+ 12)/8
Let w = 62 - 62. Suppose 24*r - 28*r + 20 = w. Factor 2*a**5 + 82*a - a**r - 82*a.
a**5
Let v(u) be the third derivative of u**8/336 + 3*u**7/14 + 29*u**6/8 - 317*u**5/12 + 70*u**4 - 96*u**3 - 1252*u**2. Factor v(c).
(c - 1)**3*(c + 24)**2
Determine o so that 100*o + 1758*o - 1065*o - 5*o**2 + 1797*o - 2585 = 0.
1, 517
Let 28/5*d**2 - 1/5*d**3 - 41*d + 90 = 0. Calculate d.
5, 18
Suppose 12 = 210*o - 206*o. Determine d, given that -34*d**2 + 3*d**o + 17*d**2 + 8*d**2 = 0.
0, 3
Let h be -7 - -1 - ((-1254)/121 - 7 - -11). Let d(t) be the first derivative of 17 - 4/11*t**3 + h*t**2 + 16/11*t - 5/22*t**4 - 2/55*t**5. Factor d(v).
-2*(v - 1)*(v + 2)**3/11
Let s be 8/10*(28146/(-36) - -6). Let l = s - -622. Solve 0 + 4/3*t + 4/3*t**2 - l*t**3 - 4/3*t**4 = 0.
-1, 0, 1
Factor 66 + 34*s + 1/2*s**2.
(s + 2)*(s + 66)/2
Suppose 138*q - 1043 = -77*q - 398. Let -1/2*c**5 + 19/2*c + q*c**3 + 10*c**2 - c**4 + 3 = 0. Calculate c.
-2, -1, 3
Let v(p) = -p**3 + 2*p**2 + 1. Let q(d) = -7*d**3 + 7*d**2 + d + 11. Suppose 3*g - 6*g = -18. Let t(s) = g*v(s) - q(s). Suppose t(b) = 0. What is b?
-5, -1, 1
Let s(t) = 26*t + 262. Let m = -950 + 940. Let y be s(m). What is w in 16/5 + 16/5*w + 4/5*w**y = 0?
-2
Factor 84 + 371 + 1390*t + 1375*t**2 - 335 + 105*t**3.
5*(t + 1)*(t + 12)*(21*t + 2)
Factor -2/19*l**4 + 6/19*l**3 + 0 + 0*l + 36/19*l**2.
-2*l**2*(l - 6)*(l + 3)/19
Let n(r) = -r**4 - 5*r**3 + r**2. Let s(d) = -9*d**4 - 45*d**3 + 123*d**2 + 27*d - 486. Let w(z) = -6*n(z) + s(z). Factor w(h).
-3*(h - 3)**2*(h + 2)*(h + 9)
Let g(k) = -4*k**2 + 143*k - 835. Let d(v) = 36*v**2 - 1296*v + 7516. Let h(r) = -3*d(r) - 28*g(r). Find c such that h(c) = 0.
13, 16
Let m(n) be the first derivative of 5*n**4/4 + 20*n**3 + 50*n**2 + 2441. Find f such that m(f) = 0.
-10, -2, 0
Let s(o) be the second derivative of 2*o**6/25 + 343*o**5/25 + 451*o**4/15 - 46*o**3/3 - 452*o**2/5 + 1560*o. Suppose s(u) = 0. What is u?
-113, -1, 2/3
Let s(a) be the third derivative of a**2 + 1/60*a**4 - 12*a - 1/300*a**6 + 0*a**3 + 0*a**5 + 0. Determine v so that s(v) = 0.
-1, 0, 1
Suppose -2*a + 14 - 6 = 0. Suppose -4*h - 2*n = -60, -n - 90 = -5*h + a*n. Solve 3*v - 4*v**4 + 8*v**2 - 4*v**4 - h*v**3 + 9*v + 4*v**5 = 0 for v.
-1, 0, 1, 3
Let x = -13276 - -13278. Let c(r) be the first derivative of -28 - 2/3*r**x + 10/3*r + 2/45*r**3. Solve c(h) = 0 for h.
5
Let z(m) be the third derivative of 7*m**5/100 + 23*m**4/40 + 8*m**3/5 - 1025*m**2. Let z(u) = 0. Calculate u.
-16/7, -1
Let z(w) be the third derivative of w**5/100 + 141*w**4/20 + 837*w**3/10 + 4*w**2 - 214*w. Factor z(o).
3*(o + 3)*(o + 279)/5
Let w(s) = -7*s**4 + 148*s**3 - 3198*s**2 + 3037*s + 5. Let a(g) = -22*g**4 + 442*g**3 - 9594*g**2 + 9110*g + 16. Let p(y) = -5*a(y) + 16*w(y). Factor p(x).
-2*x*(x - 39)**2*(x - 1)
Suppose 104 - 8 = 24*i. Let q be ((i/(-5))/((-120)/(-500)))/(-1). Solve -q - 8/3*u + 2/3*u**2 = 0 for u.
-1, 5
Let m(a) be the third derivative of -a**7/350 + 13*a**6/20 + 201*a**5/25 + 203*a**4/5 + 544*a**3/5 + 3328*a**2. Let m(v) = 0. What is v?
-2, 136
Let n(k) = -1 + 6*k - 12*k - 20*k**3 - 14*k - 7. Let g(j) = -j**3 - j**2 - 1. Let h(c) = 16*g(c) - n(c). Let h(q) = 0. What is q?
1, 2
Let t = 711065/2 + -355532. Factor 0 + t*i**2 - 35/2*i.
i*(i - 35)/2
Find n, given that -3/2*n**3 - 30 - 21/4*n**4 + 441/4*n**2 - 147/2*n = 0.
-5, -2/7, 1, 4
Let w = -12288/7 - -13728/7. Find f such that -480/7*f - 1200/7*f**3 + w*f**2 - 54/7*f**5 - 192/7 + 60*f**4 = 0.
-2/9, 2
Let s = -297 - -328. Suppose -3*x**4 + 6*x + 224*x**3 + 6*x**4 + s*x**2 - 4*x**4 - 4*x**5 - 196*x**3 = 0. Calculate x.
-2, -1, -1/4, 0, 3
Let -138 + 972/7*z - 6/7*z**2 = 0. What is z?
1, 161
Let n(c) = -41*c + 1. Suppose -4 = 2*k - 0, -y - 10 = 4*k. Let x be n(y). Factor -x*d**2 + 166*d**2 - 85*d**2 - 6*d.
-2*d*(d + 3)
Let l(f) be the second derivative of -2*f**6/45 - 526*f**5/15 - 69169*f**4/9 - 1008*f. Find r, given that l(r) = 0.
-263, 0
Suppose 11*z - 7*z - 11 = -s, -4*z + 5*s - 7 = 0. Factor -260*p - 125*p**2 - p**3 - 72 - 92*p**2 + 48*p**z - 5*p**4 - 66*p**3 - 57*p**2.
-(p + 2)**2*(p + 9)*(5*p + 2)
Let j(v) be the first derivative of 0*v + 1/12*v**3 - 80 - 2*v**2. Suppose j(i) = 0. What is i?
0, 16
Let b(c) = -c**2 + 1. Let d(y) = -5*y**2 + 5. Suppose 4*v + 41 = 37. Let z(m) = v*d(m) + 6*b(m). Let n(i) = 2*i**2 - 2. Let a(q) = n(q) - 2*z(q). Factor a(p).
4*(p - 1)*(p + 1)
Let i(c) be the first derivative of 139 + 78/7*c - 3/7*c**3 - 111/14*c**2. Let i(h) = 0. Calculate h.
-13, 2/3
Let r = 4048 - 797452/197. Let n = r - -575/788. What is h in 1/2 - n*h**3 - 1/4*h**4 + 3/4*h - 1/4*h**2 = 0?
-2, -1, 1
Factor -2000*j - 200*j**2 + 416*j**3 - 789*j**3 + 408*j**3 - j**4.
-j*(j - 20)**2*(j + 5)
Suppose -9*c = -3*c - 1476. Let x be 0 + 4 + c/(-66). Factor 0 + 0*o - 1/11*o**5 - 3/11*o**3 - x*o**4 - 1/11*o**2.
-o**2*(o + 1)**3/11
Let u be ((-56)/35)/((-2)/5). Find k, given that -u*k**2 + 49*k**3 + k**4 + 45*k**3 - 98*k**3 + k**5 = 0.
-2, -1, 0, 2
Let i be (2/(-4))/((-1548)/344). Let s(w) be the third derivative of -1/450*w**5 + 0 + i*w**3 + 0*w - 22*w**2 - 1/45*w**4. Factor s(o).
-2*(o - 1)*(o + 5)/15
Factor -29*o**2 - 7713*o + 28*o**2 + 7768*o - 106.
-(o - 53)*(o - 2)
Let r(v) be the second derivative of v**6/40 + 19*v**5/10 + 361*v**4/8 + 78*v**2 + 210*v. Let x(t) be the first derivative of r(t). Find d, given that x(d) = 0.
-19, 0
Let d = -38639 - -38639. Determine z so that d + 5/4*z + 5/4*z**2 = 0.
-1, 0
Let d(j) be the second derivative of 12/5*j**2 - 41/15*j**3 - 7/60*j**4 + 210*j + 0. Solve d(x) = 0.
-12, 2/7
Factor -9964/13*p - 2848/13 + 14/13*p**2.
2*(p - 712)*(7*p + 2)/13
Let u(m) be the second derivative of m**7/210 - 5*m**6/18 + 28*m**5/5 - 24*m**4 + 106*m**3/3 + m - 9. Let v(b) be the second derivative of u(b). Factor v(q).
4*(q - 12)**2*(q - 1)
Let v(c) = -c**2 + 46*c - 203. Let o be v(41). Solve -4 - 40*b**o + 435*b**3 + 350*b**2 + 20*b**4 - 105*b + 4 = 0.
-21, -1, 0, 1/4
Let f(n) = -4*n**3 - 99*n**2 - 155*n - 90. Let d(i) = 3*i**3 + 102*i**2 + 156*i + 90. Let b(q) = -8*d(q) - 9*f(q). Suppose b(k) = 0. Calculate k.
-3, -2, -5/4
Solve -61/2*a - 35 + 5*a**2 + 1/2*a**3 = 0 for a.
-14, -1, 5
Let s(b) be the first derivative of -3*b**4/4 - 25*b**3 - 171*b**2 + 10281. Factor s(k).
-3*k*(k + 6)*(k + 19)
Suppose -27*z + 137 + 258 - 151 = 34*z. Factor 4/5*s - 12 - 1/5*s**z + 12/5*s**3 + 9*s**2.
-(s - 15)*(s - 1)*(s + 2)**2/5
Suppose -3*u = -5*f - 80 + 39, -2*f = -4*u + 22. Factor -5/3*r**2 - u*r**3 - 1/6*r**5 + 0 - 1/2*r - r**4.
-r*(r + 1)**3*(r + 3)/6
Factor 8254*i - 8578*i**2 + 3716*i + 8575*i**2 - 11940075.
-3*(i - 1995)**2
Let d = -342 + 337. Let y be 63/49 - d - 6. Solve -2/7*t**3 - y*t**2 + 2/7*t**4 + 0 + 2/7*t = 0 for t.
-1, 0, 1
Find v such that 352*v - 692*v + 48 + 294*v - 2*v**2 = 0.
-24, 1
Let x = -75/22148 + 243853/66444. Solve 1/3*c**3 + 26/3*c + x*c**2 + 16/3 = 0.
-8, -2, -1
Suppose 0 = -2*t + 116 + 118. Factor -t*l + 3*l**4 + 87*l**2 + 98 - 27*l**3 + 98 - 142.
3*(l - 3)**2*(l - 2)*(l - 1)
Let b = 445 - 425. Suppose b*f - 80 = -20*f. Let 2/3*r**f + 8/3*r - 10/3 = 0. What is r?
-5, 1
Suppose 0 = 13*t + 71 - 123. Solve 375*d + 376*d - 754*d + 2*d**2 + d**2 - 3*d**t + 3*d**3 = 0 for d.
-1, 0, 1
Let i(o) be the third derivative of -o**6/45 + 301*o**5/30 - 2825*o**4/2 - 12769*o**3/9 + o**2 + 13*o - 50. Factor i(v).
-2*(v - 113)**2*(4*v + 1)/3
Let l(b) be the first derivative of 22*b**2 + 64 - 12*b - 56/3*b**3 - 2/3*b**6 + 4/5*b**5 + 6*b**4. Factor l(u).
-4*(u - 1)**4*(u + 3)
Let i(r) = -2*r**3 + 26*r**2 - 6*r - 6. Let c(n) = n**3 - 23*n**2 + 5*n + 5. Let g(b) = 6*c(b) + 5*i(b). Factor g(u).
-4*u**2*(u + 2)
Let l(g) be the second derivative of -g**7/294 + 251*g**6/210 - 15367*g**5/140 - 16129*g**4/28 - 1136*g - 1. Factor l(f).
-f**2*(f - 127)**2*(f + 3)/7
Let k be 1/(-8) + (-408)/(-1728) + 133/1881. Find b, given that -4/11*b**3 - 4/11 + 2/11*b + k*b**5 - 4/11*b**4 + 8/11*b**2 = 0.
-1, 1, 2
Solve 4*a**5 + 594*a + 1233*a - 291*a - 36*a**4 + 1408*a**2 - 168*a**3 = 0.
-6, -1, 0, 8
Let p(z) be the first derivative of -z**3/9 + 141*z**2 - 59643*z - 1518. Factor p(v).
-(v - 423)**2/3
Let k(n) = -9*n**2 + 12357*n + 19121489. Let g(p) = -5*p**2 + 6178*p + 9560770. Let r(l) = -11*g(l) + 6*k(l). Determine i, given that r(i) = 0.
-3092
Let u(d) be the third deriv