-4/3 + 8/3*c**2 + 10/3*c - 2*c**x = 0. What is c?
-1, 1/3, 2
Let o(m) be the first derivative of 5/3*m**3 + 0*m**2 + m**5 + 0*m + 19 - 5/2*m**4. Factor o(t).
5*t**2*(t - 1)**2
Let s(k) be the third derivative of -k**8/336 - k**7/21 + k**6/120 + k**5/6 - 421*k**2. Find i, given that s(i) = 0.
-10, -1, 0, 1
Let y(c) = 4*c**2 - 12*c + 8. Let q = -1 + 6. Let v(w) = 6*w**2 - 18*w + 12. Let k(m) = q*v(m) - 8*y(m). Factor k(d).
-2*(d - 2)*(d - 1)
Let d = 96 + -96. Let k be 2 + (-4 - -3)*d. Factor 0*m + 2/15*m**k + 2/15*m**3 + 0.
2*m**2*(m + 1)/15
Let s(f) be the first derivative of 5*f**6/2 - 16*f**5 + 145*f**4/4 - 100*f**3/3 + 10*f**2 - 61. Find u, given that s(u) = 0.
0, 1/3, 1, 2
Let b(c) be the second derivative of c**6/30 - c**5/2 + 29*c**4/12 - 4*c**3/3 - 24*c**2 + 220*c + 1. Factor b(m).
(m - 4)**2*(m - 3)*(m + 1)
Suppose 5 = 5*h, -98 = -2*v - v - 2*h. Let r be (v/10)/((-15)/(-125)*5). Factor -r - 52/3*z**2 + 8*z**3 + 16*z - 4/3*z**4.
-4*(z - 2)**2*(z - 1)**2/3
Determine w, given that 20/7*w**3 + 4*w**4 + 16/7*w - 64/7*w**2 + 0 = 0.
-2, 0, 2/7, 1
Suppose 10*u = -x + 11*u, -3*u + 35 = 4*x. Solve 2/5*p**x - 2/5*p**2 + 0*p - 6/5*p**4 + 6/5*p**3 + 0 = 0.
0, 1
Let u(s) be the third derivative of s**8/70 + s**7/75 - 7*s**6/300 - s**5/75 - 35*s**2. Find q, given that u(q) = 0.
-1, -1/4, 0, 2/3
Suppose 0*d = o - 4*d - 13, 0 = 3*o - 2*d - 19. Suppose 0*s = o*s - 120. Solve 17*h + 10*h**3 - 7*h**4 + s*h**2 - 8*h**4 - 5*h - 31*h**3 = 0.
-2, -2/5, 0, 1
Factor 6/13*x**2 - 2/13 - 4/13*x.
2*(x - 1)*(3*x + 1)/13
Let j(x) be the second derivative of -5*x**4/12 + 35*x**3/2 - 10*x + 3. Find h, given that j(h) = 0.
0, 21
Factor -2/13*l**4 + 576/13*l**3 - 53747712/13 - 62208/13*l**2 + 2985984/13*l.
-2*(l - 72)**4/13
Let x be ((-4)/(-14))/((2277/126)/23). Solve x*p**2 - 2/11*p + 6/11*p**3 + 0 = 0 for p.
-1, 0, 1/3
Suppose -r = -3 + 8. Let s be 32/(((-70)/r)/1). Factor 32/7 + s*g + 2/7*g**2.
2*(g + 4)**2/7
Suppose -o + 5*o - 3*m - 302 = 0, -o + 73 = -2*m. Let a = -77 + o. Factor a*g + 0 - 2/13*g**3 + 2/13*g**2.
-2*g**2*(g - 1)/13
Let i(a) be the third derivative of 0*a + 1/120*a**6 + 0 - 12*a**2 + 1/24*a**5 - 1/48*a**4 - 1/2*a**3. Factor i(r).
(r - 1)*(r + 2)*(2*r + 3)/2
Let j be 287/35 + ((-27)/(-15) - 2). Suppose 0 = 13*p - j + 8. Factor p + 2/5*f**2 + 2/5*f.
2*f*(f + 1)/5
Let x(h) be the first derivative of -26*h**4 + 68*h**3/3 - 4*h**2 - 83. Let x(m) = 0. Calculate m.
0, 2/13, 1/2
Suppose -325*j = -317*j - 80. Factor 5/3*p**4 - 20/3*p + j*p**2 + 25/3*p**3 - 40/3.
5*(p - 1)*(p + 2)**3/3
Suppose 0 = -4*c - 7*z + 3*z + 592, 2*c + 3*z - 295 = 0. Factor 25*n**2 - 3*n**5 - 2*n**5 - c*n**4 + 10*n + 15*n**3 + 144*n**4.
-5*n*(n - 2)*(n + 1)**3
Let b(l) be the third derivative of l**7/70 - 9*l**6/40 + 13*l**5/20 + 9*l**4/8 - 7*l**3 - 292*l**2. Let b(r) = 0. What is r?
-1, 1, 2, 7
Let s = -42 - -38. Let m(r) = -9*r**2 + 7*r + 3. Let f(b) = -8*b**2 + 8*b + 4. Let u(v) = s*m(v) + 3*f(v). Factor u(y).
4*y*(3*y - 1)
Let j(d) be the first derivative of -1/16*d**6 + 0*d**2 + 0*d - 6 + 3/32*d**4 + 1/8*d**3 - 3/40*d**5. Solve j(z) = 0.
-1, 0, 1
Factor -90 + 867*w + 3*w**3 - 83 + 102*w**2 + 173 + 0*w**3.
3*w*(w + 17)**2
Let f(s) = 48*s + 196. Let y be f(-4). Suppose 2*z = 3*c - 4, -4*c + 0*z + z = -12. Factor 8*i**3 + 7*i**y - 3*i**4 + 0*i**c.
4*i**3*(i + 2)
Determine y, given that -29*y**2 + 41 + 10 + 17*y**2 + 48*y + 9*y**2 = 0.
-1, 17
Let k(u) = 7*u**2 + 5*u + 3. Let f be k(-1). Let z(r) = 6*r - 29. Let w be z(f). What is b in -4/3*b - 1/3*b**2 - w = 0?
-3, -1
Let n(x) = -7*x**2. Let w be n(2). Let p be ((-16)/w)/(18/7). Solve -p*i**2 - 8/9 + 8/9*i = 0.
2
Find g such that 98/5*g**2 + 2*g**3 + 46*g - 10 = 0.
-5, 1/5
Let f(y) be the third derivative of 0*y**3 + 0 - 1/70*y**6 + 3*y**2 + 4/105*y**5 + 1/1176*y**8 + 0*y**7 + 0*y - 1/28*y**4. Factor f(k).
2*k*(k - 1)**3*(k + 3)/7
Let m(g) be the first derivative of 2*g**6 - 27*g**5/5 - 21*g**4/2 + 36*g**3 - 12*g**2 + 131. Suppose m(q) = 0. Calculate q.
-2, 0, 1/4, 2
Factor 0 + 0*n + 2/9*n**3 - 40/9*n**2.
2*n**2*(n - 20)/9
Let u(n) = -2*n**3 + 22*n**2 + 63*n - 141. Let s be u(13). Factor 0 + 2/3*l**4 + 8/3*l**s + 0*l - 10/3*l**3.
2*l**2*(l - 4)*(l - 1)/3
Let z(h) be the first derivative of h**4/6 - 92*h**3/9 + 89*h**2/3 - 88*h/3 + 489. Determine s, given that z(s) = 0.
1, 44
Let b(q) = -2*q - 9. Suppose 12 = 3*c - 5*c. Let h be b(c). Factor 3*d**2 - 3*d - 3*d**2 - d**3 + 4*d**h.
3*d*(d - 1)*(d + 1)
Let a(i) be the second derivative of i**9/3024 - i**8/560 - i**7/210 + 29*i**3/6 + 35*i. Let p(d) be the second derivative of a(d). Solve p(f) = 0.
-1, 0, 4
Let r(x) = -x**4 - 4*x**3 + 2*x + 2. Let c be (-4)/((-12)/(-9)) + 1. Let p(u) = -5*u**4 - 17*u**3 + 9*u + 9. Let m(h) = c*p(h) + 9*r(h). Solve m(l) = 0.
0, 2
Factor 0*k + 9/4*k**2 + 1/4*k**4 - 5/2*k**3 + 0.
k**2*(k - 9)*(k - 1)/4
Let j = -415/4 + 104. Let w(q) be the second derivative of 0 + 0*q**2 - 3/10*q**6 - j*q**4 + 9/20*q**5 + 1/14*q**7 - 2*q + 0*q**3. Factor w(h).
3*h**2*(h - 1)**3
Let q(u) be the first derivative of u**5/20 - 49*u**4/16 + 667*u**3/12 - 1587*u**2/8 + 281. Factor q(x).
x*(x - 23)**2*(x - 3)/4
Let l(p) = -p**3 - 6*p**2 + 94*p + 43. Let g be l(-13). Factor 10/9*f**3 - 2/3*f**2 + 20/9 + 2/9*f**g - 26/9*f.
2*(f - 1)**2*(f + 2)*(f + 5)/9
Let b(k) be the second derivative of 2*k**6/15 - 4*k**5/5 + 5*k**4/3 - 4*k**3/3 - 3*k - 13. Factor b(i).
4*i*(i - 2)*(i - 1)**2
Suppose -2*j**3 + 50*j**2 + 3*j**3 + 4*j**3 + 0*j**3 + 0*j**3 + 45*j = 0. What is j?
-9, -1, 0
Let g(a) = -5*a**2 + 39*a + 10. Let q be g(8). What is b in -2/15*b**q - 2/15 + 4/15*b = 0?
1
Suppose 9/5*l**3 + 0*l + 8/5*l**2 + 1/5*l**4 + 0 = 0. Calculate l.
-8, -1, 0
Suppose -2/3*t**2 + 0 + 6*t = 0. Calculate t.
0, 9
Let z be -11 + (-553)/(-49) - (-165)/84. Factor -z + 3/2*i - 1/4*i**2.
-(i - 3)**2/4
Let u(v) be the first derivative of v**3/3 + v**2/2 - 3*v - 5. Let n(i) = 2*i**2 + 2*i - 5. Let z(m) = -3*n(m) + 7*u(m). Find s, given that z(s) = 0.
-3, 2
Let f(p) be the third derivative of -28*p**2 + 0*p + 0*p**3 + 0 + 0*p**4 + 1/900*p**6 - 1/450*p**5. Suppose f(y) = 0. Calculate y.
0, 1
Let y = -15 - -19. Factor -2*i**3 + 8*i**2 - 13*i**4 - 5*i**2 + 12*i**y.
-i**2*(i - 1)*(i + 3)
Let q = -6465/92 + 1806/23. Let -21/8*h**3 - 3 + q*h + 69/8*h**2 = 0. Calculate h.
-1, 2/7, 4
Let t(x) = -2*x**2 + x. Let f(z) = -9*z**2 + 8*z + 32. Let s(r) = -f(r) + 4*t(r). Factor s(d).
(d - 8)*(d + 4)
Let c(t) be the first derivative of -t**4 - 20*t**3/3 - 14*t**2 - 9*t + 16. Let i(o) = -1. Let n(y) = c(y) + 3*i(y). Factor n(g).
-4*(g + 1)**2*(g + 3)
Let j(o) = -o**2 + 40*o + 563. Let z be j(51). Let w(b) be the first derivative of 4/9*b + 5 + 11/9*b**z + 2/3*b**3. Factor w(a).
2*(a + 1)*(9*a + 2)/9
Let c = 4 + -1. Suppose -c*d - 18 = -6*d. Suppose d - 6*t**2 - 2*t + 2*t**4 - 2 - 2*t**3 + 4*t**3 = 0. Calculate t.
-2, -1, 1
Let s(w) be the second derivative of -w**4/12 + 4*w**3/3 + 9*w**2/2 - 77*w. Factor s(n).
-(n - 9)*(n + 1)
Let o(j) = -j**5 - j**4 - j**3 - j + 2. Let a(f) = 3*f**4 + 3*f**3 - 8*f**2 + 8*f - 4. Let x(k) = a(k) + o(k). Let x(z) = 0. Calculate z.
-2, 1
Let q(d) = 14*d + 2. Let r be q(0). Let a(z) = -z + 4. Let p be a(2). What is c in -r*c**3 + 2*c**3 - c**4 - 2*c**3 - 2*c**2 + c**p = 0?
-1, 0
Suppose -44 = 4*u - 52. Determine v so that 409*v + u*v**2 + 5 + 3 - 401*v = 0.
-2
Suppose 1/4*x**3 + 2*x**2 + 0 - 9/4*x = 0. Calculate x.
-9, 0, 1
Solve -20*t**3 - t**5 - 70*t + 10 + 91*t + 2*t**2 + 3*t**4 - 15*t**4 = 0.
-10, -1, 1
Let w(m) be the third derivative of -m**6/24 + m**5 - 35*m**4/8 + 25*m**3/3 - 2*m**2 - 14*m. Let w(f) = 0. What is f?
1, 10
Let g(y) = y**4 - y**3 + 1. Let a = -36 - -51. Let h = 16 - a. Let v(p) = -2*p**4 - 7*p**3 - 3*p**2 + 1. Let s(u) = h*g(u) - v(u). Factor s(k).
3*k**2*(k + 1)**2
Suppose 0 = 4*t + 3*a - 40, -2*t + 2 = 5*a - 32. Suppose -t = -7*m + 7. Factor 4/11 + 2/11*n**m - 6/11*n.
2*(n - 2)*(n - 1)/11
Suppose -51*b = 82*b + 42*b. Find j such that -16/5*j**2 - 4/5*j + b = 0.
-1/4, 0
Let n be -2*20/(-16)*(-3)/(-5). Solve -6*k + n*k**3 + 12 - 3*k**2 = 0 for k.
-2, 2
Let y(t) be the first derivative of -18*t**5/5 - 69*t**4 + 496*t**3/3 - 118*t**2 + 34*t + 781. Find h, given that y(h) = 0.
-17, 1/3, 1
Find b, given that 4*b**4 + 4*b**4 - 2*b**5 + 5*b**4 - 233*b**2 - 34*b**3 + 3*b**4 + 253*b**2 