*2 - 2*t + 5. Let j(n) = -635 - 3*n**2 + 4*n**2 + 634. Let r(x) = h(x) + 6*j(x). Determine d, given that r(d) = 0.
-1
Let p(n) = 116*n**2 + 1715*n + 731025. Let x(s) = -23*s**2 - s. Let g(r) = p(r) + 5*x(r). Factor g(j).
(j + 855)**2
Let x = -1087531/231 - -14111/3. Let f = x - -50/11. Determine z so that -6/7*z - f*z**3 + 2/7 + 6/7*z**2 = 0.
1
Let m(t) be the third derivative of t**7/840 - t**6/240 - t**5/80 + t**4/24 + t**3/6 - 2638*t**2. Let m(f) = 0. Calculate f.
-1, 2
Let c(q) be the third derivative of q**6/24 + 5*q**5/4 - 195*q**4/8 - 9295*q**3/6 - 4738*q**2. Solve c(u) = 0 for u.
-13, 11
Suppose 1597536/7*d**2 - 274776192/7*d + 2/7*d**4 - 3096/7*d**3 + 0 = 0. What is d?
0, 516
Let b(m) be the second derivative of m**8/13440 + m**7/1260 - m**6/1440 - m**5/60 + 19*m**4/6 - 119*m. Let c(t) be the third derivative of b(t). Factor c(f).
(f - 1)*(f + 1)*(f + 4)/2
Let k(i) = -2*i**3 - 24*i**2 + 14*i + 128. Let f(d) = 5*d**3 + 71*d**2 - 40*d - 379. Let j(u) = -4*f(u) - 11*k(u). Suppose j(y) = 0. What is y?
-2, 3, 9
Let c(s) be the third derivative of s**5/80 - 101*s**4/16 + 10201*s**3/8 - 5*s**2 - s - 19. Let c(j) = 0. Calculate j.
101
Let m(a) be the second derivative of 8/15*a**3 - 8/5*a**2 - 4/25*a**5 + 0 - a + 1/5*a**4 + 2/75*a**6. Determine f, given that m(f) = 0.
-1, 1, 2
Let h = 461/18 + -449/18. Suppose 0 = -49*y + 47*y + 4. Factor 4/3*a - h*a**y + 0.
-2*a*(a - 2)/3
Let k(l) = 14*l**2 + 26*l. Let v be k(2). Factor -3*x**2 - x**2 - v*x + 140*x + 80.
-4*(x - 10)*(x + 2)
Suppose -9 + 3 = 2*p, 4*o + 1 = -3*p. Let u(y) = y**2 + y + 1. Let b be u(1). Let -5*i**o - b*i**2 + 0*i**2 - 20*i - 16 + 4*i**2 = 0. Calculate i.
-4, -1
Let u = 497 - 493. Let k(m) = -m**2 - 4*m + 6. Let t be k(-5). Factor 617*d**u - 4*d**3 - 1 + t - 614*d**4 + d**2.
d**2*(d - 1)*(3*d - 1)
Let j(r) be the second derivative of 0 - 151*r - 1/60*r**6 + 17/48*r**4 + 7/80*r**5 + 3*r**2 - 29/12*r**3. Solve j(l) = 0 for l.
-3, 1/2, 2, 4
Let t(o) = o**3 - 44*o**2 + 473*o + 530. Let z(x) = x**3 - 43*x**2 + 471*x + 531. Let r(y) = 4*t(y) - 3*z(y). Factor r(w).
(w - 31)*(w - 17)*(w + 1)
Solve -5105*x**5 + 513*x**4 + 21174*x - 5334*x - 6108*x**2 - 1968*x**3 + 5102*x**5 + 32064 = 0.
-2, 4, 167
Let w(x) be the third derivative of -44*x**4 - 1/660*x**6 - 45*x**2 + 7744/3*x**3 + 0 + 0*x + 2/5*x**5. Suppose w(y) = 0. Calculate y.
44
Suppose 5*b + 6*o - 2*o = -8, -10 = 4*b + 5*o. Suppose -2*j - 3*k + 9 = b, -3*j + 3 = -0*j + k. Factor -4/9*d**3 + j*d**2 + 4/3*d - 8/9.
-4*(d - 1)**2*(d + 2)/9
Let q = 192 - -4. Factor -19*y**2 + q + 370*y - 39*y**2 - 118*y + 139*y**2.
(9*y + 14)**2
Let a be (-3)/69 + (65 - (-78813)/(-1242)). Let -a*y**2 - 12*y + 0 = 0. Calculate y.
-8, 0
Let w = -1060 - -1059. Let m be -8 + (8 - w - -2). Factor 2/7*k**4 + 10/7*k**m + 2*k + 18/7*k**2 + 4/7.
2*(k + 1)**3*(k + 2)/7
Suppose 342*m - 3*m**2 - 2*m**2 - 11115 - 14661 + 4*m**2 - 3465 = 0. Calculate m.
171
Let d(p) = p**2 + p - 4. Let l be d(-3). Let g be 299/11 + l/(-11). Find n such that 2*n - 2*n - g - 3*n**2 + 39 = 0.
-2, 2
Let f(p) = -2*p**4 - 16*p**3 + 56*p**2 - 38*p + 3. Let y(r) = -3*r**4 - 33*r**3 + 110*r**2 - 74*r + 5. Let n(j) = -5*f(j) + 3*y(j). Suppose n(l) = 0. What is l?
0, 1, 2, 16
Find n such that -120*n**2 + 163*n**2 + 336*n - 177*n**3 - 334*n - 43*n**4 + 175*n**5 = 0.
-1, -1/25, 0, 2/7, 1
Let z = 6 - 2. Suppose z*v - 11 = 3*v. What is a in 4*a**5 + 8*a**4 + v*a**3 - 7*a**3 + 4*a**2 - 4*a**2 = 0?
-1, 0
Solve -9428*k**4 + 4950*k**3 + 1655*k - k**5 - 4*k**5 + 11068*k**4 + 4960*k**2 = 0.
-1, 0, 331
Let l(k) = 39*k + 57 - 225 + 9*k + 8*k. Let i be l(3). Suppose -2/3*q**4 - 2/3*q**5 + 0 + 2/3*q**3 + 2/3*q**2 + i*q = 0. Calculate q.
-1, 0, 1
Let x(w) be the third derivative of w**5/90 + 227*w**4/36 + 8286*w**2. Suppose x(v) = 0. What is v?
-227, 0
Let d(r) be the first derivative of 75*r**3 - 159/2*r**2 + 27*r + 27/4*r**4 - 140. Solve d(q) = 0 for q.
-9, 1/3
Suppose 64*f - 2*g = 124, -2*f - 4*g - 12 = -24. Let b = 67/22 + -6/11. Factor b*m**f - m**3 + 1/2 - 2*m.
-(m - 1)**2*(2*m - 1)/2
Let -267801737 + 12156*t**4 + 6220416*t - 41*t**5 - 1047868*t**3 + 3606612*t**2 + 5*t**5 + 270032857 = 0. Calculate t.
-2/3, 5, 167
Let t(b) = -b**3 + 19*b**2 + 4. Let v be t(19). Let s(q) be the first derivative of 0*q + 1/3*q**v + 1/9*q**3 + 1 - 1/2*q**2. Find l, given that s(l) = 0.
-1, 0, 3/4
Let q(s) = -125*s**2 + 4605*s + 25535. Let y(v) = 9*v**2 - 327*v - 1824. Let b(c) = -4*q(c) - 55*y(c). Let b(a) = 0. What is a?
-4, 91
Let p(h) be the second derivative of h**5/40 + 91*h**4/12 + 179*h**3/3 + 178*h**2 + 262*h + 14. Suppose p(l) = 0. What is l?
-178, -2
Suppose 4*c - 3*n = -n + 18, 4*c + 3*n = 23. Let j be (2 + 1 - 1) + -2. Find f, given that j*f**4 + 0 - 2*f**4 + 0 + 5*f**c = 0.
0, 2/5
Let b(v) = -2*v**3 - 106*v**2 + 221*v + 374. Let r(j) = -8*j**3 - 372*j**2 + 776*j + 1308. Let m(a) = 24*b(a) - 7*r(a). Determine p so that m(p) = 0.
-9, -1, 5/2
Let a be (-621)/138*(-8)/9. Solve -7/2*v**2 + 1/4*v**3 + 1/4*v**5 - 2 + v**a - 5*v = 0 for v.
-2, -1, 2
Let m(u) be the second derivative of u**5/20 - 10*u**4/3 - 43*u**3/6 + 41*u**2 - 29*u - 46. Factor m(g).
(g - 41)*(g - 1)*(g + 2)
Let g(j) be the second derivative of j**6/35 - 31*j**5/70 + 25*j**4/21 + 52*j**3/7 + 72*j**2/7 - 660*j + 2. Determine i so that g(i) = 0.
-1, -2/3, 6
Let b(d) be the third derivative of -1/20*d**5 + 0 + d + d**2 - 14*d**3 + 29/8*d**4. Factor b(c).
-3*(c - 28)*(c - 1)
Let q(t) = -625*t**3 - 6915*t**2 - 4830*t + 1980. Let r(n) = 26*n**3 - n**2 - 2*n - 1. Let a(g) = -q(g) - 20*r(g). Solve a(u) = 0 for u.
-196/3, -1, 2/7
Let p(t) be the second derivative of -t**4/6 - 23*t**3/3 - 60*t**2 - 10*t - 71. Determine d, given that p(d) = 0.
-20, -3
Let n(v) be the first derivative of -v**6/8 + 39*v**5/20 - 69*v**4/16 + 11*v**3/4 + 203. Factor n(g).
-3*g**2*(g - 11)*(g - 1)**2/4
Let f(j) be the third derivative of 7/12*j**4 + 4/3*j**3 + 1/20*j**5 - 11*j**2 + 0*j + 2. Factor f(v).
(v + 4)*(3*v + 2)
Let o(w) be the first derivative of -w**4 - 464*w**3/3 + 8*w**2 + 1856*w + 3012. Factor o(r).
-4*(r - 2)*(r + 2)*(r + 116)
Suppose -97/3*o**3 - 357*o - 294 + 605/3*o**2 + 5/3*o**4 = 0. What is o?
-3/5, 6, 7
Let f(n) be the first derivative of -114*n**3 + 228 + 163*n**2 + 8/5*n**5 + 4*n**4 - 80*n. Determine w, given that f(w) = 0.
-8, 1/2, 5
Let n(x) be the third derivative of 1/24*x**4 + 0 + 0*x - 1/120*x**6 - 1/36*x**5 + 2/9*x**3 + 296*x**2 + 1/630*x**7. Factor n(g).
(g - 4)*(g - 1)*(g + 1)**2/3
Suppose -3*v - 2*j = -23, 2*v - 15 = j + 5. Let x be (5 + (-51)/v)*4/(-8). Factor -5/6*r + 1/2*r**2 + x.
(r - 1)*(3*r - 2)/6
Let y(o) be the third derivative of 0*o + 0 + 4*o**3 - 1/30*o**5 - 41*o**2 - 11/12*o**4. Suppose y(p) = 0. What is p?
-12, 1
Let l(m) be the third derivative of 1/60*m**6 - 2*m**3 + 2/15*m**5 - 163*m**2 + 1/12*m**4 + 0 + 0*m. Factor l(v).
2*(v - 1)*(v + 2)*(v + 3)
Suppose -74*a**2 - 2603*a - 2534*a - 32*a**4 + 5167*a - 176*a**3 = 0. Calculate a.
-5, -3/4, 0, 1/4
Factor 2/3*r**2 - 630*r + 1888/3.
2*(r - 944)*(r - 1)/3
Let p = -284 + 319. Let m be (88/(-20))/(p/(-25)). Factor -18/7*n**2 - m*n**4 + 0 + 30/7*n**3 + 4/7*n + 6/7*n**5.
2*n*(n - 1)**3*(3*n - 2)/7
Let f = -356 - -372. Determine d so that 12*d**4 - 2*d**5 + 6*d**5 - f - 16*d**2 + 16 = 0.
-2, 0, 1
Suppose 35*a = 21*a + 336. Solve -a*g**2 - 16 + 3*g**3 - 9*g**3 + 7*g**3 + 36*g + 3*g**3 + 0 = 0.
1, 4
Let i(l) be the first derivative of 5*l**3/12 - 55*l**2/8 + 35*l - 3505. Determine y so that i(y) = 0.
4, 7
Let d(i) be the second derivative of -529*i**2 - 47/6*i**4 - 47*i - 575/3*i**3 + 2 - 1/10*i**5. Factor d(y).
-2*(y + 1)*(y + 23)**2
Let w(g) be the third derivative of -2888/3*g**3 - 1/15*g**5 + 85*g**2 + 0 + 38/3*g**4 + 0*g. Suppose w(r) = 0. What is r?
38
Let q(i) be the first derivative of 363*i**2 - 7986*i + 12 - 22/3*i**3 + 1/18*i**4. Let q(f) = 0. Calculate f.
33
Let u(r) be the third derivative of 9*r**7/70 - 41*r**6/10 + 252*r**5/5 - 270*r**4 + 216*r**3 + 363*r**2 - 6*r. Factor u(i).
3*(i - 6)**3*(9*i - 2)
Let v = -971522/5 + 194308. Determine h so that -3*h + 6/5*h**2 + 3/5*h**4 - 3/5*h**5 - 9/5 + v*h**3 = 0.
-1, 1, 3
Let h(r) be the first derivative of 3*r**4/4 - 237*r**3 + 38745*r**2/2 + 408483*r + 13912. Let h(l) = 0. What is l?
-9, 123
Let g(d) be the second derivative of -d**6