 z so that -z**3 + 45*z**2 + 85*z + 2*z**3 + 49 - 4 - 6*z**3 - j*z**2 = 0.
-1, 9
Let v(s) be the first derivative of -43 - 59049/2*s - 81/2*s**3 - 3/8*s**4 - 6561/4*s**2. Factor v(n).
-3*(n + 27)**3/2
Let p(s) = -21*s**2 - 9*s + 12. Suppose 19*c + 154 - 496 = 0. Let d(b) = -b**2 - b - 1. Let k(f) = c*d(f) - p(f). Factor k(x).
3*(x - 5)*(x + 2)
Let p(g) be the third derivative of -g**6/160 + 21*g**5/20 + 171*g**4/32 + 43*g**3/4 - 53*g**2 + g + 1. Determine m, given that p(m) = 0.
-1, 86
Let 976*j**2 + 84*j**4 + 864 - 160*j**2 - 85*j**4 - 211*j**3 - 331*j - 1393*j + 256*j**2 = 0. What is j?
-216, 1, 2
Suppose -3*k**2 - 521 - 745 + 794*k - 1244*k + 1089*k = 0. Calculate k.
2, 211
Factor -208/7*k + 2/7*k**2 + 206/7.
2*(k - 103)*(k - 1)/7
Suppose -471/4*z - 9/2*z**2 - 39/2 = 0. Calculate z.
-26, -1/6
Determine i, given that -167/4*i**2 + 1029/4*i - 1557/4 - 1/4*i**3 = 0.
-173, 3
Let l = 2031 - 2028. Let q(x) be the second derivative of 0*x**l - 1/40*x**5 + 7/120*x**6 - 1/48*x**4 + 18*x - 1/42*x**7 + 0*x**2 + 0. Factor q(r).
-r**2*(r - 1)**2*(4*r + 1)/4
Let q(n) be the third derivative of n**7/1260 - n**5/60 - n**4/12 - 67*n**3/6 - 102*n**2. Let z(t) be the second derivative of q(t). Factor z(f).
2*(f - 1)*(f + 1)
Let q(r) be the third derivative of r**7/315 - 37*r**6/90 + 782*r**5/45 - 578*r**4/3 + 135*r**2. Determine a, given that q(a) = 0.
0, 6, 34
Suppose -3 = -4*x + 13. Suppose -16*i + 18*i = x. What is j in -56*j + 55*j + 6*j**2 - i*j**3 + 3*j**3 + 6*j**3 = 0?
-1, 0, 1/7
Let z(x) be the second derivative of x**8/280 - x**7/84 - x**6/45 + x**5/15 - 3*x**3/2 - x**2/2 - 45*x. Let q(i) be the second derivative of z(i). Factor q(g).
2*g*(g - 2)*(g + 1)*(3*g - 2)
Suppose 0 = 4*a + 3*g + 164 - 193, -3*a - 22 = -4*g. Let h(b) be the first derivative of -b**4 - 4 - 20*b**a + 44/3*b**3 + 0*b. Factor h(c).
-4*c*(c - 10)*(c - 1)
Let z(f) be the second derivative of -f**6/180 + 131*f**5/120 - 383*f**4/72 - 131*f**3/36 + 32*f**2 - 8611*f. Let z(i) = 0. Calculate i.
-1, 1, 3, 128
Factor 1/2*n**3 - 69 - 205/2*n - 33*n**2.
(n - 69)*(n + 1)*(n + 2)/2
Let v(x) be the second derivative of 4/57*x**4 - 2/285*x**6 + 0*x**3 + 28*x + 1/399*x**7 + 2 - 2/95*x**5 + 0*x**2. Determine q, given that v(q) = 0.
-2, 0, 2
Let v(a) be the first derivative of a**4/8 + 59*a**3/6 + 935*a**2/4 + 4477*a/2 - 5721. Solve v(t) = 0 for t.
-37, -11
Let n be ((-279)/6)/((-26)/8 + 4). Let v = n - -67. Let -2 + 12*m - 25*m**3 + 5*m**5 + 22 + v*m**4 + 8*m - 25*m**2 = 0. What is m?
-2, -1, 1, 2
Suppose -5*c = -0*s + s - 13, 4*c - 14 = -2*s. Let i be 10/(-15)*(23/(-7) + c). Solve i - 15/7*w - 3*w**2 = 0.
-1, 2/7
Let f be (-11)/((-363)/11)*(12 + 0). Suppose -f = z, -3*z - 29 + 7 = -5*l. Factor 17/2*x**2 + 0*x - 9*x**3 - l + 5/2*x**4.
(x - 2)*(x - 1)**2*(5*x + 2)/2
Determine g, given that 0 - 2*g**3 + 1152/5*g + 284/5*g**2 = 0.
-18/5, 0, 32
Let t = -1478 + 1478. Let r(m) be the first derivative of 1/6*m**6 + 0*m**5 - 1/4*m**4 + t*m**2 + 0*m**3 - 9 + 0*m. Let r(p) = 0. What is p?
-1, 0, 1
Let x(h) = -2*h**2 + 61*h + 3. Let g be x(0). Let l(v) be the first derivative of -5/2*v - 9 + 1/12*v**g + 3/8*v**2. Solve l(k) = 0.
-5, 2
Let l(a) be the third derivative of -a**4/24 - 2*a**3/3 - 4*a**2 - 47*a. Let y be l(-8). Solve 0 + 0*s**2 + 0*s + 0*s**3 + 1/3*s**y = 0 for s.
0
Suppose -v + 34 = -18. Suppose 5*o - 3*o = -2*w + v, 0 = 2*o - w - 46. Let -66*c - 42*c + 6*c**2 - o - 9*c**3 + 36*c**3 = 0. What is c?
-2, -2/9, 2
Let t(g) be the second derivative of g**6/150 - 39*g**5/100 + 89*g**4/30 - 46*g**3/5 + 68*g**2/5 - 12*g - 22. Let t(k) = 0. Calculate k.
1, 2, 34
Let o = 51/26 - 70/39. Let a(x) be the second derivative of 17*x + 1/12*x**4 + 0 + o*x**3 + 0*x**2. Solve a(f) = 0 for f.
-1, 0
Let q be (-2 - 1)*(2 - 3)/3. Let u be (-4)/6*48/(-160)*q. Solve 0*n**4 + 0*n**2 - u*n**5 + 2/5*n**3 + 0 - 1/5*n = 0.
-1, 0, 1
Suppose 2*k - 6*k - 9 = 3*i - 3*k, 9 = -k. Solve -8/13*j**3 - 2/13*j**4 - 6/13*j**2 + i*j + 0 = 0.
-3, -1, 0
Let k be ((-72)/(-2) + -1)*2660/6650. Factor k + 2/7*x**2 + 4*x.
2*(x + 7)**2/7
Suppose -10*o - 35 = -55. Factor 0*i - 2*i + o - i**3 - i**4 + 2 + 9*i**2 - 9*i.
-(i - 1)**3*(i + 4)
Suppose -3*t - 287 = j - 0*t, 861 = -3*j + 4*t. Let r = j - -1439/5. Factor d + 2/5 - 1/5*d**5 - 4/5*d**4 - r*d**3 + 2/5*d**2.
-(d - 1)*(d + 1)**3*(d + 2)/5
Let m(x) be the first derivative of -50 - 1/8*x**4 + 1/6*x**3 - 1/2*x + 1/4*x**2. Determine v, given that m(v) = 0.
-1, 1
Let k(f) = f**3 + 5*f**2 + 2*f + 4. Let m be k(-5). Let w be (-42)/m + -1*3. Let 6*j**3 - 4*j**2 + 3*j + 6*j**w + 2*j**5 - 3*j + 6*j**2 = 0. Calculate j.
-1, 0
Let j = 2/176117 + 9510296/1937287. Factor 392/11*h**3 + 336/11*h**2 + 2/11 - j*h.
2*(h + 1)*(14*h - 1)**2/11
Factor 16/9*q**2 + 40/9*q - 22/9*q**3 + 0 + 2/9*q**4.
2*q*(q - 10)*(q - 2)*(q + 1)/9
What is l in -558/7*l**2 + 38070/7*l + 2/7*l**3 + 119286/7 = 0?
-3, 141
Let b(d) = 25*d**2 - 12200*d - 24350. Let j(l) = 11*l**2 - 6095*l - 12174. Let p(i) = 2*b(i) - 5*j(i). Suppose p(x) = 0. Calculate x.
-2, 1217
Let q(n) be the third derivative of n**8/84 - 2*n**7/15 + n**6/30 + 47*n**5/15 - n**4/3 - 80*n**3/3 + 1186*n**2. Suppose q(l) = 0. What is l?
-2, -1, 1, 4, 5
Let a = 1830 + -1827. Let t be (1/(-6))/((-31)/62). Factor -b**2 + 2/3 + 1/3*b**4 + 1/3*b - t*b**a.
(b - 2)*(b - 1)*(b + 1)**2/3
Let o(v) = -16*v**2 + 0*v - 2*v + 19*v**2 + 0*v. Let t(a) = 42*a**2 - 3*a - 40*a**2 + 2*a + 0*a. Let p(w) = -3*o(w) + 5*t(w). Factor p(g).
g*(g + 1)
Let v(k) = -3*k**3 + 13*k**2 + 1. Let d(m) = -34*m**3 + 34*m**2 + 172*m - 34. Let f(r) = -d(r) + 6*v(r). Factor f(b).
4*(b - 2)*(b + 5)*(4*b - 1)
Let m(h) be the second derivative of -3/20*h**5 + 24 + 2700*h**2 + 2*h - 29/2*h**4 - 390*h**3. Factor m(q).
-3*(q - 2)*(q + 30)**2
Let p be (18/27)/(-1 + 51/45). Let a be (-1 + 1)/((-315)/(-21) - 14). Factor 0*d + 2/13*d**p - 4/13*d**3 + a + 0*d**2 + 2/13*d**4.
2*d**3*(d - 1)*(d + 2)/13
Let u(f) be the third derivative of f**7/315 - 13*f**6/90 + 8*f**5/3 - 224*f**4/9 + 1024*f**3/9 + 217*f**2. Let u(v) = 0. What is v?
2, 8
Let u(n) = -n**3 + 17*n**2 - 19*n + 50. Let f be u(16). Factor 5*t**3 + 4093*t - 640 + 70*t**f - 1922*t - 2011*t.
5*(t - 2)*(t + 8)**2
Let u(i) = 21*i**2 + 2132*i - 378077. Let t(d) = -96*d**2 - 8529*d + 1512309. Let v(a) = -2*t(a) - 9*u(a). Factor v(q).
3*(q - 355)**2
Let f(d) be the second derivative of d**7/294 + 4*d**6/15 + 78*d**5/35 + 152*d**4/21 + 200*d**3/21 - 10801*d. Determine k, given that f(k) = 0.
-50, -2, 0
Factor 11/3 + 7/2*o - 1/6*o**2.
-(o - 22)*(o + 1)/6
Let y be (-1 - -7*(-2)/(-13)) + 4375/585. Determine t, given that 2/9*t**5 - 28/9*t**2 + 50/9 + y*t**3 - 70/9*t - 22/9*t**4 = 0.
-1, 1, 5
Let u = 546 + -428. Factor -9*p**2 - 140 - p**3 + p - u + 217 + 50*p**2.
-(p - 41)*(p - 1)*(p + 1)
Suppose -2*q - 15 = -5*q. Let c(b) = 3*b**2 - 9*b - 5. Let g be c(q). Factor -g - 20*i**4 + 53 - 5*i + 4*i**5 + 8*i**2 + 24*i**3 - 16 - 23*i.
4*(i - 3)*(i - 1)**3*(i + 1)
Let i(y) be the first derivative of 138 - 2/9*y**3 - 26/3*y**2 + 18*y. Factor i(z).
-2*(z - 1)*(z + 27)/3
Let n(m) be the first derivative of 14*m**6/3 + 83*m**5/5 - 1293*m**4/4 + 2056*m**3/3 + 10*m**2 - 144*m + 267. Find f such that n(f) = 0.
-9, -1/4, 2/7, 2, 4
Let d(w) be the first derivative of -3*w**4/32 + 17*w**3/8 - 99*w**2/8 - 986. Factor d(f).
-3*f*(f - 11)*(f - 6)/8
Let y(p) be the third derivative of 0 - 5/336*p**8 + 5/8*p**6 + 5/4*p**4 + 0*p**3 + 1/14*p**7 - 47*p + 17/12*p**5 + p**2. What is d in y(d) = 0?
-1, 0, 6
Suppose -1948*z + 1944*z = -20. Solve 5/4*t**z - 5/4*t + 0*t**3 + 0 - 5/2*t**2 + 5/2*t**4 = 0 for t.
-1, 0, 1
Let k be 1211/(-21)*(-108)/(-9). Let r = 2769/4 + k. Factor -1 + 5/4*z**3 - 1/4*z**5 - 2*z - r*z**2 + 1/4*z**4.
-(z - 2)**2*(z + 1)**3/4
Let p be (46/6)/(5*6/90). Let g = p - 68/3. Factor 1/3*j**3 + 0*j - 2/3*j**2 + 0 + g*j**4.
j**2*(j - 1)*(j + 2)/3
Factor 2*s**2 - 20*s + 2/5*s**3 + 0.
2*s*(s - 5)*(s + 10)/5
Suppose 0*h + 4 = -r - 4*h, 3*r - 4*h = 4. Suppose 8*f - 12*f + 8 = r. Factor -2/3*d + 2/3*d**4 - 2/3*d**f + 0 + 2/3*d**3.
2*d*(d - 1)*(d + 1)**2/3
Let d(n) = 6*n - 11. Let i be d(2). Suppose -i = 6*q - 1. Solve -699*a**2 + q*a + 24*a + 3 + 747*a**2 = 0.
-1/4
Let s(p) be the first derivative of -p**7/280 - 7*p**6/60 - 3*p**5/2 - 9*p**4 - 2*p**3 - 2*p + 42. Let x(c) be the third deriva