+ h**6/1680 + 4*h**4/3 + 2*h. Let k(z) be the third derivative of d(z). Factor k(f).
-3*f*(f - 1)*(3*f + 1)**2/7
Suppose 2*r**3 + 4 + 35/3*r - 1/3*r**5 + 32/3*r**2 - 4/3*r**4 = 0. Calculate r.
-4, -1, 3
Let t(v) be the first derivative of -25*v**5/4 + 725*v**4/12 - 260*v**3/3 + 50*v**2 + 40*v + 7. Let k(p) be the first derivative of t(p). Factor k(h).
-5*(h - 5)*(5*h - 2)**2
Let f = 517 + -181. Suppose -f = -5*r - r. Determine p, given that -p**5 - 2*p**4 + 2*p - 3*p + 58*p**3 - r*p**3 + 4*p**2 - 2 = 0.
-2, -1, 1
Let g = -322 - -327. Let d(p) be the third derivative of -g*p**2 - 1/40*p**5 + 0 + 3/140*p**7 - 1/20*p**6 + 0*p + 1/8*p**4 + 0*p**3. Factor d(a).
3*a*(a - 1)**2*(3*a + 2)/2
Let s(l) be the first derivative of l**4/3 - 4*l**3/3 - 6*l**2 + 2*l + 3. Let a(c) be the first derivative of s(c). Find f, given that a(f) = 0.
-1, 3
Let m(r) be the second derivative of -r**4/30 - 232*r**3/15 - 13456*r**2/5 - r + 128. What is v in m(v) = 0?
-116
Find w, given that -21*w - 6*w**2 - 18 + 3*w**3 - 31 + 37 = 0.
-1, 4
Let t(d) be the third derivative of 0*d**3 - 5/672*d**8 + 0*d + 0 + 5*d**2 + 3/80*d**6 - 1/12*d**4 + 1/15*d**5 - 2/105*d**7. Determine j, given that t(j) = 0.
-2, -1, 0, 2/5, 1
Suppose v - 7*v**3 - 10*v + v + 5*v**3 - 24 + 14*v**2 = 0. Calculate v.
-1, 2, 6
Let u be (495/(-165))/(1 - (-15)/(-2)). Factor -4/13*w**2 - 2/13 + u*w.
-2*(w - 1)*(2*w - 1)/13
Suppose 3*r - 4*a = 2, 2*a = 33*r - 35*r + 6. Factor 0 + 1/8*n**3 + 0*n + 0*n**r.
n**3/8
Let i(g) = -65*g**2 - 34*g - 23. Let v(l) = -29*l**2 - 16*l - 12. Let t(o) = -4*i(o) + 9*v(o). Factor t(f).
-(f + 4)**2
Let m(d) be the first derivative of 1/9*d**6 - 2/27*d**3 + 0*d + 15 + 2/9*d**5 + 1/18*d**4 + 0*d**2. Factor m(o).
2*o**2*(o + 1)**2*(3*o - 1)/9
Solve 1/2*w**5 - 60*w - 50 + 119/2*w**3 + 21/2*w**4 + 79/2*w**2 = 0 for w.
-10, -1, 1
Let n = 3487/3 + -1159. Factor 5/3*g**2 + 5/3*g - n.
5*(g - 1)*(g + 2)/3
Let k(d) = 2*d**2 + 32*d - 158. Let q(t) = 4*t - 2*t + 1 - 3*t + t**2. Let v(n) = -k(n) + 4*q(n). Let v(x) = 0. Calculate x.
9
Let q(v) = -2*v**2 - 10*v - 42. Let i(s) = 6*s**2 + 32*s + 124. Let b(l) = -5*i(l) - 14*q(l). Suppose b(z) = 0. Calculate z.
-8, -2
Suppose -5*v = -10*v + 55. Let k be 1/((33/36)/v). Factor -9*g**4 + 1052 - k*g**5 - 1052 + 3*g**3.
-3*g**3*(g + 1)*(4*g - 1)
Let k(u) = -u**3 + 6*u**2 + 4*u + 16. Let b be k(7). Let z be b/(-2)*52/26. Factor 2/7*v**z - 6/7*v - 6/7*v**4 + 2/7 + 4/7*v**3 + 4/7*v**2.
2*(v - 1)**4*(v + 1)/7
Let w(m) be the second derivative of -5*m**4/12 - 20*m**3/3 - 81*m. Determine v so that w(v) = 0.
-8, 0
Let r(g) be the third derivative of -g**8/140 - g**7/105 + g**6/10 - g**5/6 + g**4/10 - 6*g**2 - 24*g. What is i in r(i) = 0?
-3, 0, 1/2, 2/3, 1
Let m(w) be the second derivative of -2*w**6/45 - 2*w**5/15 - 2*w. Factor m(k).
-4*k**3*(k + 2)/3
Let z(t) be the third derivative of -5*t**2 - 1/80*t**5 + 0*t + 0 - 9/8*t**3 + 3/16*t**4. Factor z(n).
-3*(n - 3)**2/4
Suppose 41*i = 48*i - 14. Factor 0*m - 1/2*m**3 + 0*m**i + 0.
-m**3/2
Let z be (-35)/28 + (1012/(-270) - -5). Let r(i) be the third derivative of 4/9*i**4 + 64/27*i**3 + 2/45*i**5 + 11*i**2 + 0*i + z*i**6 + 0. Factor r(p).
2*(p + 4)**3/9
Let l be 72/8 - (1 + 4). Let g(v) be the first derivative of 6/5*v**5 + 5/2*v**4 - 4/3*v**3 - l + 0*v**2 + 0*v. Factor g(p).
2*p**2*(p + 2)*(3*p - 1)
Let k = -4 + 0. Let n(f) = f + 4*f - f**3 - 10*f + 4*f + f**2. Let h(y) = -2*y**3 + 8*y**2 - 2*y. Let b(a) = k*n(a) + h(a). Let b(j) = 0. Calculate j.
-1, 0
Let r = -120 + 6. Let v = 346/3 + r. Factor -1/3 - v*l + 5/3*l**2.
(l - 1)*(5*l + 1)/3
Suppose 8*l - b = 12*l - 185, 0 = -3*l - 3*b + 150. Suppose a - l = -14*a. Find m such that -3/2*m**2 - 1/2 + 3/2*m + 1/2*m**a = 0.
1
Let g(a) be the third derivative of 0 + 0*a + 1/3*a**4 - 8/3*a**3 - 7*a**2 + 1/120*a**6 + 7/60*a**5. Factor g(m).
(m - 1)*(m + 4)**2
Suppose -4*c + c - 40 = -13*c. Factor -1/3*u**5 - 2*u**c - 2/3 - 14/3*u**3 - 3*u - 16/3*u**2.
-(u + 1)**4*(u + 2)/3
Let p(i) be the third derivative of 22*i**2 + 0*i**4 + 0*i**3 + 0*i + 5/84*i**8 + 0*i**5 + 0 + 0*i**6 - 4/105*i**7. Factor p(v).
4*v**4*(5*v - 2)
Suppose -11 = -2*i - 2*b + 3, 5 = 3*i - b. Let a be (2/9)/(28/8 - i). What is o in 2/9*o**5 - a*o**4 - 2/9*o + 4/9*o**2 + 0 + 0*o**3 = 0?
-1, 0, 1
Let d(p) be the first derivative of 1/9*p**3 + 1/3*p + 1/3*p**2 - 5. Suppose d(t) = 0. What is t?
-1
Let d(c) = -3*c**4 - 31*c**3 + 189*c**2 - 293*c + 123. Let a(b) = -4*b**4 - 47*b**3 + 284*b**2 - 439*b + 185. Let o(z) = 5*a(z) - 7*d(z). Factor o(j).
(j - 8)**2*(j - 1)**2
Let o(r) = 7*r**4 - 13*r**3 - 13*r**2 + 52*r - 9. Let b(p) = -p**4 - 1. Let n(q) = 3*b(q) + o(q). Determine h, given that n(h) = 0.
-2, 1/4, 2, 3
Let h(y) = 3*y - 6. Let j be h(4). Let -j*a**2 + 2 + a**2 + a**2 - 2*a = 0. What is a?
-1, 1/2
Suppose -14*d + 13*d - 8 = 0. Let w(p) = 5*p**4 - 5*p**3 - 8*p**2 + 8. Let t(k) = 2*k**4 - 2*k**3 - 3*k**2 + 3. Let m(n) = d*t(n) + 3*w(n). Solve m(l) = 0.
0, 1
Let y(d) be the third derivative of d**7/70 - 3*d**6/40 - 9*d**5/20 - 5*d**4/8 + 2*d**2 - 14*d. Factor y(q).
3*q*(q - 5)*(q + 1)**2
Let u be 21/(42/4) - 27/15. Factor -u + 1/5*t**4 - 2/5*t**3 + 2/5*t + 0*t**2.
(t - 1)**3*(t + 1)/5
Let s be (-11)/8 + 105/70. Let f(p) be the first derivative of s*p**4 + 1/4*p**2 + 1/3*p**3 + 2 + 0*p. Factor f(i).
i*(i + 1)**2/2
Let x(g) = -g - 6. Let a be x(-13). Let b be 14/a*(1 + 0). Find i, given that 5*i**b - i**2 + 5*i**2 + 6*i = 0.
-2/3, 0
Factor -25*i**3 - 4*i**4 - i**4 + 70*i + 59*i - 29*i - 280 + 90*i**2.
-5*(i - 2)**2*(i + 2)*(i + 7)
Let p(b) be the first derivative of -2*b**3/3 - b**2 + 4*b + 103. Solve p(i) = 0.
-2, 1
Let x(y) be the first derivative of y**5/45 - y**4/36 - 26*y**3/27 - 4*y**2/3 - 454. Factor x(u).
u*(u - 6)*(u + 1)*(u + 4)/9
Let w = 7 - 13. Let z be 1/w*(-17 - -1). Find j such that -z*j**2 + 7/3*j**4 + 4/3*j**5 + 1/3 - 2/3*j**3 - 2/3*j = 0.
-1, 1/4, 1
Let j(z) = -z**2 + z - 1. Let w(c) = c**2 - 15*c + 13. Let x be w(14). Let m(f) = -11*f**2 + 11*f - 6. Let t(n) = x*m(n) + 6*j(n). Let t(s) = 0. Calculate s.
0, 1
Let y be -1 - (-3)/2 - (2800/48 - 58). Factor -1/6*x**5 - y*x**3 + 0*x + 1/3*x**4 + 0*x**2 + 0.
-x**3*(x - 1)**2/6
Let q = 601/39 + -196/13. Factor 1/3*u**3 + 1/6*u**2 - q*u + 0 - 1/6*u**4.
-u*(u - 2)*(u - 1)*(u + 1)/6
Let x(i) be the first derivative of 15*i**3 - 51*i**2/2 + 16*i - 8. Let f(p) = 112*p**2 - 128*p + 40. Let k(v) = -5*f(v) + 12*x(v). Factor k(l).
-4*(l - 1)*(5*l - 2)
Let z(r) be the first derivative of -r**6/12 + 3*r**5/10 + r**4/2 - 209. Factor z(c).
-c**3*(c - 4)*(c + 1)/2
Let v(o) be the first derivative of o**5/5 + o**4/3 - 4*o**3/3 - 24*o - 4. Let h(z) be the first derivative of v(z). Factor h(j).
4*j*(j - 1)*(j + 2)
Let b(n) be the second derivative of n**4/8 + n**3/2 + 237*n. Find y, given that b(y) = 0.
-2, 0
Let o(z) be the second derivative of 0 + 0*z**2 - 1/12*z**4 + 2/3*z**3 - 13*z. Let o(m) = 0. Calculate m.
0, 4
Suppose -n - 2*n = 5*j - 31, -13 = -j - 4*n. Let -10 + 9*w**4 - 15*w**2 + 3*w + j*w**3 - 4*w**4 - 28*w = 0. What is w?
-1, 2
Let 8 - 4*k**3 + 25*k - 21*k - 5*k**2 + 8*k**2 - 7*k**2 - 4 = 0. Calculate k.
-1, 1
Let x(z) = 8*z**4 + 7*z**3 - 5*z**2 - 8*z - 4. Let d(a) = -25*a**4 - 22*a**3 + 16*a**2 + 26*a + 13. Let p(q) = 4*d(q) + 13*x(q). Factor p(f).
f**2*(f + 1)*(4*f - 1)
Let n(r) be the first derivative of -r**6/21 + 12*r**5/35 - 2*r**4/7 - 4*r**3/7 + 5*r**2/7 - 228. Solve n(u) = 0.
-1, 0, 1, 5
Let a be (8/10)/((-4)/(-20)). Let i = -8 - -10. Determine w so that -5*w - a + w - w**i + 0 = 0.
-2
Let a be -4 + (-8)/2 + 15. Suppose 2*y + 10 = a*y. Determine q so that -4*q**3 + 5*q**4 - 4*q**y - q**4 + 2*q**5 + 2*q**5 = 0.
-1, 0, 1
Let s(w) be the second derivative of -5*w**5 + 16*w**2 + 24*w**3 + 0 + 34/3*w**4 - 14/5*w**6 - 17*w + 20/21*w**7. Suppose s(y) = 0. Calculate y.
-1, -1/2, -2/5, 2
Let z be 29 + (-25)/(-125)*-125. Suppose 0 + h - 3/2*h**z - 1/2*h**3 + 3/2*h**2 - 1/2*h**5 = 0. Calculate h.
-2, -1, 0, 1
Let g = 209/290 + -32/145. Suppose o + g*o**2 + 1/2 = 0. Calculate o.
-1
Suppose -3*x + 4*q = -25, -1462*q = 4*x - 1457*q + 8. Factor 1/3*o**x + 1/2*o**2 + 1/2 - 4/3*o.
(o - 1)*(o + 3)*(2*o - 1)/6
Let k(a) be the third derivative of a**6/120 + a**5/2 + 21*a**4/2 + 196*a**3/3 + 2*a**2 + 43*a. Let k(t) = 0. Calculate t.
-14, -2
Let h = 2 + 2. 