*(r - 1)/5
Let n be 2/((-18)/4 - -5). Suppose 3*b + 2 - n + 808*b**3 - 809*b**3 = 0. Calculate b.
-2, 1
Let g(f) be the first derivative of 2*f**5/55 + 7*f**4/11 + 32*f**3/11 - 1529. Factor g(d).
2*d**2*(d + 6)*(d + 8)/11
Factor 1/3*n**2 + 67500 - 300*n.
(n - 450)**2/3
Let g be -6 - (392/(-60) + (24/16)/3). Let c(n) be the second derivative of -36/5*n**2 + 0 - 11*n + 4/5*n**3 - g*n**4. Factor c(d).
-2*(d - 6)**2/5
Suppose -8*l - 23 - 17 = 0. Let j(z) = z**4 - 7*z**3 - 9*z**2 + 9*z - 6. Let y(u) = -u**4 + 6*u**3 + 9*u**2 - 9*u + 5. Let d(t) = l*j(t) - 6*y(t). Factor d(k).
k*(k - 3)*(k - 1)*(k + 3)
Factor -424*d - 13247 + 26407 - 13580 - 4*d**2.
-4*(d + 1)*(d + 105)
Let u(s) be the second derivative of 2*s**6/105 - 83*s**5/140 - 2*s**4/7 + 3*s**3/2 - s + 703. Factor u(k).
k*(k - 21)*(k + 1)*(4*k - 3)/7
Let r be (-1 + 3)/(((-18)/(-14))/(24/28)). Determine q so that 1/3*q**2 + r*q + 4/3 = 0.
-2
Let c be ((-16)/(-18))/((-12)/(-9)). Let i(f) be the first derivative of 24 - 4*f - c*f**3 - 3*f**2. Let i(q) = 0. What is q?
-2, -1
Suppose 4*m - 36 = -4654*b + 4657*b, 2*m - 18 = 0. Let c(z) be the first derivative of -7/9*z**2 + b*z + 2/27*z**3 + 49. Factor c(h).
2*h*(h - 7)/9
Let t(u) be the first derivative of 2/3*u**6 + 5*u**4 - 99 + 16/5*u**5 + 8/3*u**3 + 0*u + 0*u**2. What is i in t(i) = 0?
-2, -1, 0
Let v(k) be the second derivative of -k**5/210 + k**4/3 - 28*k**3/3 - 27*k**2/2 - 2*k - 81. Let y(u) be the first derivative of v(u). Factor y(o).
-2*(o - 14)**2/7
Let o(u) be the second derivative of u**4/6 - u**3/3 - 42*u**2 - 123*u. Let l be o(7). Factor 2/7*h**4 + l - 2/7*h**3 + 2/7*h**5 + 0*h - 2/7*h**2.
2*h**2*(h - 1)*(h + 1)**2/7
Let d(m) be the third derivative of 2*m**7/105 - 13*m**6/30 - 14*m**5/15 - 874*m**2. Solve d(g) = 0 for g.
-1, 0, 14
Suppose -196*d**3 - 46*d**4 - 457*d**5 - 144*d - 296*d**2 + 419*d**5 + 36*d**5 = 0. Calculate d.
-18, -2, -1, 0
Let j = -483 + 488. Let d(o) be the third derivative of -1/80*o**6 - 15*o**2 + 0*o**3 - 1/32*o**4 + 0*o + 3/80*o**j + 0. Determine n, given that d(n) = 0.
0, 1/2, 1
Factor -2/3*b**3 - 208*b + 896/3 + 45/2*b**2.
-(b - 16)**2*(4*b - 7)/6
Let o be (-28)/(-35) + (-226)/12*(-22)/55. Factor -10*h + o*h**2 - 5/3*h**3 + 0.
-5*h*(h - 3)*(h - 2)/3
Suppose -2*p - 20 = -2*l, 4*p + 2*l + 20 = 4. Let k be (-6 + 13 + -7)/p. Let k - 2*h**4 - 2/3*h**5 - 2/3*h**3 + 2*h**2 + 4/3*h = 0. Calculate h.
-2, -1, 0, 1
Suppose 0 = -3*l - 3*k + 14 + 4, -k + 12 = 3*l. Factor 27*p + l*p**2 - 333 + 375 + 0*p.
3*(p + 2)*(p + 7)
Let x(s) be the first derivative of 3*s**4/2 - 3*s**3 - 21*s**2 - 788. What is r in x(r) = 0?
-2, 0, 7/2
Let m be (-14)/3*24/(-504). Let g be 0 + -4 + (-266)/(-63). Find u such that 2/9 - g*u - m*u**2 + 2/9*u**3 = 0.
-1, 1
Let d(p) be the third derivative of p**8/504 - 41*p**7/315 - p**6/90 + 41*p**5/45 + p**4/36 - 41*p**3/9 + 84*p**2 + 11*p. Determine j so that d(j) = 0.
-1, 1, 41
Let c be ((-4)/(-8))/((-9)/10 - -1). Factor -8*r**2 + r**2 + r + c*r**2 - r**3 + 2.
-(r - 1)*(r + 1)*(r + 2)
Let i be -16 + (5 - -2) - (-26 + 13). Find h such that 16/13*h - 4/13*h**3 + 24/13 - 14/13*h**2 + 2/13*h**i = 0.
-2, -1, 2, 3
Find y such that 190*y + 47/2*y**4 - 71/2*y**3 - 69*y**2 - 3*y**5 - 100 = 0.
-2, 5/6, 2, 5
Suppose 0 = -13*o + 147 + 178. Factor -92*z - 49*z**2 + 5*z**5 + o*z**2 - 36*z**2 - 55*z**3 + 10*z**4 + 272*z.
5*z*(z - 2)**2*(z + 3)**2
Let d(k) be the first derivative of 0*k - 100 + 2/5*k**3 + 0*k**2 - 1/30*k**4. Factor d(r).
-2*r**2*(r - 9)/15
Let d(z) be the first derivative of z**6/72 - 7*z**5/8 + 25*z**4/6 + z**3 + 8*z + 106. Let l(w) be the third derivative of d(w). Suppose l(o) = 0. Calculate o.
1, 20
Let f(q) be the third derivative of 0 + 1/360*q**5 - q**2 - 2/3*q**3 - 81*q + 23/144*q**4. Determine k, given that f(k) = 0.
-24, 1
Let k = -6810 + 6812. Let z(h) be the first derivative of 5*h**k - 2*h**3 - 16 - 5/2*h**4 - 2/5*h**5 + 8*h. Factor z(o).
-2*(o - 1)*(o + 1)**2*(o + 4)
Let l(r) = -r**4 + 4*r**3 + 2*r. Let k(b) = 12*b**4 - 920*b**3 - 60480*b**2 - 1368608*b + 2985984. Let f(j) = -k(j) - 16*l(j). What is d in f(d) = 0?
-72, 2
Let n be (-6)/(-207) - 6500/(-85215). Solve -6/19*v**4 + 0*v + 14/19*v**2 - 8/19 - 2/19*v**5 + n*v**3 = 0 for v.
-2, -1, 1
Let z(r) be the first derivative of -r**6/4 - 123*r**5/5 - 5511*r**4/8 - 3198*r**3 - 4563*r**2 - 6241. Factor z(d).
-3*d*(d + 2)**2*(d + 39)**2/2
Let u = -493883 - -493886. Factor 3/4*d**u - 135/4*d - 63/4*d**2 - 69/4.
3*(d - 23)*(d + 1)**2/4
Let c(w) be the second derivative of w**4/30 - 151*w**3/15 - 306*w**2/5 + 1359*w. Factor c(h).
2*(h - 153)*(h + 2)/5
Factor -34*k**3 - 175*k**4 - 190*k**4 + 142*k**3 + 363*k**4.
-2*k**3*(k - 54)
What is g in 105 + 85*g**2 - 6968*g + 14036*g - 6778*g = 0?
-3, -7/17
Suppose 0 = 27*j - 12*j + 9735. Let p = 653 + j. Let -12/5*u + 1/5*u**3 - 1/5*u**p + 0 + 8/5*u**2 = 0. Calculate u.
-3, 0, 2
Let m(f) be the third derivative of 6*f**7/35 + 149*f**6/2 - 1493*f**5/15 + 83*f**4/2 - f**2 - 5*f - 152. Factor m(t).
4*t*(t + 249)*(3*t - 1)**2
Let o(z) be the third derivative of z**6/600 + 29*z**5/300 - 7*z**4/12 - 124*z**3/15 - 2*z**2 + 1411*z. Factor o(a).
(a - 4)*(a + 2)*(a + 31)/5
Let p = 43517 + -43517. Let t be (1/5*2)/(221/85). Factor -8/13*o**2 + p - 8/13*o - t*o**3.
-2*o*(o + 2)**2/13
Let f = 686462/11 - 62402. Solve -f*s + 46/11*s**2 - 8/11 - 12/11*s**3 = 0 for s.
-1/6, 2
Let f(h) be the second derivative of -h**4/27 - 176*h**3/27 - 1280*h**2/9 + 1265*h + 2. Factor f(x).
-4*(x + 8)*(x + 80)/9
Let n be (27/(-420))/(180/(-150))*14/72. Let t(x) be the second derivative of -23*x + n*x**4 + 1/160*x**5 + 0*x**3 + 0*x**2 + 0. Factor t(o).
o**2*(o + 1)/8
Let c(z) be the second derivative of -z**6/90 - z**5/3 - 7*z**4/4 + 10*z**3/9 + 32*z**2/3 + 31*z - 23. Solve c(u) = 0.
-16, -4, -1, 1
Let b(x) = x**5 - x**4 - 2*x**2 + 1. Let j(p) = 20*p**5 - 20*p**4 - 7*p**3 - 37*p**2 + 6*p + 19. Let m(w) = -38*b(w) + 2*j(w). Find s, given that m(s) = 0.
-2, -1, 0, 1, 3
Let q = -63 + 56. Let y be -1 + 21/q - 51/(-12). Factor -y*d - 1/2*d**2 + 1/2 + 1/4*d**3.
(d - 2)*(d - 1)*(d + 1)/4
Let x(s) be the first derivative of 396*s**5/5 - 113*s**4 + 8*s**3 + 16*s**2 + 1283. Solve x(p) = 0.
-2/9, 0, 4/11, 1
Let z(k) be the second derivative of k**4 + 4/25*k**5 + 32/15*k**3 - 63*k - 1 + 11/5*k**2 - 1/75*k**6. Factor z(d).
-2*(d - 11)*(d + 1)**3/5
Let i(q) = -17*q + 315. Let w be i(14). Let z be 12 - 7*110/w. Factor 0*t + 12/7 - 3/7*t**z.
-3*(t - 2)*(t + 2)/7
Suppose l = -3*l - 12 + 20, -3*k + 1 = -4*l. Let 24/5*j**4 + 96/5*j**2 - 48/5*j + 0 - 3/5*j**5 - 72/5*j**k = 0. Calculate j.
0, 2
Let u be 2*-2*(23 + 14 + 3542/(-66)). Factor 20/3*d**2 - 2/9*d**3 + 2000/9 - u*d.
-2*(d - 10)**3/9
Let z(b) be the third derivative of -b**2 + 0*b**3 + 0*b - 9/160*b**6 + 12 + 27/80*b**5 + 1/280*b**7 - 27/32*b**4. Factor z(a).
3*a*(a - 3)**3/4
Suppose -6172 - 30116 = -168*o. Suppose -9/5 - 511/5*v**2 - o*v**4 - 80*v**5 - 111/5*v - 1089/5*v**3 = 0. What is v?
-1, -3/5, -1/4
Let t(l) = l**2 + 11*l - 771. Let o be t(-34). Let n(k) be the first derivative of 0*k + 1/14*k**2 - 1/21*k**3 + o. Factor n(m).
-m*(m - 1)/7
Suppose -59/11*g - 45/11 - 15/11*g**2 - 1/11*g**3 = 0. Calculate g.
-9, -5, -1
Let i(u) be the first derivative of u**6/30 + 29*u**5/25 + 113*u**4/20 - 1649*u**3/15 - 867*u**2/5 + 129. Let i(q) = 0. Calculate q.
-17, -1, 0, 6
Let n(k) be the third derivative of -k**5/30 - 121*k**4/12 - 238*k**3/3 - 1463*k**2. Let n(t) = 0. What is t?
-119, -2
Let m = -367 - -402. Let w be 16/(-72)*(-45)/m. What is q in -w*q**2 - 30/7*q**3 - 2*q**5 - 38/7*q**4 + 0 + 4/7*q = 0?
-1, 0, 2/7
Let b be 1*((-1)/3 - (-50)/15). Suppose b*j - 18 = 105. Suppose -44*n**2 - 10 - n - 54*n - j*n**2 - 30*n**3 = 0. What is n?
-2, -1/2, -1/3
Let l(a) be the third derivative of -a**7/315 + a**6/36 - a**5/15 - 160*a**2 + 14. Factor l(h).
-2*h**2*(h - 3)*(h - 2)/3
Let u(v) = -v**2 - 29*v + 30. Let t(n) = -2*n**2 - 88*n + 90. Suppose -2*r = -8*r + 2*r. Suppose r = -5*o + 6*o - 17. Let f(a) = o*u(a) - 6*t(a). Factor f(b).
-5*(b - 6)*(b - 1)
Let v(d) be the third derivative of -144/5*d**6 + 81/14*d**7 - 18*d**3 - 277/20*d**5 + 17*d**2 + 7*d + 0 + 69/2*d**4. Find f, given that v(f) = 0.
-3/5, 2/9, 3
Let q(x) be the first derivative of x**5/20 + 53*x**4/12 + 364*x**3/3 + 338*x**2 - 82*x - 6. Let 