
-v*(v + 1)
Let p(d) be the second derivative of d**5/10 - 245*d**4/54 - 52*d**3/3 + 116*d**2/9 + 113*d + 2. Solve p(g) = 0.
-2, 2/9, 29
Let -42/5*c**3 - 8 - 374/5*c**2 + 456/5*c = 0. Calculate c.
-10, 2/21, 1
Let o(b) be the third derivative of b**8/504 + 4*b**7/945 - 61*b**6/540 + 61*b**5/135 - 23*b**4/27 + 8*b**3/9 + 634*b**2 + 4. Suppose o(c) = 0. What is c?
-6, 2/3, 1, 2
Let d(n) be the third derivative of -n**8/2688 + 19*n**7/2520 + n**6/90 + n**4/12 - 51*n**2. Let s(p) be the second derivative of d(p). Factor s(t).
-t*(t - 8)*(5*t + 2)/2
Let g = 23527/5 - 4705. Suppose 8*y**2 - g*y**3 + 0 + 42/5*y = 0. What is y?
-1, 0, 21
Let s(w) = 13*w**4 - 90*w**3 + 156*w**2 - 7*w. Let d(k) = 45*k**3 + 2389*k - 4771*k - 78*k**2 + 2386*k - 7*k**4. Let n(y) = -7*d(y) - 4*s(y). Factor n(t).
-3*t**2*(t - 13)*(t - 2)
Suppose -3*c + 0*c = -12. Suppose s - c*w - 56 = -3*s, 3*s - 4*w - 47 = 0. Suppose -49*q + 51 + 4*q**2 + 86 + s*q - 37 = 0. Calculate q.
5
Let x(p) be the second derivative of 31*p**3/6 + p**2 - 277*p. Let k be x(0). Factor -18/7*y + 27/7 + 3/7*y**k.
3*(y - 3)**2/7
Let d(r) be the first derivative of 4*r**3/21 + 748*r**2/7 + 139876*r/7 - 686. Solve d(i) = 0.
-187
Let l(g) be the first derivative of 2*g**2 - 6*g**2 + 75*g**3 + 70 - 64*g**3 - 5*g**2. Factor l(a).
3*a*(11*a - 6)
Let i(r) = -r**2 + 8*r + 1. Let q be i(7). Let k be -5 - 136/(-32) - (-19)/4. Factor k*p**2 - 18*p + p**2 + q*p.
5*p*(p - 2)
Factor 1/7*u**2 + 100/7 - 29/7*u.
(u - 25)*(u - 4)/7
Let y(v) be the second derivative of -v**4/4 - 89*v**3 + 42*v + 27. Determine b so that y(b) = 0.
-178, 0
Let c(i) be the first derivative of 0*i - 1/15*i**5 - 2*i**2 - 1/2*i**4 - 4/3*i**3 + 5. Let p(y) be the second derivative of c(y). Find j such that p(j) = 0.
-2, -1
Let h = 2/2969 - -26717/5938. Determine m, given that -3/2*m**4 + 0 - 3/2*m - h*m**3 - 9/2*m**2 = 0.
-1, 0
Let r be (-8)/28 + (-32)/(-14). Let m be r/(-11) + (-360)/(-165). Determine w so that 3*w - 4*w**3 - 23*w + 16*w**m + 8 + 2*w**3 - 2*w**3 = 0.
1, 2
Let i(y) = y**3 + 48*y**2 + 428*y - 7056. Let s(p) = -48*p**2 - 426*p + 7056. Let w(z) = -3*i(z) - 4*s(z). Find v, given that w(v) = 0.
-12, 14
Let z be (-3225)/(-75) - (-440)/(-11). Factor -3*l**2 - 2*l + 0 - 1/2*l**z + 3/4*l**4 + 1/4*l**5.
l*(l - 2)*(l + 1)*(l + 2)**2/4
Let w(o) be the second derivative of 3*o**5/100 + 11*o**4/4 + 53*o**3/5 - 396*o - 12. What is n in w(n) = 0?
-53, -2, 0
Let q(v) be the second derivative of -7*v**6/10 - 166*v**5/5 + 89*v**4/4 + 59*v**3 + 32*v**2 + 1374*v. Let q(b) = 0. Calculate b.
-32, -1/3, -2/7, 1
Factor 189/4*a**2 + 3/4*a**3 - 45177/4 + 1665/4*a.
3*(a - 11)*(a + 37)**2/4
Let j(q) be the third derivative of -2 - 1/50*q**5 - 1/600*q**6 - 11/120*q**4 + 14*q**2 - 1/5*q**3 + 0*q. Factor j(n).
-(n + 1)*(n + 2)*(n + 3)/5
Determine u, given that 12 + 18*u**4 + 2 + 284*u + 373*u**2 + 63*u**4 - 11 + 33 - 774*u**3 = 0.
-2/9, 1, 9
Let a = -8618 + 8631. Let t(d) be the first derivative of a + 4/17*d**3 + 16/17*d - 1/34*d**4 - 12/17*d**2. Factor t(c).
-2*(c - 2)**3/17
Let n = 372007/10 - 37199. Let k(r) be the first derivative of 1/30*r**6 - n*r**2 + 0*r**4 - 6/5*r + 37 + 4/25*r**5 - 14/15*r**3. What is y in k(y) = 0?
-3, -1, 2
Let t = 2655 - 966. Factor -4*g**3 - 20*g**2 + t - 20*g**3 - 4*g**4 - 1689.
-4*g**2*(g + 1)*(g + 5)
Let r(n) = 20*n**2 + 43*n + 88. Let a(f) = 11*f**2 + 22*f + 48. Let l(z) = -11*a(z) + 6*r(z). Factor l(t).
-t*(t - 16)
Solve o**2 - 60158 + 316673 - 969*o - 13466 - 17*o = 0 for o.
493
Let q be 61/9 + (-106)/(-477). Factor -52*u**3 + 8*u**3 + u**2 - q*u**2 - 2*u**2.
-4*u**2*(11*u + 2)
Let y be -1 + -1 + (-2 - -6). Factor 2*k**2 - 323 - 3*k**y + 324.
-(k - 1)*(k + 1)
Determine w so that -60/7*w + 0 - 3/7*w**4 + 24/7*w**3 - 33/7*w**2 = 0.
-1, 0, 4, 5
Let h(i) = -i**3 - 48*i**2 + 95*i - 95. Let x be h(-50). Determine l so that -103*l**2 + 53 + 18*l**2 + x*l + 5*l**3 + 7*l**3 - 2*l**3 + 47 = 0.
-1/2, 4, 5
Suppose 5*q = -15 - 35. Let w be (-52)/q + (-5)/25. Factor w*t**2 + 2*t**4 + 10*t**3 - t**4 + 4*t**4.
5*t**2*(t + 1)**2
Determine h so that -2000/7*h - 2/7*h**2 + 286 = 0.
-1001, 1
Suppose -342 = -240*b + 112*b + 110*b. Let d(t) be the first derivative of -1/8*t**2 + 1/12*t**3 + b + 0*t. Factor d(a).
a*(a - 1)/4
Factor -4/7*d**4 + 808/7*d**3 + 0*d - 804/7*d**2 + 0.
-4*d**2*(d - 201)*(d - 1)/7
Let j(o) be the third derivative of -o**6/210 - 89*o**5/105 - 170*o**4/21 + 827*o**2 + 2. Factor j(g).
-4*g*(g + 4)*(g + 85)/7
Let i = -7236 - -7241. Let k(p) be the second derivative of 0 - 2*p**2 + 3/4*p**i + 32*p + 31/12*p**4 + 0*p**3. Suppose k(b) = 0. Calculate b.
-2, -2/5, 1/3
Let p(x) be the third derivative of -10*x**3 - 15 + 0*x + 5/3*x**4 + 37/12*x**5 - 11/14*x**7 - 15/112*x**8 - 3*x**2 - 7/24*x**6. Let p(y) = 0. What is y?
-3, -1, 2/3
Let r(k) be the first derivative of -5/4*k**4 - 375/2*k**2 - 625*k + 23 - 25*k**3. Let r(u) = 0. Calculate u.
-5
Let s(n) = -n**2 - 31*n + 43. Let h be s(-33). Let m(z) = 3*z + 72. Let y be m(h). Factor k + 0*k**2 - 2/3 - 1/3*k**y.
-(k - 1)**2*(k + 2)/3
Suppose -12*w - 2*h = -42, 3*w - 44*h + 40*h + 30 = 0. Factor 2/13*p**3 + 14/13 + 18/13*p**w + 30/13*p.
2*(p + 1)**2*(p + 7)/13
Let r = 45051 - 45049. Let -2/7*u**r - 8/7 - 10/7*u = 0. Calculate u.
-4, -1
Let q(u) be the second derivative of 0 - 103*u + 2/15*u**3 + 1/90*u**4 + 8/15*u**2. Find v, given that q(v) = 0.
-4, -2
Let k = 1185920/11 + -107810. Factor k*l + 4/11 - 14/11*l**2.
-2*(l - 1)*(7*l + 2)/11
Let u(t) be the first derivative of -t**4/4 + 12*t**3 - 335*t**2/2 + 300*t + 2059. Factor u(x).
-(x - 20)*(x - 15)*(x - 1)
Let o(g) be the first derivative of -3/5*g**5 - 44 - 15*g - 26*g**3 + 57/2*g**2 + 21/2*g**4 - 1/2*g**6. Factor o(u).
-3*(u - 1)**4*(u + 5)
Let r be (-15)/2*(-24)/15. Suppose 4*w = -2*w + r. Factor -4*k**w + 0*k**3 + k**3 + k**2.
k**2*(k - 3)
Let t(m) be the third derivative of -m**6/300 + 23*m**5/300 - 2*m**4/3 + 5*m**3/2 - 1094*m**2. What is o in t(o) = 0?
3/2, 5
Let c = -229 + 1028. Let x = -797 + c. Suppose 2/5 + 14/5*y**x + 16/5*y = 0. What is y?
-1, -1/7
Let j be (-140)/(-3)*((-61)/(-5) + -11). Suppose -32*q = -4*q - j. Factor 0 + 0*v + q*v**5 + 0*v**2 + 0*v**3 + 4/3*v**4.
2*v**4*(3*v + 2)/3
Let q(r) = 13*r**2 - 1443*r + 272344. Let x(j) = -j**2 - 3*j - 2. Let b(y) = q(y) + 11*x(y). Determine n so that b(n) = 0.
369
Let i(t) be the second derivative of t**5/5 - 8*t**4/3 - 128*t**3/3 + 1024*t**2 - 1245*t. What is o in i(o) = 0?
-8, 8
Let y(v) be the second derivative of -v**6/180 + v**5/120 + 5*v**4/36 - v**3/9 - 2*v**2 + 994*v. Factor y(i).
-(i - 3)*(i - 2)*(i + 2)**2/6
Factor 2/9*y**3 + 5044/9*y + 562/3*y**2 + 1120/3.
2*(y + 1)*(y + 2)*(y + 840)/9
Let f(w) = -10*w**4 + 22*w**3 + 50*w**2 - 202*w - 555. Let r(t) = -7*t**4 + 15*t**3 + 33*t**2 - 135*t - 375. Let a(i) = 5*f(i) - 7*r(i). Factor a(q).
-(q - 5)**2*(q + 2)*(q + 3)
Let f be 1*290/(-232)*(-8)/5. Let q be f/(-6) + (-371)/(-42) - 6. Suppose 7/6*s**2 - 3 - 1/6*s**4 - q*s + 1/2*s**3 = 0. Calculate s.
-2, -1, 3
Let -16/5*y + 1/5*y**2 - 36/5 = 0. What is y?
-2, 18
Factor 18/7*i**2 - 48/7*i - 2/7*i**3 + 40/7.
-2*(i - 5)*(i - 2)**2/7
Let w be (78 - -1 - 2)*(8 + -7). Suppose 22*q = -33 + w. Factor -8/11 - 2/11*f**q - 8/11*f.
-2*(f + 2)**2/11
Let t be (-12 + 290/20)*(-4)/(-5). Let k(g) be the second derivative of 15*g - 1/2*g**t + 0 - 1/12*g**4 + 1/3*g**3. Factor k(b).
-(b - 1)**2
Let r = 7177/420 - 256/15. Let a(n) be the second derivative of r*n**5 - 1/28*n**4 + 7*n + 0*n**3 + 1/70*n**6 + 0 + 0*n**2 - 1/98*n**7. Factor a(c).
-3*c**2*(c - 1)**2*(c + 1)/7
Suppose 0 = -4*r - 2*f + 726, 3*r + 94 = f + 631. Let c = -538/3 + r. Let -c*w**2 + 0 + 2/3*w = 0. What is w?
0, 1
Let a(c) = -4 - 588*c - 907*c - 556*c. Let m be a(-1). Factor -m + n**2 - n**4 + 2047.
-n**2*(n - 1)*(n + 1)
Let h(i) be the first derivative of 77*i**6/3 - 4692*i**5/5 + 18409*i**4/2 - 5480*i**3 + 900*i**2 - 630. Find y, given that h(y) = 0.
0, 2/11, 2/7, 15
Let f(h) = -h**3 + 83*h**2 - 669*h + 222. Let d be f(74). Find s, given that d + 3/2*s**2 - 117/2*s = 0.
0, 39
Let v(y) be the second derivative of 43/15*y**5 - 7/45*y**6 + 0*y**2 - 26*y + 0 + 8*y**3 - 46/3*y**4. Factor v(q).
-2*q*(q - 6)**2*(7*q - 2)/3
Let w(d) be the third derivative of d**6/2880 + d**5/240 - d**4/16 - d**3/3 + 31*d**2 + 2. Let z(n) be the