 - 1)*(v + 18)*(2*v - 3)/2
Let c(q) be the first derivative of -q**6/33 - 12*q**5/55 + 17*q**4/11 - 112*q**3/33 + 39*q**2/11 - 20*q/11 + 211. Factor c(u).
-2*(u - 1)**4*(u + 10)/11
Suppose 3*p + 12 = 0, 4*j - 28 + 4 = 4*p. Factor r**2 + 0*r**2 + 20*r - 4*r**j - 2*r**2 - 20.
-5*(r - 2)**2
Let m(f) = 2*f**2 + 3*f - 3. Let s be m(-6). Factor -11*r**3 - 12*r**4 - 4*r**2 + 51*r - 4*r**5 - r**3 - s*r.
-4*r**2*(r + 1)**3
Let n(w) be the second derivative of -3*w**5/20 + 2*w**4 - 13*w**3/2 + 9*w**2 + 121*w + 2. Suppose n(z) = 0. What is z?
1, 6
Let w(k) = -8*k**2 + 7*k + 30. Let z(b) = 26*b**2 - 22*b - 90. Let n(p) = -20*w(p) - 6*z(p). What is u in n(u) = 0?
-3, 5
What is c in 18 + 23840*c**2 + 6 + 22*c + 3*c - 23839*c**2 = 0?
-24, -1
Let s(u) be the third derivative of 0 + 37*u**2 + 0*u**4 - 2/45*u**5 - 1/36*u**6 + 0*u + 0*u**3 - 1/315*u**7. Find p such that s(p) = 0.
-4, -1, 0
Determine y, given that 1295*y**2 - 196*y + 1290*y**2 - 2584*y**2 = 0.
0, 196
Factor 0 - 632/9*k**2 + 4/9*k**3 + 24964/9*k.
4*k*(k - 79)**2/9
Let j(y) be the third derivative of -y**7/42 + 5*y**6/24 + 11*y**5/6 + 10*y**4/3 - 26*y**2 - 9*y. Factor j(u).
-5*u*(u - 8)*(u + 1)*(u + 2)
Let t**4 + 5*t**2 + 32/3*t**3 + 0 - 2/3*t**5 + 0*t = 0. Calculate t.
-3, -1/2, 0, 5
Let o(b) be the third derivative of 0*b**5 + 0*b**4 + 9*b**2 + 0 - 1/525*b**7 + 0*b + 0*b**3 + 1/100*b**6. Let o(p) = 0. Calculate p.
0, 3
Let t(k) be the first derivative of -5*k**6/4 - 729*k**5/40 - 51*k**4/16 + 3*k**3 - 3. Let t(g) = 0. Calculate g.
-12, -2/5, 0, 1/4
Let t(a) = -18*a - 70. Let x be t(-4). Let r(u) be the third derivative of -1/20*u**5 + 0 + 0*u + 0*u**3 + 6*u**x + 0*u**4. Suppose r(g) = 0. What is g?
0
Let t be (-1)/(548/(-136) + 4). Suppose -k - 5*b + t = 2*k, 2*b - 22 = -4*k. Factor -k*j - 26*j**2 + 6 - 7*j + j + 11*j**2.
-3*(j + 1)*(5*j - 2)
Let y be (-187)/(-238) - ((-22)/4 + 6). Factor -2*f - y*f**3 + 6/7 + 10/7*f**2.
-2*(f - 3)*(f - 1)**2/7
Let x = 23627/5 - 4725. Factor -14/5 + x*p**2 - 12/5*p.
2*(p - 7)*(p + 1)/5
Let z(l) be the third derivative of l**7/945 - 13*l**6/270 + 169*l**5/270 + l**2 - 144. What is v in z(v) = 0?
0, 13
Let a be -3 + 5 + (-12)/1. Let x be 93/30 + -2 + (-4)/a. Factor x*d - 3/2*d**3 + 0*d**2 + 0.
-3*d*(d - 1)*(d + 1)/2
Let h(z) = 12*z**5 + 4*z**4 + 5*z**3 - 9*z**2 - 11*z. Let n(m) = 4*m + 4*m - 10*m + m**2 + 3*m - m**5. Let y(j) = 2*h(j) + 22*n(j). Let y(c) = 0. Calculate c.
-2, -1, 0
Factor 5272 + 96*x + 93*x**2 - 3*x**3 - 5272.
-3*x*(x - 32)*(x + 1)
Let k(y) be the third derivative of y**8/2520 + 8*y**7/1575 + y**6/60 - 4*y**5/225 - 4*y**4/45 - 66*y**2. Find n, given that k(n) = 0.
-4, -1, 0, 1
Let i(o) be the second derivative of o**4/66 - o**2/11 + 24*o - 1. Determine l, given that i(l) = 0.
-1, 1
Suppose 2*f + 0*f - 4*c = -8, -2*f + c = 2. Suppose -t + f = -2. Determine k, given that 4*k**2 - t*k**2 - 4*k**3 + 5 - 7*k - 7 + 11*k**3 = 0.
-1, -2/7, 1
Let f = -60 - -70. Factor -f*s + 0*s - 13*s**2 - 2*s**3 + 25*s**2.
-2*s*(s - 5)*(s - 1)
Let w = 83/21 + -23/7. Let b = -50 + 53. Suppose -2*j**2 - w*j**b - 4/3*j + 0 = 0. Calculate j.
-2, -1, 0
Let f(j) = 35*j**2 - 67*j + 110. Let t(v) = 183*v**2 - 336*v + 549. Let r(l) = 21*f(l) - 4*t(l). Factor r(u).
3*(u - 19)*(u - 2)
Suppose 0 = -2*u + 4*o + 8, -11 = -5*u + 2*u + 5*o. Solve -4*h**2 + 4*h + 5*h**2 - 8 + 2*h**u + h**2 = 0 for h.
-2, 1
Let y(u) be the second derivative of 0*u**3 - 11*u + 0 + 5/42*u**7 + 1/3*u**6 - 1/4*u**5 + 0*u**2 - 5/6*u**4. Find h, given that y(h) = 0.
-2, -1, 0, 1
Factor -21/4*r**3 + 153/4*r**2 - 147/2*r + 18.
-3*(r - 4)*(r - 3)*(7*r - 2)/4
Suppose -2*n + 6 + 12 = 0. Suppose -n*l**4 + 48*l + 8 - 9*l**4 + 0 + 38*l**3 - l**2 - 14*l**5 + 83*l**2 = 0. Calculate l.
-1, -2/7, 2
Let v(r) be the first derivative of r**3/4 + 5*r**2/4 - 2*r - 52. Factor v(k).
(k + 4)*(3*k - 2)/4
Suppose -21*p + 24*p + 0 = 6. Suppose 0 = -2*s + 7*s - 5*n - 15, 5*s - 3*n - 9 = 0. Factor s + 1/4*q**p + 1/4*q.
q*(q + 1)/4
Let c(w) = 5*w**2 + 37*w - 314. Let x(p) = p**2 + 7*p - 62. Let r(m) = 2*c(m) - 11*x(m). Factor r(d).
-(d - 6)*(d + 9)
Let 2/5*q**3 + 0 - 2/5*q**5 + 0*q - 48/5*q**4 + 48/5*q**2 = 0. Calculate q.
-24, -1, 0, 1
Let f(n) = -5*n**2 - 11*n - 6. Let s(t) = -65*t**2 + 3*t - 4*t + 64*t**2. Let r(o) = f(o) - 2*s(o). Factor r(a).
-3*(a + 1)*(a + 2)
Suppose 87*j = -4 + 178. Factor c - 1/2*c**j + 3/2.
-(c - 3)*(c + 1)/2
Let t be 0 - (0 + 3/(-1)). Suppose 0*y - y + 2 = 0. Suppose 21*x**t - 15*x**y - 3 - 48*x - 11 + 2 + 0*x**3 = 0. Calculate x.
-1, -2/7, 2
Let i be 57/2 + (-31)/(62/12). Let y(l) be the first derivative of -i*l**4 + 0*l - 39/5*l**5 - 12*l**2 - 4 - l**6 - 28*l**3. Factor y(v).
-3*v*(v + 2)**3*(2*v + 1)
Let m(h) be the first derivative of h**6/360 + h**5/45 + h**4/24 + 10*h**2 + 15. Let j(x) be the second derivative of m(x). Let j(y) = 0. Calculate y.
-3, -1, 0
Let u(p) be the first derivative of -3*p**5/5 - 3*p**4 - 3*p**3 + 56. Solve u(y) = 0.
-3, -1, 0
Let a(x) be the second derivative of 3*x**5/20 + 5*x**4/2 + 21*x**3/2 - 88*x. Factor a(n).
3*n*(n + 3)*(n + 7)
Suppose 20 = 29*s - 24*s. Suppose 3 = -s*v + 167. Factor j**3 + 21 - v + 20.
j**3
Let k(p) be the second derivative of p**9/1512 - p**8/840 - p**7/420 + p**6/180 + 3*p**3/2 - p. Let x(b) be the second derivative of k(b). Factor x(j).
2*j**2*(j - 1)**2*(j + 1)
Let r be ((-4)/10)/(4/(-20)). Let l(f) = -2*f - 14. Let c be l(-12). Factor c - 14*g**2 - 3*g - r*g - g**2.
-5*(g + 1)*(3*g - 2)
Let m(t) be the third derivative of -t**8/50400 - t**7/12600 + t**5/60 - 9*t**4/8 - 9*t**2 + 2*t. Let r(p) be the third derivative of m(p). Factor r(a).
-2*a*(a + 1)/5
Suppose 2*d = -8, r = 2*d + d + 14. Factor 5*n**2 + 0*n**2 - r + n + 0*n**2 + 2*n**3.
(n + 1)*(n + 2)*(2*n - 1)
Let f(s) be the third derivative of 2/23*s**3 + 0*s + 9*s**2 - 1/345*s**5 - 5/276*s**4 + 0 + 1/1380*s**6. Determine g so that f(g) = 0.
-2, 1, 3
Let r be (23 - 20)*(-4)/(-60). Factor -3/5*t**2 - r - t + 4/5*t**4 + t**3.
(t - 1)*(t + 1)**2*(4*t + 1)/5
Let a(z) = -4*z**4 + 2*z**3 + 5*z**2 - 6*z - 3. Let q(y) = -3*y**4 + 3*y**3 + 6*y**2 - 8*y - 2. Let l(w) = -2*a(w) + 3*q(w). Factor l(m).
-m*(m - 6)*(m - 1)*(m + 2)
Let f be 333/270 - (-43)/430. Solve 26/3*q + f*q**3 - 25/3*q**2 - 5/3 = 0.
1/4, 1, 5
Let x(o) be the first derivative of o**3/2 + o**2/2 - 5*o/2 - 57. Factor x(l).
(l - 1)*(3*l + 5)/2
Let y(w) = 7*w**2 + 110*w - 135. Let g(h) = 2*h**2 + 28*h - 34. Let c(n) = -9*g(n) + 2*y(n). Determine s so that c(s) = 0.
-9, 1
Let n be 0/(0 - -5) + (-94)/(-60). Let u = n + -11/30. Factor 6/5*d - 4/5 - 14/5*d**3 + u*d**2 + 6/5*d**4.
2*(d - 1)**3*(3*d + 2)/5
Factor 22/7*w**2 - 12/7*w - 16/7 + 6/7*w**3.
2*(w - 1)*(w + 4)*(3*w + 2)/7
Let h = 89 + -87. Factor -n - 12*n + 3*n - 2*n**2 + h*n.
-2*n*(n + 4)
Let w(h) be the first derivative of 2*h**6/3 - 4*h**5 + 4*h**4 - 209. Factor w(y).
4*y**3*(y - 4)*(y - 1)
Suppose -i + 6 = 2*g + 1, 5*g - i - 9 = 0. Determine f so that 47*f - 33*f - 5*f**g + 16*f = 0.
0, 6
Let g(o) be the first derivative of 5/3*o**3 + 8 - 15*o - 5*o**2. Factor g(k).
5*(k - 3)*(k + 1)
Suppose 3 = t - 0*t. Suppose -14 = t*u - 4*x, -3*u + 6*u = x + 1. Find g such that -4*g**2 - u + 16*g - 1 - 9 = 0.
1, 3
Let i(n) be the second derivative of -n**5/4 + 65*n**4/12 - 3*n. Determine d, given that i(d) = 0.
0, 13
Let s = -4525 - -4543. Factor s*y**2 + 8*y + 8/9.
2*(9*y + 2)**2/9
Let f(y) be the second derivative of -y**4/12 - 402*y. Determine r, given that f(r) = 0.
0
Let j(t) be the second derivative of t**7/14 - 3*t**6/5 + 33*t**5/20 - t**4/2 - 6*t**3 + 12*t**2 - 530*t. Factor j(p).
3*(p - 2)**3*(p - 1)*(p + 1)
Let i = -2079 - -2083. Let a(f) be the second derivative of 0 - 6*f - 3/2*f**3 - 9/2*f**2 - 1/4*f**i - 1/60*f**5. Factor a(b).
-(b + 3)**3/3
Let m(w) be the first derivative of -10*w**3/39 - 3*w**2 + 16*w/13 - 86. Suppose m(r) = 0. What is r?
-8, 1/5
Let p(j) = 2*j**3 - 2*j**2 + 17*j + 3. Let u(s) = -9*s**3 + 9*s**2 - 84*s - 12. Let w(t) = -24*p(t) - 5*u(t). Factor w(y).
-3*(y - 2)*(y - 1)*(y + 2)
Let d = 3073/390 + -102/13. Let p(t) be the third derivative of 0*t + 1/6*t**4 + 0 - 9*t**2 - d*t**5 - 1/3*t**3. Factor p(g).
-2*(g - 1)**2
Suppose -20 = 2*x - 4*v, 2*v + 24 = -3*x + 6*v. Let o be 15/36 - 1/x. Let -l**2 + 5/3*l + o = 0. What is l?
-1/3, 2
Let f(m) be the first derivative of 