r**8/2016 - r**7/630 - r**6/720 + 11*r**2 - 2*r. Suppose c(f) = 0. What is f?
-1, 0
Let i(r) be the first derivative of -2*r**3/9 - 92*r**2/3 - 120*r - 946. Find o such that i(o) = 0.
-90, -2
Suppose -5*p = -2*j - 25, -4*j - 10 = -3*p + 5. Let k(c) be the third derivative of 3*c**2 - 1/12*c**4 + 1/2*c**3 - 1/60*c**p + 0 + 0*c. Factor k(h).
-(h - 1)*(h + 3)
Factor -22 + 245*c + 51*c**2 - 20*c**2 + 99*c**2 + 142 + 5*c**3.
5*(c + 1)**2*(c + 24)
Let x be -1 + 2/3 + (-13)/(-3). Let q be (-4)/(-9) + (4 - x). Determine b so that 8/9*b + 8/9 - 2/3*b**2 + 2/9*b**4 - q*b**3 = 0.
-1, 2
Let p(x) be the second derivative of x**5/4 + 5*x**4/2 + 15*x**3/2 + 10*x**2 - x + 53. Suppose p(r) = 0. Calculate r.
-4, -1
Let p(v) be the first derivative of v**4/4 + 17*v**3/3 - 9*v**2 - 42. Let m be p(-18). Factor 2/9*j**4 - 2/9*j**2 + 0*j + m + 0*j**3.
2*j**2*(j - 1)*(j + 1)/9
Let t(m) = -3. Let i = 12 - 8. Let z(b) = -b**2 - b - 2. Let u(l) = i*t(l) - 3*z(l). Let u(j) = 0. Calculate j.
-2, 1
Let b(o) be the first derivative of -o**5/5 - 5*o**4/4 - 2*o**3 - 55. Suppose b(c) = 0. What is c?
-3, -2, 0
Determine h, given that -13*h**2 + 24*h + 45*h**2 - 23*h**2 + 23 - 8*h**2 = 0.
-23, -1
Let n(y) be the second derivative of -9*y**6/70 - 9*y**5/28 - y**4/4 - y**3/14 - 162*y. Factor n(x).
-3*x*(x + 1)*(3*x + 1)**2/7
Let f(j) be the second derivative of -5*j + 11/27*j**3 + 2/9*j**2 + 4/27*j**4 - 7/30*j**5 + 0. Find t, given that f(t) = 0.
-1/3, -2/7, 1
Let p = -19 - -19. Let h(k) = -2*k + 4. Let n be h(p). Let -17*l**4 + 9*l**2 + 2*l**3 - 2*l - l**2 + 9*l**n = 0. What is l?
-1, 0, 1/4, 1
Let o be 18/45*(-1 + (-22)/(-12)). Let w(k) be the second derivative of 0 + 0*k**2 + 3/10*k**5 + 1/9*k**3 - k + o*k**4. Solve w(c) = 0.
-1/3, 0
Suppose 129*q**2 + 0 - 5547*q - 3/4*q**3 = 0. Calculate q.
0, 86
Let y(j) be the third derivative of -j**5/30 + 13*j**4/12 - 15*j**2. Factor y(b).
-2*b*(b - 13)
Suppose a = -3*b - 75, 4*a - 3*a - 75 = 3*b. Let l be (1 + -3)*5/b. Factor 1/5*u**3 + l + 4/5*u**2 + u.
(u + 1)**2*(u + 2)/5
Let y(a) be the first derivative of -a**3/3 - 7*a**2 - 81. Solve y(s) = 0.
-14, 0
Let r = 2195/132 + -182/11. Let l(n) be the first derivative of 1/24*n**4 + r*n**2 - 1/9*n**3 + 0*n + 5. Find p, given that l(p) = 0.
0, 1
Let q(a) be the third derivative of 1/15*a**5 + 10/21*a**3 - 1/210*a**6 - 11/42*a**4 - 4*a**2 + 0 + 0*a. Factor q(m).
-4*(m - 5)*(m - 1)**2/7
Suppose 0 = 3*k + 4*q - q - 63, -5*k = 3*q - 107. Factor 2 + c**2 - 6*c**2 + k*c + 3*c**2 - 20*c - 2*c**3.
-2*(c - 1)*(c + 1)**2
Find w, given that -2/5*w**3 - 28/5*w**2 + 48/5*w + 0 + 2/5*w**4 = 0.
-4, 0, 2, 3
Solve 762*y + 20*y**2 - 6 + 3*y**3 + 755*y - 1506*y = 0 for y.
-6, -1, 1/3
Let u(g) be the third derivative of -g**8/448 - g**7/56 - g**6/16 - g**5/8 - 5*g**4/32 - g**3/8 - g**2 + 64. Solve u(y) = 0.
-1
Let a = -183 + 186. Determine p so that 4 + 2*p - 1/2*p**a - p**2 = 0.
-2, 2
Let a = -140 + 143. Let n(b) be the first derivative of 8 + 3/5*b**2 + 2/15*b**a + 4/5*b. Factor n(s).
2*(s + 1)*(s + 2)/5
Let u = -59 - -64. Solve -18*m**2 + 43*m**2 - 5*m - 20*m**2 + u*m**3 - 1 - 4 = 0 for m.
-1, 1
Find z, given that -4/5*z + 0 - 3/5*z**2 + 1/5*z**3 = 0.
-1, 0, 4
Let g(k) be the third derivative of -k**7/105 + k**6/4 - 8*k**5/5 - 16*k**4/3 + 79*k**2. Factor g(z).
-2*z*(z - 8)**2*(z + 1)
Let y = 46 - 44. Suppose -28*r - 168 = -168. Factor 2/9*q - 1/9*q**y - 1/9*q**3 + r.
-q*(q - 1)*(q + 2)/9
Let q(d) = d**3 + 2*d**2 - 1. Let m(n) = -15*n**4 + 56*n**3 - 33*n**2 + 10*n - 6. Let x(p) = m(p) - 6*q(p). Factor x(h).
-5*h*(h - 2)*(h - 1)*(3*h - 1)
Let x(h) = 8*h**4 - 15*h**3 - 6*h**2 + 20*h - 3. Let z(f) = 65*f**4 - 120*f**3 - 50*f**2 + 160*f - 25. Let p(y) = 25*x(y) - 3*z(y). Let p(l) = 0. Calculate l.
-1, 0, 2
Let a(l) be the second derivative of -7*l**6/15 - 13*l**5/5 - 9*l**4/2 - 4*l**3/3 + 4*l**2 + 63*l. Determine w, given that a(w) = 0.
-2, -1, 2/7
Let t be (18/45)/(78/65). Factor 5/3*u + 2/3 + 4/3*u**2 + t*u**3.
(u + 1)**2*(u + 2)/3
Suppose -21*q + 102*q + 69 - 231 = 0. Factor 0 + 5/4*c**q + 15/4*c.
5*c*(c + 3)/4
Suppose -5*d + 3 = 8, 2*n - 2*d = -38. Let g = 20 + n. Factor 12 - 6*r**2 - 4 + g*r**2 - 2*r**3.
-2*(r - 1)*(r + 2)**2
Let v(m) be the third derivative of -m**7/210 + 7*m**5/60 + m**4/4 + 20*m**2. Factor v(p).
-p*(p - 3)*(p + 1)*(p + 2)
Let t(o) be the second derivative of 3/40*o**5 + 9*o + 1/4*o**3 + 0*o**2 + 1/4*o**4 + 0. Factor t(n).
3*n*(n + 1)**2/2
Factor -a**5 - 16*a + 3*a**3 + 32*a + 0*a**5 + 6*a**4 - 4*a - 20*a**2 + 0*a**5.
-a*(a - 6)*(a - 1)**2*(a + 2)
Let l(m) = 2*m - 28. Let w be l(16). Let g be 16/(-156)*(-6)/w. Let 0*z + g*z**2 - 2/13 = 0. Calculate z.
-1, 1
Let c(m) = 12*m**2 + 116*m + 24. Let a(x) = 5*x**2 + 39*x + 9. Let s(k) = -8*a(k) + 3*c(k). Determine t, given that s(t) = 0.
0, 9
Let b(h) = -16*h**3 + h**2 + 31*h + 51. Let w(m) = 3*m**3 - 6*m - 10. Suppose 0 = -2*d - 60 + 16. Let f(l) = d*w(l) - 4*b(l). Determine t, given that f(t) = 0.
-2, 2
Suppose 4*h = -2*o - o + 10, o - 5 = -3*h. Suppose 4*w**o + 673*w**3 - 676*w**3 - w**2 = 0. What is w?
0, 1
Let d be 0/(((-2)/(-7))/(2/14)). Suppose 14 = 7*c - d*c. Let 4/11 - 2/11*r - 2/11*r**c = 0. Calculate r.
-2, 1
Let n = 6261 + -18782/3. Factor 16/3 + n*p**2 + 8/3*p.
(p + 4)**2/3
Suppose -4*i = -4*o - 4, -5*i + 7*o - 3*o + 9 = 0. Let m(g) be the first derivative of g**4 - 6/5*g**i - 5 + 8/3*g**3 - 2*g - 2*g**2. Find t such that m(t) = 0.
-1, -1/3, 1
Let r(k) = 21*k**2 + 189*k + 320. Let b(n) = 5*n**2 + 47*n + 80. Let x(o) = 26*b(o) - 6*r(o). Suppose x(d) = 0. Calculate d.
-20, -2
Let q(f) = -2*f**2 - 1. Let h(g) = g**3 - 2*g**2 - g - 1. Let b(s) = h(s) - q(s). Factor b(z).
z*(z - 1)*(z + 1)
Let m be (-11 - (-26)/72*38) + (-2)/9. What is r in -m*r - 3/2*r**3 - 1/4*r**4 - 3/4 - 3*r**2 = 0?
-3, -1
Let u(s) = -4*s**2 - 10*s + 14. Let c be -1 + 0 + -1 - -1. Let t(b) = b - 1. Let j(h) = c*u(h) - 2*t(h). Factor j(n).
4*(n - 1)*(n + 3)
Let 22*m**5 + 833 + 385*m**4 + 1705*m**2 + 8*m**5 - 870*m - 1410*m**3 - 673 = 0. What is m?
-16, 1/2, 2/3, 1
Let k(n) be the third derivative of 49*n**8/288 - 21*n**7/20 + 161*n**6/120 - 13*n**5/18 + n**4/6 - 87*n**2. Suppose k(o) = 0. What is o?
0, 2/7, 3
Suppose -4*m - m - i + 25 = 0, -2*m + 3*i = -10. Suppose 8*h**2 + 32*h**4 - 21*h**3 - 11*h**3 - h**3 + m*h**3 - 12*h**5 = 0. What is h?
0, 2/3, 1
Suppose -1 = -3*h - 88*c + 89*c, 5*h - 4*c = 4. Let l(v) be the second derivative of h + 1/3*v**3 + 0*v**2 - 1/4*v**4 - 8*v. Determine j, given that l(j) = 0.
0, 2/3
Let c be 2*20/(-70) + (-136)/(-42). Let d(z) be the first derivative of c*z**3 - 10*z**2 - 8*z - 10 + 5*z**4. Suppose d(n) = 0. What is n?
-1, -2/5, 1
Factor -18*c**2 - 3*c**3 - 48*c**2 + 2*c**3 - c**3.
-2*c**2*(c + 33)
Suppose 23*g - 1484 = 9*g. Let j = g + -104. What is f in -f**3 + 17/3*f**j - 22/3*f + 8/3 = 0?
2/3, 1, 4
Let k(w) be the first derivative of -w**4/34 - 88*w**3/51 - 401. Determine z so that k(z) = 0.
-44, 0
Let m be 1 + (-3 - 98/(-36)). Let w = m + -1/2. Solve 2/9*v**2 - 4/9 + w*v = 0.
-2, 1
Let w(p) be the third derivative of 10*p**2 + 2/3*p**3 - 1/30*p**5 + 0 - 1/12*p**4 + 0*p. Determine y so that w(y) = 0.
-2, 1
Factor -67*b**2 + 91*b**2 + 15*b**3 + 0*b**4 + 3*b**4 + 12*b.
3*b*(b + 1)*(b + 2)**2
Let l(z) be the first derivative of z**6/840 - z**5/420 - z**4/84 - 6*z**2 + 9. Let h(q) be the second derivative of l(q). Factor h(j).
j*(j - 2)*(j + 1)/7
Let u(g) be the first derivative of 5*g**7/21 - g**6/2 + 5*g**4/12 + 11*g - 8. Let w(r) be the first derivative of u(r). Find k such that w(k) = 0.
-1/2, 0, 1
Let z(g) = g**2 + 10*g + 18. Let b(l) = l**2 + 15*l + 6. Let h be b(-14). Let m be z(h). Factor 0 + 0*w**3 - 3/4*w**4 + 3/4*w**m + 0*w.
-3*w**2*(w - 1)*(w + 1)/4
Let f be 3 - (-2)/12*-3*0. Factor 3 + m**3 + 96*m**4 - 94*m**4 - f*m**2 - 2 - m.
(m - 1)*(m + 1)**2*(2*m - 1)
Let t(w) be the first derivative of w**7/2520 - w**6/270 + w**5/120 + 11*w**3/3 + 10. Let y(a) be the third derivative of t(a). Factor y(n).
n*(n - 3)*(n - 1)/3
Let a = -16/329 + 706/987. Factor a*t**3 + 4/9*t**2 + 0 - 2/9*t.
2*t*(t + 1)*(3*t - 1)/9
Let w = 54 + -51. Suppose -w*j + 11 = 5. Let 4*x - 7/3*x**j + 4/3 = 0. Calculate x.
-2/7, 2
Let i(k) = k**4 - k**3 + k**2 - k - 1. Let h(r) = -6*r**4 + 6*r**3 + 6*r**2 + 2*r + 2. Let c(f) = h(f) + 2*i(f). Let c(p) = 0. Cal