of 2 - d*p**4 + 4/21*p**3 - 1/7*p**2 + 0*p. Suppose i(h) = 0. Calculate h.
0, 1
Find d such that 0 - 9/4*d**3 + 3*d**2 + d - 7/4*d**4 = 0.
-2, -2/7, 0, 1
Let m(w) be the first derivative of w**3 - 15*w**2/2 - 16. Factor m(t).
3*t*(t - 5)
Let g(y) be the first derivative of 6 + 3/8*y**4 + 3/5*y**5 + 1/4*y**6 + 0*y**2 + 0*y + 0*y**3. Suppose g(t) = 0. Calculate t.
-1, 0
Let d(s) = 3*s**2 + 9*s + 6. Let y(z) = 3*z**2 + 8*z + 5. Let t(u) = 2*d(u) - 3*y(u). Factor t(o).
-3*(o + 1)**2
Let f(z) be the third derivative of -z**6/480 - z**5/160 + z**4/16 - 7*z**3/6 - z**2. Let p(x) be the first derivative of f(x). Solve p(k) = 0.
-2, 1
Let c(j) be the first derivative of 2/3*j**6 + 0*j**3 + 3 + 0*j**2 - 7/5*j**5 - 1/2*j**4 + 0*j. Suppose c(a) = 0. What is a?
-1/4, 0, 2
Let w be (-5 + (-2 - -4))/(-1). Solve -3*a**5 + w*a**4 - a**4 + 0*a**4 - 2*a**2 - 2*a**3 + 5*a**5 = 0 for a.
-1, 0, 1
Let w be (-429)/(-52) - (-1)/(-4). Solve b**3 + 10*b - w - 10*b**2 + b**3 + 6*b = 0 for b.
1, 2
Suppose p = 3*p - 18. Let u = p + -5. Factor 2/5*t**2 + 9*t**5 + 0*t + 0 - 7/5*t**3 - 12/5*t**u.
t**2*(3*t - 1)**2*(5*t + 2)/5
Let u(s) = -4*s**2 + 2*s - 3. Let d(z) = -3*z + 7. Let g be d(3). Let m(v) = -3*v**2 + v - 2. Let f(x) = g*u(x) + 3*m(x). Let f(q) = 0. What is q?
-1, 0
Let d be 1/(-2)*(-5)/2. Let x(k) be the first derivative of 1/2*k**2 + 2 + 1/3*k**3 + 3/5*k**5 + 0*k - d*k**4. Factor x(f).
f*(f - 1)**2*(3*f + 1)
Let w(x) = x**2 - 6*x - 24. Let z be w(9). Let l(g) be the third derivative of 0*g + 1/72*g**4 + 0 - 1/90*g**5 + 1/360*g**6 + 0*g**z - 2*g**2. Factor l(o).
o*(o - 1)**2/3
Let l(x) be the first derivative of 3*x**4/28 - 6*x**3/7 + 18*x**2/7 - 24*x/7 + 7. Let l(t) = 0. What is t?
2
Let x be (-2)/2 - (2/(-5) + -1). What is o in 0 + x*o**2 - 2/5*o**4 - 2/5*o**3 + 2/5*o = 0?
-1, 0, 1
Let b(w) = w**3 - w. Let y(v) = -38*v**3 + 28*v**2 - 15*v. Let j(r) = -22*b(r) + 2*y(r). Factor j(f).
-2*f*(7*f - 2)**2
Let u(z) be the third derivative of 7*z**8/144 + 7*z**7/45 - 53*z**6/360 - 53*z**5/90 + z**4/18 + 4*z**3/9 + 13*z**2. Let u(h) = 0. What is h?
-2, -1, -2/7, 2/7, 1
Let f be (-1)/4 - 136/(-32). Let -40*x**5 - 46*x**3 - 11*x**2 + 12*x + 2*x + 4 - 15*x**2 + 94*x**f = 0. Calculate x.
-2/5, -1/4, 1
Let p = -1 - -4. Factor -5*g**4 + g**5 + 5*g**2 - g**p + 0*g**3 + 4*g**4 - 4*g**2.
g**2*(g - 1)**2*(g + 1)
Let p = 339 + -4405/13. Find b such that 0*b + 0 - p*b**5 - 6/13*b**4 + 0*b**3 + 8/13*b**2 = 0.
-2, 0, 1
Let n(z) be the first derivative of 3 - 1/12*z**4 + 1/3*z**2 + 1/9*z**3 + 0*z. What is s in n(s) = 0?
-1, 0, 2
Suppose 0 = -2*s - 2*s + v - 17, 3*s - 3*v + 15 = 0. Let y = s - -6. Factor g**4 - 5*g**y + 5*g**2 + g**3 - 2*g**2.
g**2*(g - 1)*(g + 2)
Suppose -3*g = -0*g. Suppose 3*w - 6 + 0 = g. Factor -i - 2*i**2 + 4*i + 2*i**4 - i - w*i**3.
2*i*(i - 1)**2*(i + 1)
Let t(b) be the third derivative of b**6/280 - b**4/56 + 4*b**2. Suppose t(l) = 0. Calculate l.
-1, 0, 1
Let p(r) be the first derivative of 4/3*r**3 - 4*r + 0*r**2 - 2. Factor p(s).
4*(s - 1)*(s + 1)
Let a be (-2*(-14)/12)/(12/8). Factor a*f**4 - 32/9*f**3 + 22/9*f**2 + 0 - 4/9*f.
2*f*(f - 1)**2*(7*f - 2)/9
Let x(d) be the third derivative of -d**5/15 + d**4/3 - 5*d**2. Solve x(w) = 0 for w.
0, 2
Suppose 57*o - 34*o = 46. Find q such that -2*q**o + 2*q - 2/3 + 2/3*q**3 = 0.
1
Let r = -13 - -19. Let f(q) = -4*q**3 - 8*q**2 - 13*q + 13. Let x(u) = -2*u**3 - 4*u**2 - 6*u + 6. Let y(p) = r*f(p) - 13*x(p). Suppose y(l) = 0. Calculate l.
-2, 0
Let a(h) be the second derivative of 2*h**7/21 - 4*h**6/15 + h**5/5 - 7*h. Factor a(l).
4*l**3*(l - 1)**2
Suppose 0 = -19*c + 16*c + 6. Determine n, given that -9/4 - 3/2*n - 1/4*n**c = 0.
-3
Let h(p) be the second derivative of -p**6/240 - p**5/120 - p**2 + 8*p. Let o(t) be the first de