 12
Let -774*b**2 - 1273*b**4 + 288*b**2 + 2*b**5 + 408*b**4 + 415*b**4 + 270*b**3 + 408*b**4 = 0. Calculate b.
0, 3, 9
Let s(j) be the second derivative of -j**9/30240 - 29*j**8/13440 + 17*j**4/6 + 12*j. Let w(m) be the third derivative of s(m). Factor w(v).
-v**3*(v + 29)/2
Let i(b) be the third derivative of -1/30*b**4 + 0 - 46*b**2 + 1/12*b**6 - 23/150*b**5 + 0*b + 0*b**3. Determine o so that i(o) = 0.
-2/25, 0, 1
Let l(r) be the first derivative of r**3/6 - 519*r**2/4 - 260*r - 5220. Determine z so that l(z) = 0.
-1, 520
Let f be (-4290)/495 - -9*1. Let g(c) be the second derivative of 11*c + 1/30*c**5 - f*c**2 - 1/9*c**3 + 0 + 1/18*c**4. Solve g(b) = 0.
-1, 1
Suppose 21*m = 13*m. Suppose b = 4*h + 13 - 1, -3*h - 6 = m. Let 3/7*d**5 - 3/7*d**3 + 0*d + 12/7 - 3*d**2 + 9/7*d**b = 0. What is d?
-2, -1, 1
Let a = 25764 - 25762. Factor -4/7*n**a - 16/7 + 16/7*n.
-4*(n - 2)**2/7
Let x(l) = -8*l**2 + 385*l + 110. Let v(s) = -11*s**2 + 513*s + 150. Let w(m) = 11*v(m) - 15*x(m). Factor w(d).
-d*(d + 132)
Find o, given that -184143*o**3 + 184140*o**3 - 58042 - 16824 - 26 - 20619*o - 486*o**2 = 0.
-79, -4
Suppose -14*x + 15 = -13. Factor 58*y**2 - 776*y + 152*y - 52*y**3 + 2*y**4 + 288 + 328*y**x.
2*(y - 12)**2*(y - 1)**2
Let b(m) = -m**3 - 13*m**2 + m. Let l(u) = -5*u**3 + 35*u**2 + 136*u - 40. Let o(i) = -6*b(i) - 3*l(i). Factor o(t).
3*(t - 5)*(t + 4)*(7*t - 2)
Let y(g) be the first derivative of 253 - 80/3*g - 22/3*g**2 - 2/9*g**3. Factor y(x).
-2*(x + 2)*(x + 20)/3
Let n(r) = r**3 + 8*r**2 - 10*r - 80. Let z be n(-8). Let l be ((-6)/8)/((-21)/14 + z). Let 1/4*o**3 + 0*o + 0 - l*o**2 = 0. Calculate o.
0, 2
Let p = 3152 + -1712. Find q such that -130*q**2 + 14*q**3 - 9*q**3 - 92*q - p + 1052*q = 0.
2, 12
Let w = 4380 - 8757/2. Let n(p) be the second derivative of 4*p + 1/4*p**4 + 3*p**2 + 0 - w*p**3. Suppose n(m) = 0. What is m?
1, 2
Solve -328 - 3484*a**4 + 324*a**2 + 108*a**3 + 3486*a**4 - 2*a**5 + 54*a - 372 + 214 = 0.
-3, 1, 9
Let c(k) = -k**3 + 20*k**2 - 10*k - 18. Let x be c(19). Factor 151 - n + 15*n**3 - 304 + x - 55*n**2 + 31*n.
5*n*(n - 3)*(3*n - 2)
Let p(o) be the third derivative of -5*o**8/336 - o**7/42 + 19*o**6/8 + 257*o**5/12 + 215*o**4/3 + 120*o**3 + 840*o**2. Find l, given that p(l) = 0.
-4, -1, 9
Let h(s) = 4*s**2 + 356*s - 632. Let y(v) = -126 - 4*v**2 - 6*v**2 - 7*v**2 + 18*v**2 + 71*v. Let n(z) = 5*h(z) - 24*y(z). Find l such that n(l) = 0.
2, 17
Let b(j) be the second derivative of -5*j**7/42 - 3*j**6/2 - 21*j**5/4 + 5*j**4/12 + 25*j**3 - 47*j - 23. Let b(i) = 0. What is i?
-5, -3, -2, 0, 1
Let -790/3 - 125/2*m + 5/6*m**2 = 0. What is m?
-4, 79
Suppose -19*h = -12*h - 28. Factor -292*a**3 + h*a**4 + 149*a**3 + 2*a**2 + 149*a**3.
2*a**2*(a + 1)*(2*a + 1)
Let n(t) be the second derivative of -t**6/1620 - 2*t**5/45 + 51*t**3/2 + 80*t. Let h(w) be the second derivative of n(w). Suppose h(m) = 0. Calculate m.
-24, 0
Factor -147852/5 - 39639/5*h**2 + 678/5*h**3 + 150516/5*h - 3/5*h**4.
-3*(h - 111)**2*(h - 2)**2/5
Determine u so that -836*u**2 - 7*u**3 + 0*u**3 + 396*u**2 - 850 + 6*u**3 + 6*u**3 + 1285*u = 0.
1, 2, 85
Let p(i) be the second derivative of i**4/30 - i**3/3 - 10*i**2 - 9*i + 24. Factor p(m).
2*(m - 10)*(m + 5)/5
Let s(j) be the second derivative of -j**6/30 + j**4/3 + j**3/6 - j**2/2 - 5*j - 9. Let l(q) = q**4 + 12*q**2 + 3*q - 3. Let k(h) = l(h) - 3*s(h). Factor k(p).
4*p**4
Let o be (-22)/(374/221) - 237/(-18). Suppose -4*a - 2*k - 6 = -0*k, -3*a - 3 = k. Factor o*x**2 + a + 1/6*x.
x*(x + 1)/6
Let j(i) = i**5 - 141*i**4 - 836*i**3 + 5851*i**2 + 5. Let m(d) = 140*d**4 + 836*d**3 - 5836*d**2 - 4. Let o(l) = 4*j(l) + 5*m(l). Factor o(v).
4*v**2*(v - 4)*(v + 19)**2
Let q = 24 - 24. Let x(w) = -w**2 - 143*w - 1920. Let b be x(-15). Find o such that -2/5*o**3 + b*o**2 + q*o - 8/5*o**5 + 0 + 2*o**4 = 0.
0, 1/4, 1
Suppose -640 + 198 = -221*a. What is w in -a*w**2 + 48/7*w**3 - 18/7*w**4 + 8/7 - 24/7*w = 0?
-2/3, 1/3, 1, 2
Let m(p) be the third derivative of p**7/70 + p**6/4 + 17*p**5/20 - 13*p**4/2 - 30*p**3 + 818*p**2. Let m(v) = 0. What is v?
-6, -5, -1, 2
Let f(c) be the first derivative of -c**6/600 - 2*c**5/25 - 6*c**4/5 - 7*c**2/2 - c + 85. Let z(i) be the second derivative of f(i). Factor z(q).
-q*(q + 12)**2/5
Suppose 697*v**2 + 1/2*v**3 + 0 - 1395/2*v = 0. Calculate v.
-1395, 0, 1
Let j(o) = o**2 + 16*o + 34. Let x be j(-14). Suppose 10 = 8*i - x. Solve -i*c**4 + 0*c**4 - 21*c + c**3 - c**5 + 2*c**2 + 21*c = 0 for c.
-2, -1, 0, 1
Let w(x) = -14*x**2 + 1168*x + 352836. Let m(d) = 3*d**2 + 4*d. Let t(n) = -15*m(n) - 3*w(n). Factor t(h).
-3*(h + 594)**2
Let m(r) = -35*r**3 + 260*r**2 + 245*r - 470. Let z(f) = -f**3 - f + 2. Let a(s) = m(s) - 30*z(s). Factor a(d).
-5*(d - 53)*(d - 1)*(d + 2)
Suppose a - 48 = -2*x, 0*a - 16 = -4*a. Factor 23*i**2 + 75*i**3 + x*i**2 + 19*i**4 + 16*i**4 + 5*i**5.
5*i**2*(i + 1)*(i + 3)**2
Let d(h) be the first derivative of -4*h**3/3 + 312*h**2 - 2432*h - 1204. Find f, given that d(f) = 0.
4, 152
Let u(y) be the third derivative of -5*y**8/336 - 3*y**7/14 - 19*y**6/24 + 7*y**5/4 + 35*y**4/3 - 40*y**3 - 861*y**2. Determine i so that u(i) = 0.
-4, -3, 1
Let s = 881201 - 881201. Find w, given that 1/4*w**2 - 7/2*w + s = 0.
0, 14
Let t(d) be the third derivative of -d**8/616 - 13*d**7/385 - 9*d**6/44 - 7*d**5/22 + 23*d**4/22 + 48*d**3/11 - 408*d**2 + 1. What is k in t(k) = 0?
-8, -3, -2, -1, 1
Let v be 470/(-150) + 4/30. Let z be ((-6)/v)/((-16)/(-24)). Find f such that -z - 5*f**2 - f**3 + 3 + 3*f**2 = 0.
-2, 0
Let z(g) be the second derivative of -g**4/3 - 38*g**3/3 - 168*g**2 + 1013*g. Let z(s) = 0. What is s?
-12, -7
Let t(k) = 4*k**2 - 5*k - 16. Let d be t(-5). Suppose 14*i - d + 25 = 0. Factor 3/5*q**2 + 15 + i*q.
3*(q + 5)**2/5
Let s be -2 + ((-27)/450)/(36/(-1205)). Let q(j) be the second derivative of -2*j - 1/72*j**4 + 0*j**2 + 0 + 1/18*j**3 - s*j**5. Factor q(w).
-w*(w - 1)*(w + 2)/6
Let l(w) be the first derivative of -4*w**3/3 - 696*w**2 - 121104*w - 1567. Find u such that l(u) = 0.
-174
Suppose 129*k - 252*k = -128*k + 10. Determine y, given that 2/17*y**3 + 2/17 - 2/17*y - 2/17*y**k = 0.
-1, 1
Let w be 450/9 - (0 + 1). Let z = w - 43. Find b, given that -10*b + z*b + b**2 + b - 4 = 0.
-1, 4
Let c(a) be the second derivative of 0*a**2 + 1/6*a**6 - a**5 + 25/12*a**4 - 7*a + 5 - 5/3*a**3. Suppose c(b) = 0. What is b?
0, 1, 2
Let m = 24488 - 72715/3. Let w = m - 249. Factor 2*l**2 + 0*l + 0 + w*l**3.
2*l**2*(l + 3)/3
Let i(m) = -m**2 + 5*m. Let x(z) = -12*z**2 + 1634*z - 313632. Let a(o) = 20*i(o) - 2*x(o). Factor a(h).
4*(h - 396)**2
Suppose 5*d + 52 = -5*a + 132, -2*a + 24 = -2*d. Let -68/9*p - 2/9*p**4 - 28/9*p**3 - 22/9 - 8*p**d = 0. What is p?
-11, -1
Let w(l) be the first derivative of l**5/10 - 13*l**4/2 + 101*l**3/6 - 25*l**2/2 + 2685. Factor w(z).
z*(z - 50)*(z - 1)**2/2
Solve -2/5*q**5 - 20*q**4 - 3232/5*q - 256 - 866/5*q**3 - 544*q**2 = 0 for q.
-40, -4, -1
Let a(z) = z**2 - 176*z + 2420. Let j be a(15). Factor 24/19*v**2 + 2/19*v**j + 8/19*v + 0 + 12/19*v**4 + 26/19*v**3.
2*v*(v + 1)**2*(v + 2)**2/19
Let z(g) be the second derivative of 48*g + 0 + 1/60*g**6 + 1/6*g**3 - 1/24*g**4 - 1/20*g**5 + 0*g**2. Suppose z(b) = 0. Calculate b.
-1, 0, 1, 2
Let w = 725633 + -5078663/7. Solve w + 3/7*a**2 + 96/7*a = 0 for a.
-16
Factor 2157312*z - 53592*z**5 - 435475*z**3 + 5082*z**4 + 53595*z**5 - 4309536*z**2 + 2582614*z**3.
3*z*(z - 1)**2*(z + 848)**2
Let j(t) be the first derivative of t**3/12 - 67*t**2/4 + 133*t/4 + 9453. Suppose j(i) = 0. What is i?
1, 133
Let c(f) be the first derivative of 2/3*f**2 - 36 + 0*f + 2/27*f**3. Find y such that c(y) = 0.
-6, 0
Let l(r) = r**3 - 20*r**2 + 21*r + 274. Let w be l(18). Let d = 0 - -6. Factor d*i**3 - 9*i**w - 4*i**3 + 4*i**4.
-i**3*(5*i - 2)
Suppose 263*q - 273*q = 440. Let o be -2 + -1 + 2 + (-44)/q. Factor 4*t**3 + o - 8/3*t**2 - 4/3*t**4 + 0*t.
-4*t**2*(t - 2)*(t - 1)/3
Let y(g) = 0 + g**3 + 5*g - 1 - 6*g. Let r(q) = 3*q**2 - 5 + q**3 + 495*q - 500*q + 2 + q**2. Let t(i) = 2*r(i) - 6*y(i). What is n in t(n) = 0?
0, 1
Suppose -252*z**2 + 4*z**4 + 72*z**3 - 458*z - 1448 - 274*z + 660*z**3 + 1696*z**2 = 0. What is z?
-181, -2, -1, 1
Let q(b) = -64*b - 1149. Let u be q(-18). Suppose 174/5*v**2 + 48778/5 + 5046/5*v + 2/5*v**u = 0. 