
Factor -1/2*f**4 - 1015/2*f**2 + 67/2*f**3 + 0 - 3675/2*f.
-f*(f - 35)**2*(f + 3)/2
Let o = 470845 - 6120955/13. Suppose -4/13*x**4 + 14/13*x - 12/13*x**2 + 0 - o*x**3 = 0. What is x?
-7, -1, 0, 1/2
Let j(y) be the second derivative of -y**5/90 + 191*y**4/54 - 1835*y**3/27 + 4525*y**2/9 - 2914*y. Factor j(u).
-2*(u - 181)*(u - 5)**2/9
Let i(s) be the third derivative of -s**7/16380 + s**6/1170 + s**5/156 + s**4/8 - 4*s**3 + 2*s**2 + 6*s. Let k(d) be the second derivative of i(d). Factor k(p).
-2*(p - 5)*(p + 1)/13
Let b(v) = -v**5 + v**4 + v**3 - v**2 + 2*v + 1. Let c(o) = -16*o**5 + 130*o**4 + 1586*o**3 - 18*o**2 + 36*o + 18. Let x(z) = 36*b(z) - 2*c(z). Factor x(j).
-4*j**3*(j + 28)**2
Let r(z) be the first derivative of z**4/10 + 194*z**3/5 + 4320*z**2 + 124416*z/5 - 1480. Solve r(k) = 0.
-144, -3
Let i(v) = -729*v - 78001. Let a be i(-107). Solve 8712/7*j + 6/7*j**3 - 63888/7 - 396/7*j**a = 0 for j.
22
Let j(p) be the second derivative of p**7/84 + 11*p**6/60 + 3*p**5/8 - 95*p**4/24 - 49*p**3/3 - 24*p**2 + 7764*p. Let j(q) = 0. Calculate q.
-8, -4, -1, 3
Find r, given that -86*r - 528 - 14*r - 3*r**2 + 4*r**2 - 3*r**2 = 0.
-44, -6
Let v = 3463 - 3459. Let m(o) be the second derivative of -8/21*o**3 + 9/140*o**5 + 0 + 6*o + 3/28*o**v + 2/7*o**2. Factor m(n).
(n + 2)*(3*n - 2)*(3*n - 1)/7
Suppose 356*w - 371*w + 34230 = 0. Let v = 6869/3 - w. Factor 4 + v*h**2 + 5/3*h**3 - 40/3*h.
(h - 1)*(h + 6)*(5*h - 2)/3
Let g(s) = -65*s**2 - 8275*s - 7510. Let d(a) = -11*a**2 - 1379*a - 1248. Let i(h) = -35*d(h) + 6*g(h). Suppose i(x) = 0. Calculate x.
-276, -1
Let v = 1/106 - -131/159. Let m(u) be the first derivative of v*u**2 + 0*u + 5/9*u**3 + 18. Factor m(s).
5*s*(s + 1)/3
Let u(z) be the third derivative of -21*z**6/80 - 127*z**5/240 + 251*z**4/96 + z**3/12 - 616*z**2 + 2*z. Factor u(h).
-(h - 1)*(h + 2)*(126*h + 1)/4
Let o(m) = 0*m - m**2 + 1 + 0*m + m - 3*m + 0*m. Let f(t) = -t**3 + 8*t**2 + 12*t - 6. Let i(z) = -f(z) - 6*o(z). Let i(v) = 0. What is v?
0, 2
Let -530/11*r**2 + 35378/11 - 34846/11*r - 2/11*r**3 = 0. Calculate r.
-133, 1
Let b = -968582 + 968585. Factor 0 + 0*k + 8*k**2 - 20/3*k**b + 4/3*k**4.
4*k**2*(k - 3)*(k - 2)/3
Suppose 2/5*x**4 - 454 + 6808/5*x - 6804/5*x**2 + 2264/5*x**3 = 0. What is x?
-1135, 1
Let i(y) be the third derivative of y**8/336 + 8*y**7/105 + y**6/3 + y**5/6 - 41*y**4/24 - 13*y**3/3 + 168*y**2 - 3*y. Solve i(w) = 0.
-13, -2, -1, 1
Factor 120*s + 1/3*s**4 - 28*s**2 + 0 - 2/3*s**3.
s*(s - 6)**2*(s + 10)/3
Suppose -62/5*j - 2/5*j**2 - 336/5 = 0. What is j?
-24, -7
Let u(t) = 4*t**4 + 3*t**3 + 3*t**2 + t. Let z(w) = 10*w**4 + 2*w**3 - 10*w**2 + 2*w. Let l(v) = -2*u(v) + z(v). Factor l(x).
2*x**2*(x - 4)*(x + 2)
Let 96/7*r + 0 - 7416/7*r**2 + 6/7*r**4 - 459/7*r**5 + 5508/7*r**3 = 0. What is r?
-4, 0, 2/153, 2
Let q(h) be the third derivative of -h**7/70 + 11*h**6/4 - 4273*h**5/20 + 8580*h**4 - 194688*h**3 + 51*h**2 - 2*h - 1. Suppose q(a) = 0. Calculate a.
16, 39
Suppose -6*o + 10*o = 3*b - 3374, -2*b - 5*o = -2280. Let n = 21474/19 - b. Solve 0*m + 0 + 2/19*m**3 + n*m**2 = 0.
-2, 0
Let x(w) = 3*w - 41. Let z(g) = -4*g + 41. Let y(j) = -2*x(j) - 3*z(j). Let l be y(8). Suppose -3*c**4 + 11*c + l*c**3 - 15*c**2 + 5*c**3 - 5*c = 0. What is c?
0, 1, 2
Let b be -363 + 335 + 0 + 33. Solve -10*u**2 + 5/2*u**4 - 5*u + 15/2 + b*u**3 = 0.
-3, -1, 1
Suppose 0 = c - a - 1021, -3*a - 175 - 838 = -c. Let b be (41/c)/(1/5). Factor 0 - b*s**2 + 1/5*s.
-s*(s - 1)/5
Let -96/7*c + 14 - 2/7*c**2 = 0. What is c?
-49, 1
Let k = -12255 + 12255. Let a(h) be the third derivative of 7*h**2 + 2/75*h**6 + 17/120*h**4 - 1/15*h**3 + k + 0*h - 2/15*h**5. Factor a(t).
(t - 2)*(4*t - 1)**2/5
Let y = -1 + 3. Suppose -14 + 74 = -y*k. Let a(m) = m**2 + m. Let x(d) = -d**3 + 19*d**2 - 42*d + 36. Let b(o) = k*a(o) + 5*x(o). Factor b(i).
-5*(i - 6)**2*(i - 1)
Suppose 13*r - 17*r + 20 = 0. Suppose 4*z - f = 13, r*z - 2*f - 10 = z. Factor -22*q**2 + 5*q**2 + 105*q**2 + z*q + 484*q**3.
4*q*(11*q + 1)**2
Suppose -3*k - 64*k - 39*k = 0. Let t(h) be the third derivative of 0*h + 5/42*h**7 + 11*h**2 + 1/2*h**6 + 0 + 3/4*h**5 + k*h**3 + 5/12*h**4. Factor t(y).
5*y*(y + 1)**2*(5*y + 2)
Factor 264/7*s**4 + 0 - 4/7*s**5 + 824/7*s**2 + 816/7*s**3 + 276/7*s.
-4*s*(s - 69)*(s + 1)**3/7
Suppose 0 = 2*j - 4*q - 2, 2*q + 10 = 7*q. What is w in -w**4 + j*w**3 + 12 - 9*w**2 + 4*w - 4*w**3 - 5*w**3 - 2*w**3 = 0?
-3, -2, 1
Let u be (-46 - -45)/(2/4) - -129. Suppose 115*i = u*i. Factor i - 24/11*r + 6/11*r**2.
6*r*(r - 4)/11
Let m = -614806 + 614808. What is d in m*d - 6/11*d**2 + 28/11 = 0?
-1, 14/3
Let u = 2/18931 - 1173752/283965. Let b = u - -74/15. Factor -12/5*v**2 + 4/5*v**3 - b*v + 12/5.
4*(v - 3)*(v - 1)*(v + 1)/5
Let s be 1/2*((-1824)/18)/(-19). Let u = 226 + -224. Factor 16/3 + s*r**3 - 16/3*r + 4/3*r**4 - 4*r**u.
4*(r - 1)**2*(r + 2)**2/3
Let l(h) be the third derivative of -h**7/1050 + h**6/120 + 1621*h**2. Factor l(g).
-g**3*(g - 5)/5
Let k = 291 + -131. Let a(r) = -r**3 + 43*r**2 - 37*r - 206. Let j be a(42). Find w, given that k*w**3 - j - w - 25*w - 6*w - 100*w**4 - 24*w**2 = 0.
-1/5, 1
Let v(m) be the third derivative of -m**7/1470 - 11*m**6/210 + 19*m**5/84 + 23*m**4/28 - 1043*m**2. Factor v(w).
-w*(w - 3)*(w + 1)*(w + 46)/7
Suppose 435*b - 1236 = 10*b + 464. Let -40/3*f - 20/3 - 5*f**2 + 10/3*f**3 + 5/3*f**b = 0. What is f?
-2, -1, 2
Let r(h) be the first derivative of h**4/20 - 229*h**3/5 + 58824*h**2/5 + 118336*h/5 - 880. Factor r(j).
(j - 344)**2*(j + 1)/5
Let 52/3*n**3 + 0 + 118/3*n**2 - 2/3*n**4 - 56*n = 0. What is n?
-3, 0, 1, 28
What is o in -1865*o**3 + 935*o**3 + o**2 + 0*o**2 + 929*o**3 + o - 1 = 0?
-1, 1
Let 160 + 65*f - 15/2*f**2 = 0. Calculate f.
-2, 32/3
Let o be 40/(-90) - 44/(-18). Factor 17*k**2 + 31*k**o - 39*k - 59*k + 78 + 22*k - 47*k - 3*k**3.
-3*(k - 13)*(k - 2)*(k - 1)
Let v(u) be the second derivative of 213*u**5/40 - 141*u**4/4 - 2*u**3 + u + 552. Factor v(k).
3*k*(k - 4)*(71*k + 2)/2
Let d be ((-37733)/(-7566) - 2/((-12)/(-5))) + 2/(-13). Factor 0*h + 0 - 3/2*h**2 - 9/2*h**3 - 3/2*h**5 - 9/2*h**d.
-3*h**2*(h + 1)**3/2
Let a(u) be the second derivative of -7*u - 7 - 1/6*u**3 - 1/60*u**4 + 7/5*u**2. Factor a(l).
-(l - 2)*(l + 7)/5
Suppose -3*c + 12 = -k, -6*c - k - 9 = -8*c. Find g such that -18 - 21*g + 22*g**c + 8*g**4 + g**5 + 3*g**3 + 10*g**2 - 5*g**3 = 0.
-3, -2, -1, 1
Let k(v) be the first derivative of -5*v**4/4 + 470*v**3/3 - 8925*v**2/2 - 104040*v + 3765. Factor k(y).
-5*(y - 51)**2*(y + 8)
Let j(b) = -3*b**3 + 12*b**2 - 37*b + 150. Let m be j(4). Factor 3/2*g**4 - 9/2 + 3*g**m + 6*g**3 - 6*g.
3*(g - 1)*(g + 1)**2*(g + 3)/2
Let j(d) = 5*d**4 + 30*d**3 + 145*d**2 - 605*d - 1440. Let q(h) = -7*h**4 - 30*h**3 - 146*h**2 + 606*h + 1440. Let v(n) = 6*j(n) + 5*q(n). Factor v(w).
-5*(w - 6)**2*(w + 2)*(w + 4)
Let f(c) be the first derivative of 9/2*c**2 + 74 - c**3 - 6*c. Let f(u) = 0. Calculate u.
1, 2
Suppose 0*p = 4*p - 16. Let a be (-105)/(-25) + (-4)/(-5). What is r in -5 + a - 18*r + r**4 - 3*r**p - 30*r**2 - 14*r**3 = 0?
-3, -1, 0
Let a(i) be the second derivative of -i**7/168 - i**6/24 - i**5/16 + 5*i**4/48 + i**3/4 + i + 224. Suppose a(g) = 0. Calculate g.
-3, -2, -1, 0, 1
Factor 61*k**2 + 95*k**2 + 56*k**2 - 210*k - 2*k**3 + 5 - 5.
-2*k*(k - 105)*(k - 1)
Let l(d) be the third derivative of d**6/360 - d**5/40 + d**4/12 + 20*d**3/3 - 3*d**2 + 16*d. Let g(c) be the first derivative of l(c). What is s in g(s) = 0?
1, 2
Let i(y) be the third derivative of -y**6/200 + 7*y**5/100 + 7*y**4/4 + 52*y**3/5 + 255*y**2. Factor i(j).
-3*(j - 13)*(j + 2)*(j + 4)/5
What is v in -1/8*v**3 + 308 - 156*v + 81/4*v**2 = 0?
4, 154
Suppose -49*u = -47*u + 162. Let b = 96 + u. Find o, given that b*o**2 + 0*o**4 - 5*o**5 + 12*o**4 + 2*o**4 - 29*o**4 + 5*o**3 = 0.
-3, -1, 0, 1
Let i(n) be the third derivative of 0 - 1/15*n**5 - 45*n**2 + 0*n**3 + 1/12*n**4 - 1/48*n**6 + 0*n. Determine b, given that i(b) = 0.
-2, 0, 2/5
Factor -104*p**2 - 168*p**3 + 124*p - 92*p**2 + 199*p**2 + 44*p - 3*p**4.
-3*p*(p - 1)*(p + 1)*(p + 56)
Determine o so that 768/7*o + 0 - 2/7*o**5 - 12*o**3 + 320/7*o**2 - 30/7*o**4 = 0.
-8, -2, 0, 3
Let o be (0 - (-2)/(-20)) + 17172/120. Let i = -138 + o. Factor 1/6*n**2 - 1/6*n**4 + 0 + 1/3*n + 1/6*n**i - 1/2*n**3.
n*(n - 2)