first derivative of 3/10*u**4 + 0*u**3 + 3/5*u - 3/25*u**5 - 3/5*u**2 + 1. Determine o, given that i(o) = 0.
-1, 1
Let d(k) be the first derivative of k**7/420 + k**3/3 - k - 2. Let s(r) be the first derivative of d(r). Let p(j) be the second derivative of s(j). Factor p(y).
2*y**3
Let z = -16 + 19. Let y(n) be the third derivative of -1/160*n**6 + 0*n + 1/4*n**3 + 0 + 3/32*n**4 + 0*n**5 + z*n**2. Factor y(q).
-3*(q - 2)*(q + 1)**2/4
Suppose 0 = -5*p + c + 15, 0 = 16*p - 14*p - 4*c - 24. What is t in -2/3*t + 1/3*t**p + 0 = 0?
0, 2
Factor 0*w**3 - 14/5*w**2 + 0 + 2/5*w**4 - 12/5*w.
2*w*(w - 3)*(w + 1)*(w + 2)/5
Factor 85*s**3 - 155*s**2 + 20*s**2 - 12 - 10*s**3 + 72*s.
3*(s - 1)*(5*s - 2)**2
Let k be (-47)/(1*(-3)/(-12)). Let s = k + 1318/7. Solve -4/7 + s*m - 2/7*m**3 + 6/7*m**2 - 2/7*m**4 = 0.
-2, -1, 1
Suppose -g - y = -6, 5*g + 0 = 3*y + 6. Let d(c) be the first derivative of -18/35*c**5 - 22/21*c**g + 0*c + 9/7*c**4 + 2/7*c**2 - 1. Find h such that d(h) = 0.
0, 1/3, 2/3, 1
Suppose -5*p + p + 8 = 0. Let x be (2/(-10))/((-14)/28). Factor -2/5 + 0*m + x*m**p.
2*(m - 1)*(m + 1)/5
Let t(r) be the first derivative of r - 3. Let g(p) = p**2 - p - 11. Let m(v) = 2*g(v) + 22*t(v). Factor m(l).
2*l*(l - 1)
Let a(j) = -9*j**2 - 5*j + 7. Let w(t) be the first derivative of 4*t - 5/3*t**3 - 3/2*t**2 - 2. Let x(p) = 4*a(p) - 7*w(p). Factor x(u).
-u*(u - 1)
Let x(j) be the third derivative of j**7/280 - j**6/60 - j**5/40 + j**4/4 - j**3/6 + 8*j**2. Let r(c) be the first derivative of x(c). What is v in r(v) = 0?
-1, 1, 2
Let q be 15/(-10) - 3/(-2). Let w be (2 - q)/(-3 - -10). Determine n so that -2/7*n**2 + 0*n + 0 - 2/7*n**5 + w*n**4 + 2/7*n**3 = 0.
-1, 0, 1
Let k(l) be the third derivative of l**7/210 + l**6/180 - l**5/60 - l**3/2 - 4*l**2. Let b(u) be the first derivative of k(u). Determine p so that b(p) = 0.
-1, 0, 1/2
Let l(t) be the third derivative of -t**7/140 - t**6/60 + t**5/24 + t**4/24 - t**2. Let l(f) = 0. What is f?
-2, -1/3, 0, 1
Find i, given that 4/3*i**2 + 16/9 + 8/3*i + 2/9*i**3 = 0.
-2
Let -6*y**2 - 2*y + 30*y**4 - 2*y + 0*y**5 + 2*y**5 + 2*y**3 - 24*y**4 = 0. What is y?
-2, -1, 0, 1
Let n(b) be the first derivative of b**6/3 - 3*b**4/2 + 4*b**3/3 - 3. Solve n(d) = 0 for d.
-2, 0, 1
Let b = 9 - 7. Factor -9*m + 7*m**3 + 6*m**4 - m + 5*m**3 - 4 - b*m**2 - 2*m**3.
2*(m - 1)*(m + 1)**2*(3*m + 2)
Let x(u) be the first derivative of -u**6/60 + u**4/12 + 2*u**2 - 1. Let g(c) be the second derivative of x(c). Factor g(r).
-2*r*(r - 1)*(r + 1)
Let y(q) be the third derivative of 1/240*q**5 + 0*q - 2*q**2 + 1/280*q**7 + 0*q**4 + 0 + 1/120*q**6 + 0*q**3. Factor y(c).
c**2*(c + 1)*(3*c + 1)/4
Let p(n) be the second derivative of n**5/270 + n**4/108 - n**2 - 2*n. Let y(s) be the first derivative of p(s). Let y(i) = 0. Calculate i.
-1, 0
Factor 0 - 2/5*t**2 - 1/5*t - 1/5*t**3.
-t*(t + 1)**2/5
Let n(i) be the first derivative of -i**6/5 + 14*i**5/25 - i**4/2 + 2*i**3/15 - 7. Factor n(b).
-2*b**2*(b - 1)**2*(3*b - 1)/5
Let a be 25/8 - (2 - -1). Let l(s) be the first derivative of -1/6*s**6 - 7/12*s**3 - a*s**2 + 0*s - 13/20*s**5 - 2 - 15/16*s**4. Find m, given that l(m) = 0.
-1, -1/4, 0
Let n be 1 + (1 - 918/21). Let p = n - -42. Let -2/7 - 6/7*t - p*t**3 - 6/7*t**2 = 0. Calculate t.
-1
Let x(n) = n**5 - 12*n**4 - 13*n**3 + 3*n**2 + 12*n + 4. Let t(d) = -d**5 + d**3 + d**2. Let u(r) = 5*t(r) + x(r). Factor u(p).
-4*(p - 1)*(p + 1)**4
Let y(b) be the third derivative of -1/300*b**5 + 0*b + 0 + 0*b**4 + 4*b**2 + 1/30*b**3. Let y(l) = 0. Calculate l.
-1, 1
Let f(b) = 7*b**3 + 10*b**2 + 7*b. Let a(j) = j**3 + j. Let n(z) = -2*a(z) + f(z). Determine w, given that n(w) = 0.
-1, 0
Let y(b) = -17*b**2 - 13*b + 5. Let c(u) = -8*u**2 - 6*u + 2. Let j(g) = -10*c(g) + 4*y(g). Solve j(h) = 0 for h.
-2/3, 0
Let -9*g**4 + 43*g**3 + 31*g**2 + 13*g - 102*g**2 + 18*g**2 + 6 = 0. What is g?
-2/9, 1, 3
Let h = 187 + -1307/7. Suppose -4/7 + 2/7*v**4 - 6/7*v**2 + 10/7*v - h*v**3 = 0. What is v?
-2, 1
Determine c so that -62*c + 179*c + 354*c**3 - 540*c**2 + 163*c - 60*c**4 + 3*c**5 - 37*c = 0.
0, 1, 9
Suppose -6*x = 4*p - 5*x - 4, 0 = -5*p - 2*x + 2. Factor 0 + 0*i**p + 3/5*i**3 - 3/5*i.
3*i*(i - 1)*(i + 1)/5
Let c(m) be the second derivative of m**7/14 - m**6/3 + 3*m**5/5 - m**4/2 + m**3/6 - 6*m. Factor c(n).
n*(n - 1)**3*(3*n - 1)
Let c = 35 + -29. Let q(s) be the third derivative of -1/36*s**4 - 1/126*s**8 - 13/315*s**7 - 1/12*s**c + 2*s**2 + 0 + 0*s**3 + 0*s - 7/90*s**5. Factor q(b).
-2*b*(b + 1)**3*(4*b + 1)/3
Let q(l) = l**3 - l**2 - 5*l - 3. Let j be q(4). Suppose -j = 3*v - 8*v. Suppose 0*w**2 + 0*w**2 + 3*w - 6*w**3 + 3*w**v = 0. Calculate w.
-1, 0, 1
Determine z, given that 1/9*z**2 + 11/9 - 4/3*z = 0.
1, 11
Let z(b) be the first derivative of -b**3/12 - b**2/8 + b/2 + 7. Let z(u) = 0. Calculate u.
-2, 1
Let 6*k**2 + 8*k**4 - 74*k**3 + 2*k**2 + 54*k**3 = 0. What is k?
0, 1/2, 2
Suppose -8*l + 5*l = 0. Let x(h) be the third derivative of 0*h + 1/84*h**4 - 2*h**2 + l*h**5 - 1/420*h**6 + 0*h**3 + 0. What is q in x(q) = 0?
-1, 0, 1
Let b = -4 + 10. Let j be (-15)/b*4/(-15). Factor 5/3*r**2 - 4*r**3 + j*r + 0.
-r*(3*r - 2)*(4*r + 1)/3
Factor 1/4*l**2 + l + 3/4.
(l + 1)*(l + 3)/4
Let u(y) be the first derivative of 1/900*y**6 - 1/300*y**5 + 3 + 0*y**2 + 0*y**4 + 0*y - 2/3*y**3. Let r(b) be the third derivative of u(b). Factor r(v).
2*v*(v - 1)/5
Let f = -89/84 + 8/7. Let g(x) be the third derivative of f*x**3 + 0*x - 1/60*x**5 + 0*x**6 - 2*x**2 + 1/420*x**7 + 0 + 0*x**4. Factor g(t).
(t - 1)**2*(t + 1)**2/2
Let q(x) = -80*x**4 - 55*x**3 + 80*x**2 + 55*x. Let k(s) = -3*s**4 - 2*s**3 + 3*s**2 + 2*s. Let d(g) = -55*k(g) + 2*q(g). Factor d(i).
5*i**2*(i - 1)*(i + 1)
Suppose -24 + 22 = -d. Let v(l) be the first derivative of -3/4*l**2 + 0*l + 3/4*l**4 - d + 1/2*l**3. Suppose v(b) = 0. Calculate b.
-1, 0, 1/2
Let b(q) = -5*q**5 + 3*q**4 - 7*q**3 + 5*q**2 + 4*q + 4. Let p(t) = -t**5 - t**3 + t**2 + t + 1. Let m(w) = -b(w) + 4*p(w). Factor m(d).
d**2*(d - 1)**3
Let m(j) be the first derivative of j**6/60 + j**5/15 + j**4/12 + 2*j**2 - 2. Let n(s) be the second derivative of m(s). Determine a so that n(a) = 0.
-1, 0
Let x(j) = -j - 1. Let k be x(2). Let c be (-8)/7*k/12. Suppose 6/7*p**2 + 2/7 + c*p**3 + 6/7*p = 0. Calculate p.
-1
Suppose -40/3*q - 200/3 - 2/3*q**2 = 0. Calculate q.
-10
Let c(n) be the second derivative of 0*n**2 + n + 2/15*n**3 + 1/50*n**5 + 1/10*n**4 + 0. Factor c(r).
2*r*(r + 1)*(r + 2)/5
Suppose -v = -20 + 18. Let w(u) be the third derivative of 0*u**4 + 1/360*u**6 + 2*u**v + 0 + 1/1008*u**8 + 0*u + 0*u**3 + 1/315*u**7 + 0*u**5. Factor w(h).
h**3*(h + 1)**2/3
Let b(r) be the second derivative of 3*r**7/8 - 29*r**6/40 + 3*r**5/20 + r**4/4 - 15*r. Let b(k) = 0. What is k?
-2/7, 0, 2/3, 1
Let k(p) = p**3 + 9*p**2 + 10*p + 20. Let h be k(-8). Factor -1/4*x**2 + 0*x**3 + 1/4*x**h + 0*x + 0.
x**2*(x - 1)*(x + 1)/4
Find r such that 2/3*r + 1 - 1/3*r**2 = 0.
-1, 3
Let d(q) be the first derivative of q**4/16 + 5*q**3/12 - q**2/8 - 5*q/4 + 67. Factor d(i).
(i - 1)*(i + 1)*(i + 5)/4
Let h(x) = -x**3 - 8*x**2 + 9*x + 2. Let b be h(-9). Suppose 2*a + a + k + 1 = 0, a = -2*k - b. Factor 2/3*q**2 + a*q - 2/3.
2*(q - 1)*(q + 1)/3
Let m(w) = -4*w**2 + 2*w + 2. Let i(n) = -11*n**2 + 6*n + 5. Let k(p) = -3*i(p) + 8*m(p). Factor k(y).
(y - 1)**2
Factor -4/5*z**3 - 2/5*z**4 + 0*z**2 + 0*z + 0.
-2*z**3*(z + 2)/5
Let t(w) be the second derivative of 0*w**3 - 5*w - 9/80*w**5 + 0*w**2 - 3/40*w**6 - 1/16*w**4 - 1/56*w**7 + 0. Solve t(f) = 0.
-1, 0
Let g(b) be the second derivative of -b**8/23520 + b**7/4410 - b**6/2520 - b**4/6 + 3*b. Let a(k) be the third derivative of g(k). Solve a(n) = 0.
0, 1
Let n(h) be the third derivative of -3/280*h**7 - 1/240*h**5 + 0 - 1/336*h**8 + 0*h**4 - 2*h**2 + 0*h + 0*h**3 - 1/80*h**6. Factor n(c).
-c**2*(c + 1)**2*(4*c + 1)/4
Let q(a) be the first derivative of a**6/3240 + a**5/360 + a**4/108 + a**3/3 + 9. Let r(v) be the third derivative of q(v). Find d, given that r(d) = 0.
-2, -1
Let -4/5*n**2 + 6/5 - 2*n = 0. What is n?
-3, 1/2
Let d(c) be the third derivative of 1/12*c**4 + 0*c**3 + 0 + 0*c + 1/210*c**7 + 1/40*c**6 - 1/12*c**5 - 1/336*c**8 + 4*c**2. What is u in d(u) = 0?
-2, 0, 1
Factor -5*f + 6*f - 57*f**2 + 30*f**2 + 30*f**2.
f*(3*