actor 4*p + v + 5*p**2 + 19*p + 22*p + 15*p.
5*(p + 1)*(p + 11)
Let j(m) be the first derivative of -4*m**3/3 + 576*m**2 - 82944*m - 2950. Suppose j(z) = 0. What is z?
144
Let y(w) be the first derivative of 3*w**5/5 + 21*w**4 + 75*w**3 - 6*w**2 - 300*w - 6368. What is c in y(c) = 0?
-25, -2, 1
Let f(x) be the second derivative of -x**6/6 - 20*x**5 - 2945*x**4/12 - 785*x**3 - 1080*x**2 - 6232*x. Let f(y) = 0. Calculate y.
-72, -6, -1
Let k(x) = -8*x**3 - 335*x**2 - 4366*x - 18425. Let p(r) = 4*r**3 + 168*r**2 + 2184*r + 9212. Let g(q) = -4*k(q) - 7*p(q). Suppose g(y) = 0. Calculate y.
-16, -9
Let -992/9 - 332*w**2 - 2980/9*w - 1004/9*w**3 - 4/9*w**4 = 0. What is w?
-248, -1
Let w(u) be the first derivative of -3*u**3 - 930*u**2 + 621*u - 4960. Factor w(h).
-3*(h + 207)*(3*h - 1)
What is a in 10/3*a**2 + 2/3*a**3 - 6 + 2*a = 0?
-3, 1
Suppose 48*c + 0 - 3/7*c**5 - 87/7*c**4 + 348/7*c**2 - 72/7*c**3 = 0. What is c?
-28, -2, -1, 0, 2
Let c = -43 + 284. Suppose 247*j = c*j + 12. Factor 2/21*u**3 + 10/21*u + 4/21 + 8/21*u**j.
2*(u + 1)**2*(u + 2)/21
Suppose -60 = 20*p + 20. Let v be (p/(-10)*15)/(4 - 2). Suppose 2/3*q**2 - 1/3*q**5 - q - 2/3 + 0*q**4 + 4/3*q**v = 0. What is q?
-1, 1, 2
Suppose -3*o + 1634 = w + 1631, 4*o - w - 11 = 0. Let n(g) be the third derivative of 0*g + 23*g**o + 0*g**3 + 0 + 1/3*g**4 + 1/15*g**5. Factor n(u).
4*u*(u + 2)
Let q(y) be the third derivative of 74*y**2 - 5/8*y**4 - 1/24*y**5 + 1/168*y**7 + 1/32*y**6 - 5/3*y**3 + 0*y + 0. Suppose q(o) = 0. What is o?
-2, -1, 2
Let x(s) be the second derivative of -s**4/3 + 400*s**3 + 1202*s**2 + 13*s + 26. Factor x(f).
-4*(f - 601)*(f + 1)
Suppose 0 = -39*g + 41*g + u - 31, g - 23 = 2*u. Solve 268*q + 32 + 21*q**3 + 35 - 44 + 272*q**2 + 23*q**3 + g = 0 for q.
-5, -1, -2/11
Solve -3/4*r - 903/4 + 903/4*r**2 + 3/4*r**3 = 0.
-301, -1, 1
Let z = -3191 - -3195. Let h(c) be the second derivative of 0*c**3 + 19*c + 0*c**2 + 0 + 0*c**5 - 1/54*c**z + 1/135*c**6. Let h(a) = 0. Calculate a.
-1, 0, 1
Let s(h) = h**2 + 39*h + 183. Let i be s(-34). Let l be (-34)/(-10) + (-3 - i/(-5)). Let 3/2*u - 3*u**4 + 3*u**2 + 0 + 0*u**l - 3/2*u**5 = 0. Calculate u.
-1, 0, 1
Let r(x) be the third derivative of -x**5/12 + 5*x**4/6 + 385*x**3/6 - 296*x**2 + x. Factor r(v).
-5*(v - 11)*(v + 7)
Suppose -1188 - 610*m - 3*m**2 + 0*m**2 + 1515*m - 2*m**2 + 288 = 0. What is m?
1, 180
Let c be (4 - (-168)/(-44)) + (-146)/(-44). Suppose 0 = 127*s - 133*s. Find q such that -c*q**2 + s + q = 0.
0, 2/7
Factor p**3 + 33/7*p**2 + 12/7 - 52/7*p.
(p - 1)*(p + 6)*(7*p - 2)/7
Let w(g) be the third derivative of 1/7*g**3 - 1/140*g**6 - 2*g - 14*g**2 - 1/8*g**4 + 0 + 1/20*g**5. Factor w(q).
-3*(q - 2)*(q - 1)*(2*q - 1)/7
Let w be ((-25)/275*33)/(0 + -1). Let a(t) be the first derivative of 2/3*t**w + 0*t + 0*t**2 + 1/2*t**4 - 41. Factor a(z).
2*z**2*(z + 1)
Let o be 5*((-72)/10)/(-9). Factor -6*k**4 + 8*k**o + k**5 - 14*k + 15*k**2 + 13*k**3 - 17*k**4.
k*(k - 14)*(k - 1)**2*(k + 1)
Let x = 313/9 - 34. Let z(t) be the first derivative of 0*t - 5 + 1/6*t**2 - x*t**3. Factor z(d).
-d*(7*d - 1)/3
Suppose -3*t + 26 = 2*w, -1470*t - 9 = -1474*t + w. Let u(h) be the third derivative of -1/20*h**t - 23*h**2 + 0 + 1/150*h**5 + 0*h + 0*h**3. Factor u(p).
2*p*(p - 3)/5
Let a(s) be the third derivative of -169/2*s**3 - 13/4*s**4 + 0*s + 0 - 1/20*s**5 + 112*s**2. Factor a(i).
-3*(i + 13)**2
Let h be (-504)/50*(-1530)/1071 + -14 + 4/(-35). Determine q, given that -16/7*q + 2 + h*q**2 = 0.
1, 7
Let v(g) be the second derivative of 37/51*g**3 - 16/85*g**5 - 5/357*g**7 + 10/17*g**2 - 32/255*g**6 - 2*g + 5 + 11/51*g**4. Suppose v(a) = 0. Calculate a.
-5, -1, -2/5, 1
Let d(x) be the third derivative of 1/4*x**3 - 1/560*x**7 + 1/80*x**6 + 4 + 2*x**2 - 3/160*x**5 - 1/16*x**4 + 0*x. Suppose d(u) = 0. What is u?
-1, 1, 2
Factor -1/5*z**3 - 11/5*z**2 - 2*z + 72/5.
-(z - 2)*(z + 4)*(z + 9)/5
Let l be 0/((-8)/(-20)*5). Let y(k) be the third derivative of 0 + 0*k**4 + 0*k**3 - 1/60*k**6 + 1/315*k**7 + l*k + 1/45*k**5 - 7*k**2. Factor y(v).
2*v**2*(v - 2)*(v - 1)/3
Suppose -24 + 2 = f - l, 2*l = 5*f + 101. Let c = 24 + f. Factor -h - c - h**2 + 5*h + 2*h.
-(h - 5)*(h - 1)
Let i(s) be the second derivative of -s**7/42 + 8*s**6/15 - 81*s**5/20 + 21*s**4/2 - 6*s + 1569. Let i(j) = 0. Calculate j.
0, 3, 6, 7
Let l be 29/1*(2 - (-6)/6). What is a in 91 - 5*a**2 - 5*a + l - 178 = 0?
-1, 0
Let b(r) = 4*r**2 - 379*r + 8839. Let j(p) = -37*p + 15*p + 13 + 21*p - 12. Let t(l) = b(l) - 3*j(l). Find s, given that t(s) = 0.
47
Suppose 5*s - 238*n - 32 = -240*n, 4*n + 8 = 2*s. Let g(l) be the first derivative of 3*l**4 - 2/3*l**s - 4/5*l**5 + 4*l**2 + 9 + 20/3*l**3 + 0*l. Factor g(r).
-4*r*(r - 2)*(r + 1)**3
Let k(s) be the second derivative of 2025/13*s**2 + 1/78*s**4 + 30/13*s**3 + 0 - 314*s. Solve k(z) = 0 for z.
-45
Let f(v) be the third derivative of v**7/70 + 13*v**6/20 - 7*v**5/5 - 13*v**4/4 + 27*v**3/2 - 565*v**2. Find w, given that f(w) = 0.
-27, -1, 1
Let a(v) be the second derivative of -2*v + 0*v**2 - 28 + 1/21*v**3 - 1/42*v**4. Factor a(t).
-2*t*(t - 1)/7
Factor -7*w**2 - 36*w + 3*w**2 + 92 + 692 - 58*w + 10*w.
-4*(w - 7)*(w + 28)
Let p(n) be the third derivative of n**8/560 - 197*n**7/175 + 9603*n**6/50 + 19602*n**5/25 - 1669*n**2. Suppose p(d) = 0. Calculate d.
-2, 0, 198
Find j such that -282*j**2 - 16819326 - 119286*j - 2/9*j**3 = 0.
-423
Let u = 586 - 586. Let v be 1190/630 + (u - (-2)/(-2)). Factor v*d + 8/9 + 2/9*d**2.
2*(d + 2)**2/9
Factor 0 - 8*f + 3*f**3 - 1/3*f**4 - 14/3*f**2.
-f*(f - 6)*(f - 4)*(f + 1)/3
Let n(t) = -2*t**2 + 5*t + 6. Let i be n(3). Factor -37*b - 39 - 54*b**2 - b**4 - 9*b - 42 - 12*b**i - 73*b + 11*b.
-(b + 3)**4
Let q = -294 - -297. What is w in -168*w - 1099 - q*w**2 - 136 - 607 - 510 = 0?
-28
Let v(d) be the second derivative of -8*d - 1/6*d**4 + 1/10*d**5 - 1/3*d**3 + 2 + d**2. Suppose v(y) = 0. What is y?
-1, 1
Determine p, given that 6745*p**2 - 6960*p**4 + 5*p**5 + 10335*p**4 + 9040*p - 4525*p**3 - 5620*p**4 - 9020 = 0.
-2, 1, 451
Suppose -4*t + 3*g = 9*g + 100, -2*t = -2*g - 40. Factor 0 + 8/3*y**t + y**3 - y.
y*(y + 3)*(3*y - 1)/3
Let b = -2341 - -2343. Let o(a) be the first derivative of -1/15*a**6 - 1/10*a**4 + 0*a**b + 0*a + 0*a**3 + 4/25*a**5 - 12. Factor o(q).
-2*q**3*(q - 1)**2/5
Let s(q) be the third derivative of q**5/40 - 21*q**4/16 - 11*q**3/2 - 2*q**2 - 938*q. Suppose s(x) = 0. What is x?
-1, 22
Let v(x) = -24*x - 8. Let t be v(-2). Let p be t/14 - (-9)/63. Factor -5*k**4 - 10*k - k**p + 5*k**3 - 5 + 10*k**4 + 6*k**3.
5*(k - 1)*(k + 1)**3
Let y(i) be the second derivative of 3/2*i**2 + 1/12*i**4 + 0 + 51*i + 2/3*i**3. Solve y(x) = 0 for x.
-3, -1
Let f = 251 + -256. Let w(r) = -r**3 - 5*r**2 + 3*r + 3. Let t(o) = -o**3 - 6*o**2 + 3*o + 4. Let z(c) = f*t(c) + 6*w(c). Suppose z(s) = 0. What is s?
-2, 1
Let o(b) be the first derivative of 160/7*b**2 - 92/35*b**5 - 2/3*b**6 + 8/7*b**4 - 23 + 352/21*b**3 + 64/7*b. Let o(k) = 0. Calculate k.
-2, -1, -2/7, 2
Suppose -3193*x + 420 = -2983*x. Suppose -14/13*z + 2/13*z**x - 16/13 = 0. What is z?
-1, 8
Suppose 512/17*s**3 + 1040/17 - 2/17*s**4 + 2596/17*s + 2070/17*s**2 = 0. What is s?
-2, -1, 260
Let s(c) = -c**2 + 1. Let j = 37 - 35. Let r(d) = -20 + d**2 + 24 - 2*d**2 - j*d - 5*d**2. Let i(p) = 2*r(p) - 10*s(p). Factor i(z).
-2*(z + 1)**2
Let w be (-2 - (-1072)/560) + (0 - 8/(-28)). Factor -13/5 + w*u**2 + 12/5*u.
(u - 1)*(u + 13)/5
Let t be (-20)/5 + (-2)/2. Let y(x) = -x**2 + 2*x - 3. Let b(p) = 9*p**2 + 310*p + 6415. Let a(l) = t*y(l) - b(l). Factor a(f).
-4*(f + 40)**2
Let f be 945/270*(330/45 - 2). Determine k so that -2/3*k**2 + 32/3*k - f = 0.
2, 14
Let y(g) be the third derivative of -1/20*g**5 - 1/2*g**3 + 0*g - 3 - 1/4*g**4 - 9*g**2. Factor y(v).
-3*(v + 1)**2
Let 8*s + 32*s - s**2 - 2186 + 1907 = 0. What is s?
9, 31
Let u(j) be the first derivative of 3*j**2 - 10*j + 44. Let v be u(2). Suppose 0*q**4 + q**v - 13*q**4 - 15*q**3 - 7*q**4 + 4*q**2 = 0. Calculate q.
-1, 0, 1/4
Let j(l) = 22*l**4 + 384*l**3 - 353*l**2 - 384*l + 371. Let z(q) = -8*q**4 - 192*q**3 + 178*q**2 + 192*q - 186. Let n(m) = -2*j(m) - 5*z(m). Factor n(g).
-4*(g - 47)*(g - 1)**2*(g + 1)
Factor 1/5*v**5 - 1/5*v**3 - 3/5*v**2 + 3/5*v**4 + 0 + 0*v.
v**2*(v - 1)*(v + 1)*(v + 3)/5
Determ