 derivative of 0*q**2 - 4 - 35/6*q**m + 5/12*q**4 + 9*q. Suppose k(a) = 0. Calculate a.
0, 7
Factor -212/3*v**3 - 2/3*v**5 + 140/3*v**2 + 38/3*v**4 + 686/3 + 1078/3*v.
-2*(v - 7)**3*(v + 1)**2/3
Suppose 5*o + o = -1032. Let l be o/(-6) + (-16)/(-48). Factor g + 16*g**2 - l*g - 29*g**2 - 4.
-(g + 2)*(13*g + 2)
Let x(z) be the third derivative of z**9/756 - z**7/35 + 4*z**6/45 - z**5/10 - 7*z**3/6 - 16*z**2 + 3. Let b(p) be the first derivative of x(p). Factor b(h).
4*h*(h - 1)**3*(h + 3)
Let w(a) be the third derivative of a**6/360 + 44*a**5/135 - 239*a**4/216 + 10*a**3/9 + 898*a**2. Solve w(s) = 0.
-60, 1/3, 1
Let t = -75 + 152. Suppose -1 = 5*x - 16. Factor -t*y - 3*y**2 + 4 + y**x + 77*y.
(y - 2)**2*(y + 1)
Suppose -q + 3 + 5 = -5*s, 4*s - 2*q + 4 = 0. Let c = s + 6. Factor d**4 + 1266*d**2 + 4*d - 1270*d**2 - 4*d**3 + 3*d**c.
4*d*(d - 1)**2*(d + 1)
Factor -3/7*m**2 - 978/7 - 981/7*m.
-3*(m + 1)*(m + 326)/7
Let s(x) be the second derivative of -3*x**5/40 - 9*x**4/4 - 8*x**3 - 4374*x. Factor s(i).
-3*i*(i + 2)*(i + 16)/2
Let w(d) = d**3 + 31*d**2 - 1254*d + 278. Let n be w(23). Suppose -2/7*o**n + 0 - 4/21*o - 2/21*o**3 = 0. What is o?
-2, -1, 0
Let m(w) = w + 18. Let n be m(-16). Factor 1048*u - u**3 + 13 - 490*u + 11*u**n - 533*u.
-(u - 13)*(u + 1)**2
Let a(q) = -q. Let o(u) = 4. Let d(h) = 3*a(h) + o(h). Let j be d(0). Find n such that 14*n**j - 5*n**2 - 3*n + 8*n - 45*n**3 - n**4 + 32*n**4 = 0.
-1/3, 0, 1/3, 1
Let u(j) = 15*j**3 + 95*j - 230. Let m(y) = -y**3 + 4. Let c(i) = -20*m(i) - u(i). What is o in c(o) = 0?
-5, 2, 3
Let d(j) be the first derivative of j**4/6 - 2*j**3/3 - 9*j + 25. Let i(x) be the first derivative of d(x). Find g such that i(g) = 0.
0, 2
Let h(t) be the first derivative of t**3/6 - t**2 - 6*t + 43. Determine j, given that h(j) = 0.
-2, 6
Let y(p) be the first derivative of -8*p**2 - 36*p + 1/3*p**3 - 148. Factor y(o).
(o - 18)*(o + 2)
Let m(c) be the second derivative of 6*c**2 + 0 - 3/20*c**5 + 6*c - 4*c**3 + 5/4*c**4. Factor m(o).
-3*(o - 2)**2*(o - 1)
Let f(g) be the third derivative of -g**6/96 - g**5/6 + 55*g**4/32 - g**2 + 3*g - 6. Factor f(i).
-5*i*(i - 3)*(i + 11)/4
Let w(f) be the first derivative of f**5/4 - 7*f**4/8 - 11*f**3/4 + 17*f**2/4 + 2*f - 1516. Solve w(q) = 0 for q.
-2, -1/5, 1, 4
Let g = -26 + 26. Suppose 3*t - d - 10 = g, 0 = -t - 2*d + 1. Find r such that -r**3 + 56*r - 57*r + 2*r**t = 0.
-1, 0, 1
Let a(d) be the first derivative of 34969*d**4/16 + 34595*d**3/12 - 373*d**2/8 + d/4 - 3052. Factor a(z).
(z + 1)*(187*z - 1)**2/4
Let c(y) = 24*y - 114. Let n be c(5). Let v(h) = -67*h + 406. Let i be v(n). Determine z, given that -3/2 - 27/4*z + 27/4*z**3 - 15/4*z**2 + 21/4*z**i = 0.
-1, -2/7, 1
Let b(z) = z**2 + 4596*z - 46057. Let d be b(10). Suppose 0 - 2/11*k**d - 2/11*k + 4/11*k**2 = 0. Calculate k.
0, 1
Let r = -220 + 237. Factor 3*w**2 - 3 - 10*w**3 + 90*w - 87*w - 10*w**3 + r*w**3.
-3*(w - 1)**2*(w + 1)
Let x be 2/((-4)/(-442)) - (1 - -2). Suppose -222*n + x*n = -8. Factor -2/15 + 2/15*m**3 + 2/5*m - 2/5*m**n.
2*(m - 1)**3/15
Let l(p) = p + 5. Let z be l(3). Let x = z + -6. Determine m so that -12 + 2*m**x + 4*m + 4*m + 7 - 5 = 0.
-5, 1
Suppose -5*c + 44 = 4*b, 77 = 5*c - 6*c + 7*b. Let m = 5 - 14/3. Factor c + t - m*t**2.
-t*(t - 3)/3
Let c(u) be the second derivative of -1/15*u**5 - 7/2*u**2 + 0*u**3 - 17*u + 2/3*u**4 + 0 - 1/6*u**6. Let b(g) be the first derivative of c(g). Factor b(l).
-4*l*(l + 1)*(5*l - 4)
Let l(w) be the third derivative of -w**9/5040 + w**8/448 - w**7/420 - w**6/30 - w**4/8 - 3*w**2. Let j(n) be the second derivative of l(n). Factor j(a).
-3*a*(a - 4)*(a - 2)*(a + 1)
Let q = 82171421/1888 + -43523. Let a = 30259/32096 + q. Suppose -2/17*r**2 - 14/17 + a*r = 0. What is r?
1, 7
Let u = -5675 + 5680. Let y(t) be the second derivative of -1/25*t**u - 14*t + 4/15*t**4 - 2/75*t**6 + 0*t**2 + 0 + 8/15*t**3. Factor y(h).
-4*h*(h - 2)*(h + 1)*(h + 2)/5
Let l(d) be the second derivative of -d**6/60 + d**5/30 + 49*d**4/72 + 5*d**3/6 + 6188*d. Solve l(m) = 0 for m.
-3, -2/3, 0, 5
Let q(b) = -2*b**2 + 8*b - 6. Let i be q(2). Factor 81 - 112*s + 15*s**2 - 24*s**i + 15 - 4*s**3 + 49*s**2.
-4*(s - 6)*(s - 2)**2
Determine x so that -532*x + 3*x**2 - 4*x**2 + 401*x = 0.
-131, 0
Let o(a) = a**3 - 107*a**2 - 4*a + 433. Let x be o(107). Let c(k) be the third derivative of 0 - 3*k**2 - 1/80*k**x + 1/4*k**4 - 2*k**3 + 0*k. Factor c(q).
-3*(q - 4)**2/4
Let d be 15 + 234/54 + -16. Let u(r) be the second derivative of 0 + 10/3*r**3 - d*r**4 + 2/21*r**7 - 2*r**2 - 2/3*r**6 + 2*r**5 - 5*r. Factor u(m).
4*(m - 1)**5
Let m be (12/(-9))/4*575406/(-156). Let r = m - 1228. Factor -3/2*b**2 + 3 + r*b.
-3*(b - 2)*(b + 1)/2
Let o = 643/581 - -3/83. Let k = 20467/17927 + 3/2561. What is v in 4/7*v - o*v**2 - 4/7*v**3 + k = 0?
-2, -1, 1
Let s(z) be the first derivative of z**6/450 + 2*z**5/25 - z**3/3 + 75*z + 188. Let b(c) be the third derivative of s(c). Factor b(i).
4*i*(i + 12)/5
Let h(s) be the third derivative of 7*s**6/180 + 37*s**5/90 - 22*s**4/9 - 28*s**3/9 - 251*s**2 + 3. Find c such that h(c) = 0.
-7, -2/7, 2
Suppose 0 = 38*o - 39*o + 76. Suppose o = 3*u + 61. Factor -8/5*i**2 + 0 + 0*i + 28/5*i**3 - 6*i**4 + 9/5*i**u.
i**2*(i - 2)*(3*i - 2)**2/5
Let r(w) be the third derivative of w**6/540 - 7*w**5/54 + 403*w**4/108 - 169*w**3/3 - 12*w**2 + 2*w - 9. Factor r(n).
2*(n - 13)**2*(n - 9)/9
Suppose -147*r + 146*r - n + 8 = 0, -3*r - 32 = -4*n. Let o(w) be the third derivative of 0 + 0*w + 34*w**2 - 1/20*w**5 + r*w**3 - 3/4*w**4. Factor o(i).
-3*i*(i + 6)
Let x(t) be the second derivative of -t**6/12 - 89*t**5/8 - 435*t**4/8 - 1295*t**3/12 - 215*t**2/2 + 4954*t. Let x(c) = 0. Calculate c.
-86, -1
Let x(c) = 8*c. Let o(r) = -5*r**2 - 1136*r + 1125. Let q(y) = o(y) + 2*x(y). Determine f so that q(f) = 0.
-225, 1
Suppose -28*o - 160 = 260. Let d(p) = p**3 + 17*p**2 + 31*p + 15. Let u be d(o). What is q in -q + 1/6*q**2 + u = 0?
0, 6
Suppose 0 = -6*l - 1250 + 1226. Let p(o) = 4*o**2 - 20*o - 3. Let b(a) = -2*a**2 + 10*a. Let m(v) = l*p(v) - 9*b(v). Factor m(s).
2*(s - 3)*(s - 2)
Let h(i) = i**2 + 35*i. Let v be h(0). Let r(p) be the third derivative of 1/108*p**4 + 10*p**2 - 2/27*p**3 + 1/135*p**5 + v - 1/540*p**6 + 0*p. Factor r(a).
-2*(a - 2)*(a - 1)*(a + 1)/9
Solve 102/13*v**4 - 628/13*v**2 - 2/13*v**5 + 822/13*v - 306/13 + 12/13*v**3 = 0 for v.
-3, 1, 51
Let k(l) = -l**2 - 13*l. Let a = 1715 + -1714. Let m(x) be the first derivative of -x**3/3 - x**2/2 - 1. Let f(b) = a*m(b) + k(b). What is r in f(r) = 0?
-7, 0
Suppose -29 - 63 = -4*d. Suppose -3*u - m = -2, 2*m = 2*u - 4*u - 4. Find l, given that 65*l**u + d*l - 3*l - 67*l**2 = 0.
0, 10
Let x(n) be the second derivative of 2/105*n**6 + 11/35*n**5 + 0*n**2 + 0*n**3 + 0 + 206*n - 4/7*n**4. Factor x(i).
4*i**2*(i - 1)*(i + 12)/7
Suppose 7 = -s - l, 2441 = -4*l + 2401. Factor -11 - 49/2*x**2 - 15/2*x**s - 57/2*x - 1/2*x**4.
-(x + 1)**2*(x + 2)*(x + 11)/2
Let k(o) = -o**2 - 35*o + 58. Let d(p) = -p**2 - 3*p + 1. Let f(z) = -2*d(z) + k(z). Let l be f(27). Factor -70/3*g - 50/3 - 2/3*g**3 - 22/3*g**l.
-2*(g + 1)*(g + 5)**2/3
Let g(a) = 14*a**2 + 3732*a + 4. Let p(z) = 5*z**2 - 2*z + 2. Let t(y) = g(y) - 2*p(y). Find x such that t(x) = 0.
-934, 0
Let f(s) = -17*s**2 - 5. Let i be f(-3). Let j = -156 - i. Let -2/3*p**3 - 6*p + 0 + 4*p**j = 0. Calculate p.
0, 3
Factor -5*k**3 - 46*k + 16/3 + 137/3*k**2.
-(k - 8)*(k - 1)*(15*k - 2)/3
Factor 1/3*h**2 - 81 - 26*h.
(h - 81)*(h + 3)/3
Let k(w) be the third derivative of -w**7/1365 + 12*w**6/65 - 85*w**5/78 + 47*w**4/26 + 2315*w**2. Let k(d) = 0. Calculate d.
0, 1, 2, 141
Suppose 237*h + 188*h = 199*h - 272*h. Suppose h - 5/6*z**4 + 20/3*z + 25/3*z**3 - 85/6*z**2 = 0. What is z?
0, 1, 8
Let h(z) be the second derivative of -z**7/294 - 103*z**6/210 - 413*z**5/20 - 1715*z**4/12 - 13*z - 89. Factor h(s).
-s**2*(s + 5)*(s + 49)**2/7
Suppose 3*s = 1547 - 266. Let f = -425 + s. What is k in 14/9*k**f + 0 - 4/9*k**3 - 14/9*k**4 + 4/9*k = 0?
-1, -2/7, 0, 1
Find d, given that -8056857/2 - 173889/2*d - 3/2*d**3 - 1251/2*d**2 = 0.
-139
Let f be (-13128)/9 + 0 + (-5)/15. Let v = 7323/5 + f. Factor 64/5*a**3 + 0 - v*a**4 + 8/5*a - 44/5*a**2.
-4*a*(a - 1)**2*(7*a - 2)/5
Let n(j) be the first derivative of -j**3/18 - 13*j