2 + 4*b**5 - b**5 = 0. Calculate b.
-1, 0
Suppose -2*t = 3*t - 4*h - 220, 0 = -5*h + 25. Suppose 2*p - p = t. Factor -28*g - 4*g**2 + p*g - 20*g.
-4*g**2
Let m(b) = b**3 - 28*b**2 - 34*b + 70. Let p be m(29). Let h = p - -75. Let 1/4*t**4 - 1/2*t**3 + 1/2*t - 1/4 + h*t**2 = 0. What is t?
-1, 1
Let d(f) be the third derivative of -1/12*f**4 + 175*f**2 + 1/12*f**6 + 0*f + 0 + 2/15*f**5 + 0*f**3. Determine b, given that d(b) = 0.
-1, 0, 1/5
Let p(g) = -g**2 - 37*g + 1220. Let t be p(21). Let u(x) be the first derivative of 3/8*x**4 - 12*x - 6/5*x**5 + 5*x**3 + 1/4*x**6 - 3*x**t - 35. Factor u(v).
3*(v - 2)**3*(v + 1)**2/2
Suppose 4*q - 181 = -11*f, 426*q - 429*q + 2*f - 18 = 0. Suppose 2/3*m**q - 8*m**2 + 0*m**3 + 32/3*m + 0 = 0. What is m?
-4, 0, 2
Let b(n) = -41*n - 3112. Let s be b(-76). Factor -20/3*o + 8*o**2 - 4*o**3 + 2 + 2/3*o**s.
2*(o - 3)*(o - 1)**3/3
Let a = -204 - -206. Factor 0 - 14 - 3*t + t**a + 4.
(t - 5)*(t + 2)
Let d(s) = -17*s**4 + 40*s**3 + 87*s**2 - 6*s - 40. Let l(i) = 290*i**4 - 680*i**3 - 1480*i**2 + 100*i + 680. Let h(b) = -35*d(b) - 2*l(b). Factor h(q).
5*(q - 4)*(q + 1)**2*(3*q - 2)
Let w be 53/((-32224)/(-3840)) + -6. Determine a so that -8/19*a + 14/19*a**4 - w*a**5 + 2*a**3 + 0 + 10/19*a**2 = 0.
-1, 0, 1/3, 4
Suppose 3*t - 4*p + 4 = 0, -5*p + 16 - 11 = -5*t. Let u(n) be the second derivative of t - 3*n**2 + 7/20*n**4 - 21*n + 33/10*n**3. Factor u(v).
3*(v + 5)*(7*v - 2)/5
Let n = 177313/108 - 6567/4. Let s(q) be the second derivative of 2/9*q**2 - 7*q + 0 - 1/90*q**5 - n*q**4 + 1/27*q**3. Factor s(i).
-2*(i - 1)*(i + 1)*(i + 2)/9
Let c(f) be the first derivative of f**5/25 - f**4/10 - 16*f**3/5 - 63*f**2/5 - 81*f/5 + 672. Find g, given that c(g) = 0.
-3, -1, 9
Suppose -90*k = -89*k - 30. Let i(x) = -35*x**2 + 10*x - 35. Let d(v) = v + 1. Let g(q) = k*d(q) + i(q). Factor g(a).
-5*(a - 1)*(7*a - 1)
Let q(d) be the third derivative of -d**8/56 + 16*d**7/15 + 157*d**6/30 + 8*d**5 + d**4/12 - 40*d**3/3 - 169*d**2 - 1. Let q(t) = 0. What is t?
-1, 1/3, 40
Let s(a) be the first derivative of 1/24*a**4 + 0*a - 84 + 0*a**2 + 1/5*a**5 + 0*a**3 + 5/36*a**6. Factor s(d).
d**3*(d + 1)*(5*d + 1)/6
Let b(k) be the first derivative of -5*k**4/18 - 19*k**3/9 + 4*k**2/3 + 47*k + 87. Let r(v) be the first derivative of b(v). Suppose r(j) = 0. Calculate j.
-4, 1/5
Factor 65/4*w**2 - 153/2*w + 90 - 1/4*w**3.
-(w - 60)*(w - 3)*(w - 2)/4
Let j(i) be the third derivative of 0*i**3 + 0 + 1/120*i**4 + 0*i**5 - 1/600*i**6 + 114*i**2 + 0*i. Let j(r) = 0. Calculate r.
-1, 0, 1
Let h(y) be the second derivative of 3*y**6/10 + 21*y**5/4 + 105*y**4/4 + 45*y**3/2 - 42*y**2 - 2512*y. Suppose h(n) = 0. What is n?
-7, -4, -1, 1/3
Factor -340*f + 1844853*f**3 - 120*f**2 + 1945 - 1844858*f**3 - 745.
-5*(f - 2)*(f + 6)*(f + 20)
Let m(v) = -8*v + 48. Let n be m(-28). Suppose 0 = u + 2*o + 2, -o + 1 = 3*u - 2*u. Factor -n*d**2 + 270*d**2 + u - 2*d + 0.
-2*(d - 1)*(d + 2)
Let m(w) be the first derivative of 3*w**5/5 - 9*w**4 + 17*w**3 + 135*w**2 + 1666. Suppose m(b) = 0. What is b?
-2, 0, 5, 9
Factor -3*u**2 + 358 + 5*u**2 + 0*u**2 - 551 - u**2 + 192*u.
(u - 1)*(u + 193)
Suppose -13*r = 5*r - 252. Factor 20 + 8*x + 3052*x**2 - 3050*x**2 + r*x.
2*(x + 1)*(x + 10)
Let c(m) = 10*m**2 + 625*m - 560. Let a(l) = 3*l**2 + 157*l - 140. Let q(h) = 15*a(h) - 4*c(h). Determine p so that q(p) = 0.
1, 28
Let g(z) be the third derivative of 7/24*z**6 - 1/42*z**7 - 10/3*z**3 - 5/4*z**5 + 65/24*z**4 - 3 + 0*z - 8*z**2. Let g(q) = 0. Calculate q.
1, 4
Let f(b) = 2*b**2 - 20*b - 9. Let q be f(11). Suppose 0 = -5*u - q + 88. Suppose 6 + 22*s - 16 - 19*s + 5*s**2 + u*s**3 + 5*s**4 - 18*s = 0. Calculate s.
-2, -1, 1
Let f(x) be the second derivative of x**6/1440 + x**5/120 + x**4/32 + 187*x**3/6 + 19*x - 4. Let c(w) be the second derivative of f(w). Solve c(j) = 0.
-3, -1
Let o(n) be the third derivative of -n**7/210 - n**6/120 + 59*n**5/60 - 37*n**4/8 + 9*n**3 + 2*n**2 + 417*n - 1. What is a in o(a) = 0?
-9, 1, 6
Let d be 270/324*(-6)/(-10) + (-492)/(-164). Factor -d*h**4 - 13*h**3 - 11*h - 5/2 - 18*h**2.
-(h + 1)**3*(7*h + 5)/2
Let f(c) be the first derivative of -2/21*c + 1/42*c**4 - 28 + 2/63*c**3 - 1/21*c**2. Find n, given that f(n) = 0.
-1, 1
Let r(w) = -2*w**2 + 12*w + 4. Let d be r(6). Suppose -u - g - 1 + 4 = 0, d*u - g = 32. Suppose -v**2 + 0 - u*v - 7*v - 2 + 11*v = 0. What is v?
-2, -1
Let a(y) be the third derivative of -y**6/960 - 3*y**5/160 - 5*y**4/64 + 25*y**3/48 + 6*y**2 + 52. Factor a(w).
-(w - 1)*(w + 5)**2/8
Let g = -23919/26 - -920. Let h(k) be the first derivative of -17 - 48/13*k**2 - 128/13*k - g*k**4 - 8/13*k**3. Factor h(s).
-2*(s + 4)**3/13
Factor 4/9*k**5 + 0 + 0*k - 80/9*k**3 + 8/9*k**4 + 32/3*k**2.
4*k**2*(k - 2)**2*(k + 6)/9
Let f(z) = -2*z**2 - z. Suppose c = -46 + 42. Let d(y) = 50*y**3 - 38*y**2 - 22*y - 2. Let r(q) = c*f(q) + d(q). Let r(o) = 0. Calculate o.
-1/5, 1
Let q(b) = -8*b + 18. Let x be q(-6). Let d = -62 + x. Factor -32*p - 2*p**d - 48*p**2 - 18*p**3 - 8*p**2 + 8*p**2.
-2*p*(p + 1)*(p + 4)**2
Let m(s) = -72*s**3 + 2166*s**2 - 4371*s + 2157. Let y(k) = 19*k**3 - 541*k**2 + 1093*k - 539. Let x(f) = -4*m(f) - 15*y(f). Solve x(p) = 0.
1, 181
Suppose 0 = g + 9*g - 220. Factor 6*l**5 + 34*l**4 + 4*l**5 + 42*l**3 + 3442*l - 3438*l + g*l**2.
2*l*(l + 1)**3*(5*l + 2)
Let j(q) = -q**2 + 2*q + 284 - 287 - 8*q. Let l be j(-5). Factor 8/11 + 10/11*n**l + 16/11*n + 2/11*n**3.
2*(n + 1)*(n + 2)**2/11
Let x(z) = -64*z**4 + 34*z**3 + 154*z**2 + 26*z - 87. Let w(d) = 21*d**4 - 11*d**3 - 51*d**2 - 9*d + 28. Let t(f) = 19*w(f) + 6*x(f). Solve t(v) = 0 for v.
-1, 1/3, 2
Solve -2/3*h**3 + 0 - 1/9*h**4 - 5/9*h**2 + 0*h = 0 for h.
-5, -1, 0
Solve -276/5 - 272/5*f + 4/5*f**2 = 0 for f.
-1, 69
Factor -1/4*y**2 + 129/4 + 10*y.
-(y - 43)*(y + 3)/4
Let q(m) be the second derivative of -1/6*m**4 - 73*m + 0 - 1/120*m**6 - 1/6*m**3 - 1/16*m**5 + 0*m**2. Factor q(a).
-a*(a + 1)*(a + 2)**2/4
Let w(g) be the third derivative of g**5/300 + 57*g**4/20 - 12138*g**2. Factor w(a).
a*(a + 342)/5
Let n(d) be the second derivative of 4*d**3 + 3/20*d**5 + 0*d**2 - 3/2*d**4 - 102*d + 0. Find g such that n(g) = 0.
0, 2, 4
Let p(u) be the first derivative of -u**7/2940 - u**6/70 - 17*u**5/420 + 27*u**3 + 2*u - 32. Let q(j) be the third derivative of p(j). Factor q(l).
-2*l*(l + 1)*(l + 17)/7
Let l = -1685619/7 + 240803. Factor -l*j + 1/7*j**2 + 0.
j*(j - 2)/7
Let 2/9*j**2 - 238/9 - 236/9*j = 0. What is j?
-1, 119
Find b, given that 656*b**2 + 47*b**5 - 80*b + 161*b**4 - 1354*b**2 - 1527*b**2 - 452*b**5 + 1144*b**4 + 960 + 445*b**3 = 0.
-8/9, 1, 3
Find r such that -56/3 - 592/9*r - 2/3*r**3 - 266/9*r**2 = 0.
-42, -2, -1/3
Solve 30*m + 59*m**2 + 57*m**2 - 3*m - 173*m**2 + 63*m**2 - m**3 = 0.
-3, 0, 9
Let c(f) = f**3 - 49*f**2 - 656*f - 238. Let d be c(60). Factor -2*p - d*p**2 + 0 - 1/2*p**3.
-p*(p + 2)**2/2
Let y(i) be the first derivative of 0*i**5 - 10*i**3 + 10*i**4 - 35 - 35/2*i**2 - 5/6*i**6 + 30*i. Let y(x) = 0. Calculate x.
-3, -1, 1, 2
Let y(k) be the first derivative of -k**5/150 + k**4/12 - 36*k**2 - 13. Let j(s) be the second derivative of y(s). Factor j(d).
-2*d*(d - 5)/5
Let k(j) be the third derivative of 0*j + 2/5*j**4 - 56/15*j**3 + 0 + 1/75*j**5 - 67*j**2. What is d in k(d) = 0?
-14, 2
Let y be 8 - 1/1 - 777/4704*42. Let g(q) be the second derivative of 0*q**2 + y*q**4 + 0*q**5 - 1/120*q**6 + 0 + 17*q - 1/12*q**3. Find l, given that g(l) = 0.
-2, 0, 1
Let f(g) = g**3 + 12*g**2 + 20*g + 3. Let s be f(-10). Suppose -4 + 1 = 3*a, 17 = 5*c - 2*a. Factor -20*z**s - 4*z**2 - 20*z**3 + 44*z**c.
4*z**2*(z - 1)
Let h(q) be the third derivative of 1/30*q**4 - 15*q - 1/300*q**5 + 0 + q**2 - 1/10*q**3. Factor h(o).
-(o - 3)*(o - 1)/5
Let l(g) be the first derivative of g**3/33 + 431*g**2/22 + 78*g - 6344. Solve l(k) = 0.
-429, -2
Let k(x) = -20*x**3 - 9*x**2 + 3*x + 26. Suppose -14 = -5*a - 4. Let j(o) = 0 - 9 + 3*o**a + 4*o + 0 + 7*o**3 - 5*o. Let b(v) = -17*j(v) - 6*k(v). Factor b(p).
(p - 1)*(p + 1)*(p + 3)
Let f be (25/(1000/48))/((-9)/(-30)). Suppose -2*c = -f*y + 20, 10*y - 25 = c + 5*y. Factor 4/3*b**3 + 2/3*b**2 + c*b**4 - 2/3 - 1/3*b**5 - b.
-(b - 2)*(b - 1)*(b + 1)**3/3
Let l = -28472 - -28472. Let o(k) be the second derivative of l*k**3 + 0*k**5 + 1/2*k**4 + 