1, 1
Let r be 4*(-2 - 5/(-2)). Let g(j) = j**4 + 5*j**3 + j**2 + 3. Let u(d) = d**3 + 1. Let f(l) = r*g(l) - 6*u(l). Find i, given that f(i) = 0.
-1, 0
Let b = 23 + -24. Let g be b + 3 - 49/28. Factor g*a - 1/4*a**3 - 1/4*a**2 + 1/4.
-(a - 1)*(a + 1)**2/4
Factor 0 - t**3 - 3/2*t**2 + 1/2*t**4 + 0*t.
t**2*(t - 3)*(t + 1)/2
Let x(w) = 3*w**3 - 22*w**2 + 49*w - 19. Let y(l) = 2*l**3 - 11*l**2 + 25*l - 10. Let n(q) = -6*x(q) + 11*y(q). Factor n(m).
(m - 1)*(m + 4)*(4*m - 1)
Let y(u) be the first derivative of u**6/3 + 8*u**5/5 + 5*u**4/2 + 4*u**3/3 - 1. Find z, given that y(z) = 0.
-2, -1, 0
Factor u**3 - 16*u + 3*u**3 - 8*u**3 - 16*u**2.
-4*u*(u + 2)**2
Solve -24/19*b**4 + 6/19*b**2 + 0 + 2/19*b - 4/19*b**3 - 16/19*b**5 = 0 for b.
-1, -1/2, 0, 1/2
Let h(y) be the third derivative of y**8/1008 - y**7/630 - y**6/360 + y**5/180 + 40*y**2. Let h(m) = 0. What is m?
-1, 0, 1
Let p(v) be the second derivative of -3*v**2 + 0 + 9*v - 7/4*v**4 - 23/6*v**3. Find z, given that p(z) = 0.
-2/3, -3/7
Let n = 36 - 32. Let o(a) be the second derivative of 0 + 0*a**n + 0*a**3 - 1/10*a**5 + a + 0*a**2 + 1/15*a**6. What is i in o(i) = 0?
0, 1
Factor q**4 - 11/3*q + 1 - 10/3*q**3 - 1/9*q**5 + 46/9*q**2.
-(q - 3)**2*(q - 1)**3/9
Let m be (18/(-4))/(8/16). Let x be (-90)/(-324) + (-2)/m. Factor -1/2*k**2 + x + 1/2*k - 1/2*k**3.
-(k - 1)*(k + 1)**2/2
Let m(o) = o**4 - 21*o**3 + 40*o**2 - 24*o + 7. Let g(k) = -k**4 + 42*k**3 - 81*k**2 + 48*k - 15. Let c(n) = -3*g(n) - 7*m(n). Determine x, given that c(x) = 0.
1/4, 1, 2
Factor 0 + 1/4*r**2 + 1/2*r.
r*(r + 2)/4
Factor -2 + 11*a**3 - 4 - 3*a + 24*a**2 - 15*a**3 - 11*a**3.
-3*(a - 1)**2*(5*a + 2)
Let r(a) be the third derivative of 0*a - 8/9*a**3 - 1/5*a**5 + 3*a**2 + 3/35*a**7 - 3/20*a**6 + 0 + 7/9*a**4. Let r(n) = 0. Calculate n.
-1, 2/3
Suppose 4*j = 3*r + 9, 0*j - 17 = -5*j - 2*r. Solve 1/4*y**j + 0 - 1/4*y**2 + 0*y = 0.
0, 1
Let n be 72*(-1 + 39/42). Let k = n + 93/14. Find v, given that -k*v**2 - 3/4*v**4 + 11/4*v**3 - 3*v + 2 = 0.
-1, 2/3, 2
Let g(o) be the second derivative of 5*o**4/3 + 65*o**3/6 + 15*o**2/2 - 13*o. Solve g(c) = 0.
-3, -1/4
Determine z, given that 5*z - 2*z + 67*z**2 - 68*z**2 - 2 = 0.
1, 2
Suppose -i + b = -2 - 4, 0 = -2*i - b. Let n be 28/33 - 4/22. Suppose -2/3*o**i + 0 - n*o = 0. Calculate o.
-1, 0
Let c(x) be the third derivative of -x**6/300 - x**5/50 - x**4/30 - 10*x**2. Factor c(q).
-2*q*(q + 1)*(q + 2)/5
Let f = 74/9 + -14/9. Factor -4/3*v**4 - 11*v**2 - f*v - 20/3*v**3 - 4/3.
-(v + 2)**2*(2*v + 1)**2/3
Let s(u) be the second derivative of -2*u**6/15 + u**5/5 + 5*u**4/3 + 2*u**3 - 14*u. Suppose s(k) = 0. What is k?
-1, 0, 3
Let k(v) be the first derivative of -8*v**6/3 + 56*v**5/5 - 49*v**4/4 - 4*v**3/3 + 11*v**2/2 + 2*v + 5. Find p such that k(p) = 0.
-1/4, 1, 2
Suppose -c**3 + 3*c**2 + 16*c**4 - 3*c**3 + 12*c**5 - 11*c**2 = 0. What is c?
-1, 0, 2/3
Let k = 1/153 - -763/306. Factor 13/2*n**4 - n - 1/2*n**2 + k*n**5 + 0 + 9/2*n**3.
n*(n + 1)**3*(5*n - 2)/2
Let j(y) be the first derivative of -1/5*y**5 + 0*y**3 + y**2 + y + 5 - 1/2*y**4. What is m in j(m) = 0?
-1, 1
Let i(s) be the first derivative of 2*s**3/11 - 24*s**2/11 + 96*s/11 + 49. Factor i(a).
6*(a - 4)**2/11
Let j(u) be the second derivative of -2*u + 0 + 1/12*u**4 + 1/6*u**3 - 1/20*u**5 - 1/30*u**6 + 0*u**2. Solve j(o) = 0 for o.
-1, 0, 1
Suppose -5 = -2*p + 5*v, -2*p - 4 = 2*v + 2*v. Solve p*b + 2/3*b**2 - 10/3*b**3 + 0 + 8/3*b**4 = 0.
0, 1/4, 1
Let l(r) be the second derivative of r**8/1848 - r**6/330 + r**4/132 - 3*r**2/2 + r. Let j(a) be the first derivative of l(a). Suppose j(z) = 0. Calculate z.
-1, 0, 1
Let -2/7*l**3 + 0 + 18/7*l + 16/7*l**2 = 0. Calculate l.
-1, 0, 9
Let a be ((-6)/(-8))/(2/16). Suppose -4*o + i + i + a = 0, -3*i = o - 5. Factor -b**2 - 2*b**2 - 2*b + b**2 + 3*b**o.
b*(b - 2)
Let d(b) be the second derivative of b**4/3 + 2*b**3 + 7*b. Determine t, given that d(t) = 0.
-3, 0
Let p(q) = q - 1. Let w(f) be the second derivative of f**4/12 - f**3/2 + 5*f**2/2 + 2*f. Let x = 1 - 2. Let d(t) = x*w(t) - 5*p(t). Solve d(j) = 0.
-2, 0
Let x(g) = -g**2 + 3*g + 2. Let f be x(4). Let c(s) = s + 1. Let a(w) = -2*w**3 - 2*w**2 + 4*w + 4. Let r(n) = f*c(n) + a(n). Solve r(u) = 0.
-1, 1
Let t = 1 + 3. Suppose -3*u + t*u - 2 = 0. Factor 2 + 4*v + 0*v + v**u - v.
(v + 1)*(v + 2)
Let j(m) be the first derivative of m**7/1680 - m**6/180 + m**5/48 - m**4/24 + m**3 - 3. Let q(h) be the third derivative of j(h). Determine f so that q(f) = 0.
1, 2
Factor -5/2 + 0*b**2 - 15/4*b + 5/4*b**3.
5*(b - 2)*(b + 1)**2/4
Let g(u) be the third derivative of -u**8/12600 + 5*u**3/6 - 2*u**2. Let o(q) be the first derivative of g(q). Suppose o(p) = 0. Calculate p.
0
Factor -s**3 - 3/2 - 7/2*s**2 - 4*s.
-(s + 1)**2*(2*s + 3)/2
Let g(k) be the second derivative of -k**6/360 + k**4/24 + k**3/2 + 6*k. Let d(a) be the second derivative of g(a). Find c such that d(c) = 0.
-1, 1
Suppose 3*n - 6*m + 3*m + 6 = 0, 0 = 3*n - 2*m + 4. Suppose -3*o + 0 = -3*t - 3, -3*t - 4*o + 18 = n. Factor 1/2*i**t + 1/2*i**4 + 0 + 0*i - i**3.
i**2*(i - 1)**2/2
Suppose 2*a + 42 = -0*t + 5*t, -2*t - 4*a = -12. Let l = -8 + t. What is m in 1/6*m**3 + l + 1/3*m + 1/2*m**2 = 0?
-2, -1, 0
Suppose 9*z - 8*z = 0. Find a such that z*a**2 + 1/4*a**4 - 1/2*a + 1/2*a**3 - 1/4 = 0.
-1, 1
Let h = -16 - -97. Let f = h + -403/5. Factor 0 + 0*g**2 + f*g**3 + 32/5*g**5 + 16/5*g**4 + 0*g.
2*g**3*(4*g + 1)**2/5
Let h(s) = -9*s**2 - 54*s - 186. Let k(f) = -f**2 - f + 1. Let p(z) = h(z) - 6*k(z). Factor p(x).
-3*(x + 8)**2
Let d be (0 - 2/(-4))*(-17 - -25). Determine m, given that 0 - 2/7*m - 2/7*m**2 - 6/7*m**d + 10/7*m**3 = 0.
-1/3, 0, 1
Let q(b) be the third derivative of -1/60*b**4 + 0*b**3 - 1/300*b**5 - 6*b**2 + 0 + 0*b. Factor q(c).
-c*(c + 2)/5
Let t(r) be the second derivative of r**5/20 + 9*r**4/4 + 81*r**3/2 + 729*r**2/2 - 17*r. Factor t(v).
(v + 9)**3
Let k(p) be the third derivative of 5*p**8/336 + p**7/42 - 41*p**2. Factor k(l).
5*l**4*(l + 1)
Let m be (10/6 + -2)*-12. Let y be (-28)/(-12) - 2/6. Factor 16/7*k**m + 0 + 32/7*k**5 + 2/7*k**y - 2*k**3 + 0*k.
2*k**2*(k + 1)*(4*k - 1)**2/7
Suppose -3*r + 15 = i, -7*r = -3*r - 5*i - 20. Suppose -10 = 3*g - 8*g. Factor -f**r + 4*f + 2*f**3 + g*f**3 - 2*f**3 - 5*f.
-f*(f - 1)**2*(f + 1)**2
Let r(q) be the second derivative of -q**4/6 - 2*q**3 - 9*q**2 + 2*q. Let r(n) = 0. What is n?
-3
Let p be (-16)/104 - (-124)/130. Let v(u) = -u**2 - u + 2. Let y be v(-2). Factor 4/5*m**4 + 2/5*m - 2/5*m**5 + y + 0*m**3 - p*m**2.
-2*m*(m - 1)**3*(m + 1)/5
Let l(d) = 5*d**2 + 29*d + 80. Let b(o) = 10 + 4 + o**2 + 0*o**2 + 6*o + 2. Let n(i) = 11*b(i) - 2*l(i). Determine m, given that n(m) = 0.
-4
Let z(k) be the third derivative of 0*k**4 + 1/20*k**5 + 1/28*k**8 + 1/20*k**6 - 1/10*k**7 + 0*k + 2*k**2 + 0 + 0*k**3. Factor z(m).
3*m**2*(m - 1)**2*(4*m + 1)
Factor 8/11*i**3 + 0 + 4/11*i - 2/11*i**4 - 10/11*i**2.
-2*i*(i - 2)*(i - 1)**2/11
Let s(z) = 14*z - 6. Let j(f) = -5*f + 2. Let l(o) = -11*j(o) - 4*s(o). Let q be l(0). Factor -2*g**3 - 2*g**4 + 2*g - 2*g**2 + q*g**4 + 2*g**4.
2*g*(g - 1)**2*(g + 1)
Let d(o) be the third derivative of -o**5/420 - o**4/28 - 3*o**3/14 - 10*o**2. Suppose d(m) = 0. What is m?
-3
Let i(j) = -j**3 - 6*j**2 + 7*j + 4. Let m be i(-7). Find v, given that -10 + 16*v**m - 16*v**5 + 52*v**3 - 8*v**3 - 5*v**2 - 3*v**2 + 2 - 28*v = 0.
-1, -1/2, 1, 2
Suppose -81*t = -83*t + 4. Solve -x - 2/3*x**t - 1/3 = 0 for x.
-1, -1/2
Let f be (1/(-2))/((-4)/64). Let t = -5 + f. Factor -w - 3*w - w**3 + t*w + w**2 - 3*w**2.
-w*(w + 1)**2
Let z(h) be the third derivative of h**5/30 - h**4/2 + 5*h**3/3 + 9*h**2. Suppose z(d) = 0. Calculate d.
1, 5
Let q(j) = -2*j**2 + 7*j + 4. Let w be q(4). Determine l, given that w*l - 1/3*l**2 + 0 = 0.
0
Suppose -l = l + 2*l. Let s(z) be the first derivative of 0*z + l*z**2 + 2 + 5*z**6 + 44/5*z**5 + 16/15*z**3 + 26/5*z**4. What is o in s(o) = 0?
-2/3, -2/5, 0
Factor 6/5*f - 6/5*f**3 + 0 + 0*f**2.
-6*f*(f - 1)*(f + 1)/5
Factor 12*c**2 - 3*c**4 + 0*c**2 + 9*c**4 - 13*c**3 - c**5 - 4*c.
-c*(c - 2)**2*(c - 1)**2
Factor 8/9*m**2 + 0*m - 4/9*m**3 + 0.
-4*m**2*(m - 2)/9
Factor 6*b + 5 + 4 - 6 + 3*b**2.
3*(b + 1)**2
Let x(g) = -g**2 - 10*g + 3. Let j be x(-10). Let c be (0 - 0)*(-1)/2. Factor c + 0*r - 1/3*r**j 