k).
3*(k - 1)**3*(k + 12)/8
Suppose -5*h + 19 = -6. Let s = 7591/873 - 2401/291. Factor 1372/9 + 280/9*q**2 - s*q**h + 76/9*q**4 - 424/9*q**3 + 2156/9*q.
-4*(q - 7)**3*(q + 1)**2/9
Let b(a) be the first derivative of a**7/1260 - 2*a**6/45 - 13*a**5/45 - 269*a**3/3 - 277. Let k(m) be the third derivative of b(m). Factor k(t).
2*t*(t - 26)*(t + 2)/3
Suppose 0*c - 48 = -5*c + 3*d, 0 = 5*c + 2*d - 68. Determine p so that c*p - 8*p**3 + 4*p**3 - 48 + 0*p**3 + 56 = 0.
-1, 2
Suppose -5*l = 0, -3*v - 4*l - 40 = -46. Suppose -o + 17 = 5*y, v = 5*o - 4*y + 4. Factor 0 - 1/5*d**o + d.
-d*(d - 5)/5
Let h = 15839/6 - 2639. Let o(p) be the first derivative of -50/3*p**3 - h*p**6 - 5*p**5 - 16 - 25/2*p**2 - 5*p - 25/2*p**4. Solve o(n) = 0 for n.
-1
Let n = 283/56 - 269/56. Let i(j) be the second derivative of -j**3 + n*j**4 + 0 + 0*j**2 + 16*j. Factor i(p).
3*p*(p - 2)
Let h(g) be the third derivative of g**8/336 - g**7/35 - 13*g**6/30 + 2*g**5 - 229*g**2 + 2. Factor h(p).
p**2*(p - 10)*(p - 2)*(p + 6)
Let y(j) = -j**3 - 11*j**2 - 8*j + 22. Let i be 1/2 + 63/(-6). Let w be y(i). Factor 8*b**4 - 6*b**3 - 4*b**w + 8*b**2 - 6*b**4.
2*b**2*(b - 2)*(b - 1)
Find m such that -356/3*m + 0 + 182/3*m**2 - 2/3*m**4 + 176/3*m**3 = 0.
-2, 0, 1, 89
Let x = 32 + -30. Suppose -x*j + 4 = -2*r, 0*j - 32 = -4*r - 4*j. Solve 3*b - 95*b**2 + 96*b**2 - 7 + r = 0 for b.
-4, 1
Let v = 1520450/7 + -217207. Factor 6*u - 63 - v*u**2.
-(u - 21)**2/7
Let k(a) be the third derivative of 3/200*a**6 + 0*a - 3/40*a**4 - 1/100*a**5 - 1 + 1/350*a**7 + 0*a**3 + 16*a**2. Let k(o) = 0. Calculate o.
-3, -1, 0, 1
Let h(t) be the second derivative of -t**6/225 - 19*t**5/150 - 119*t**4/90 - 49*t**3/9 - 1142*t. Find j such that h(j) = 0.
-7, -5, 0
What is f in -68 - 39*f**2 + 83*f**3 - 2*f + 138*f - 80*f**3 - 37 + 5*f = 0?
1, 5, 7
Let j be (-12)/(-42) - 2057/(-5467). Let t = j + 1/213. Determine z so that 0 + 0*z**2 + t*z**5 + 2/3*z**4 + 0*z - 4/3*z**3 = 0.
-2, 0, 1
Factor -1080/13*h + 2/13*h**3 + 24/13*h**2 + 6400/13.
2*(h - 10)**2*(h + 32)/13
Suppose 10 = -5*v, 5*v = -0*b + b - 10. Let s(n) be the third derivative of b - 1/1140*n**6 + 0*n**3 - 13*n**2 + 2/285*n**5 + 0*n - 1/57*n**4. Factor s(r).
-2*r*(r - 2)**2/19
Suppose 13*k + 12*k + 100 = 0. Let a be -3 - 3/5*30/k. Let 0 - a*p - 3/2*p**2 = 0. What is p?
-1, 0
Factor 126*g**2 + 653789*g**3 - 653735*g**3 - 373*g - 49*g + 2*g**4 + 240.
2*(g - 1)**2*(g + 5)*(g + 24)
Let t = 184 + -181. Suppose 12*d + 120*d**3 + 3*d**5 + 0*d**4 + 28*d**2 + 0*d**5 - 145*d**t - 2*d**4 = 0. What is d?
-3, -1/3, 0, 2
Let r(t) = 3*t**3 - 18*t**2 - 21*t - 18. Let n(g) = -7*g**3 + 36*g**2 + 40*g + 36. Let m(x) = -6*n(x) - 13*r(x). Let m(l) = 0. Calculate l.
-3, -2, -1
Let l(z) be the first derivative of z**8/84 - 2*z**7/35 - 3*z**6/10 - z**5/3 - 2*z**2 + 72. Let a(j) be the second derivative of l(j). Solve a(g) = 0 for g.
-1, 0, 5
Let r(o) be the third derivative of o**8/4032 + o**7/336 - 7*o**6/36 + 47*o**5/10 + 23*o**2 + 7. Let a(d) be the third derivative of r(d). Factor a(x).
5*(x - 4)*(x + 7)
Suppose -y + 4*l + 19 = 0, -5*l + 6511 - 6525 = 2*y. Factor -5/8*r**y - 9/8 + 5/8*r + 9/8*r**2.
-(r - 1)*(r + 1)*(5*r - 9)/8
Suppose -215*x - 19*x = -6786. Factor x*m**2 - 15*m**3 + 36/5 - 24*m - 1/5*m**5 + 3*m**4.
-(m - 6)**2*(m - 1)**3/5
Let g(t) be the second derivative of t**7/840 - t**5/120 + 29*t**3/3 - 2*t - 18. Let q(l) be the second derivative of g(l). Factor q(w).
w*(w - 1)*(w + 1)
Let z be -14*(((-703)/114 - -7) + -1) + 0 + 0. Solve z*x**2 - 26/3*x - 8/3 = 0 for x.
-2/7, 4
Suppose -5106 = -5*d - 32*d. Let s = -678/5 + d. Suppose s + 2*o - 2*o**2 - 2/5*o**4 - 2*o**3 = 0. Calculate o.
-3, -2, -1, 1
Let a(w) be the first derivative of -1/18*w**6 + 2/9*w**3 + 45 + 0*w**5 - 1/2*w**2 + 1/3*w**4 - 2/3*w. Find t such that a(t) = 0.
-1, 1, 2
Factor 14/3*s - 8 - 2/3*s**2.
-2*(s - 4)*(s - 3)/3
Let k(a) be the first derivative of -68*a**3/5 + 57*a**2/10 + 27*a/5 - 1313. Factor k(q).
-3*(4*q + 1)*(17*q - 9)/5
Solve -3077*m**2 + 1473*m**2 + 6656 + 1608*m**2 + 713*m - 4049*m = 0.
2, 832
Suppose w + 4 - 5 = -3*b, b - 7 = w. Let u(n) = -n**3 - 5*n**2 + 3*n - 12. Let z(p) = p**2 + 2. Let a(q) = w*z(q) - u(q). Let a(j) = 0. What is j?
-2, 1
Let m(t) be the second derivative of t**5/4 - 15*t**4/4 + 65*t**3/3 - 60*t**2 + 4599*t. Factor m(w).
5*(w - 4)*(w - 3)*(w - 2)
Let a(c) be the first derivative of 88/3*c**3 + 16*c**2 + 21*c**4 + 0*c - 32 + 2/3*c**6 + 32/5*c**5. Factor a(o).
4*o*(o + 1)**2*(o + 2)*(o + 4)
Let b(f) = 5*f + 51. Let n be b(-7). Solve -198*o**3 + n*o - 27*o**4 - 2 - 36*o**2 + 94*o**3 + 16*o**5 + 2 - 9*o**4 = 0 for o.
-1, 0, 1/4, 4
Let o(h) be the first derivative of 2*h**6/3 + 48*h**5/5 - 29*h**4 - 16*h**3 + 56*h**2 - 7998. Solve o(b) = 0 for b.
-14, -1, 0, 1, 2
Let g(l) be the third derivative of -l**8/3360 - l**7/105 - 23*l**6/400 - 41*l**5/300 - 2*l**4/15 - 1413*l**2 - 2*l - 1. Suppose g(d) = 0. Calculate d.
-16, -2, -1, 0
Let w be (-4)/7 + (-2686)/(-119). Solve 41*q**2 - w*q**3 - 80*q**2 + 49*q**2 - 2*q**5 + 14*q**4 = 0.
0, 1, 5
Let u(a) = -a - 6. Let f be u(-3). Let g(m) = 237*m**2 - 6084*m + 52737. Let p(x) = -x**3 + 236*x**2 - 6084*x + 52734. Let s(c) = f*p(c) + 2*g(c). Factor s(y).
3*(y - 26)**3
Let x(v) be the third derivative of v**7/1365 + v**6/65 + 16*v**5/195 + 6386*v**2. Factor x(p).
2*p**2*(p + 4)*(p + 8)/13
Let r be (-105)/(-175)*20/3. Factor -4*j**2 + 148*j + r*j**3 + 16 - 180*j + 32.
4*(j - 2)**2*(j + 3)
Let x = 20964 + -20964. Let u(c) be the third derivative of x*c - 1/600*c**6 + 1/60*c**5 + 0 + 1/120*c**4 - 1/6*c**3 + 9*c**2. Factor u(w).
-(w - 5)*(w - 1)*(w + 1)/5
Let a(m) be the third derivative of m**5/80 + 100*m**4 + 320000*m**3 + 103*m**2 - m - 19. Let a(w) = 0. Calculate w.
-1600
Factor -18602*g + 189 - 45*g**2 + 37428*g + 3*g**3 - 18685*g.
3*(g - 9)*(g - 7)*(g + 1)
Factor -71*d - 36*d - 2129*d**2 - 23*d - 570*d + 2133*d**2 + 696.
4*(d - 174)*(d - 1)
Let q = -1985549/150 + 13237. Let n(y) be the third derivative of -39*y**2 - 1/75*y**5 + 0 + 0*y**4 + 0*y - q*y**6 + 0*y**3. Factor n(c).
-4*c**2*(c + 1)/5
Let r(k) be the first derivative of k**5/50 - 3*k**4/40 - 3*k**3/5 - k**2/5 + 12*k/5 - 1958. Suppose r(q) = 0. What is q?
-2, 1, 6
Solve -55*g**2 + 26*g + 45*g**3 + 9*g + 18375 - 46*g**3 - 101*g - 109*g = 0 for g.
-35, 15
Let k(a) be the third derivative of -1/42*a**7 + 7*a**2 + 0 + 1/3*a**6 + 0*a**4 + 0*a**3 - 4/3*a**5 + 0*a. Suppose k(m) = 0. What is m?
0, 4
Factor 358*b**3 + 152853*b**2 + 1385*b - 154453*b**2 - 93*b**3 - 50.
5*(b - 5)*(b - 1)*(53*b - 2)
Let 50/3 - 2*a**3 + 122/9*a**2 - 254/9*a = 0. Calculate a.
1, 25/9, 3
Let j = 132 + 3195. Factor 3331*i**2 - j*i**2 + 60 - 25*i - 7*i.
4*(i - 5)*(i - 3)
Suppose g - 38 = 5*k, -3*k - 53 = 3*g - 23. Let l be 2/k + -119*(-6)/840. Let -9/5*z**2 + l*z**3 + 0 + 6/5*z = 0. Calculate z.
0, 1, 2
Let 12*m**4 + 106*m**3 + 22*m**4 + 35*m**4 + 8*m**3 - 70*m**4 - 225*m**2 + 112*m = 0. Calculate m.
0, 1, 112
Let v(t) be the first derivative of 7/5*t**2 - 1/15*t**3 + 0*t - 34. Suppose v(h) = 0. Calculate h.
0, 14
Let d(w) be the second derivative of w**5/80 + w**4/12 - 19*w**3/24 + 7*w**2/4 + 1266*w. Factor d(i).
(i - 2)*(i - 1)*(i + 7)/4
Let u = -535 + 539. Solve -3235*w + 3235*w + u*w**4 + 7*w**3 - 40*w**2 + 29*w**3 = 0 for w.
-10, 0, 1
Let b(f) be the first derivative of -95 + 0*f - 10*f**3 + 27/2*f**2 + 3/4*f**4. Factor b(o).
3*o*(o - 9)*(o - 1)
Let c be (-7)/1*1135/(-2270). Let b(k) be the third derivative of -2*k**2 + 7/40*k**5 + 0 + 47/16*k**4 - c*k**3 + 2*k. Let b(q) = 0. Calculate q.
-7, 2/7
Let d be 6/(-15) + 88/(-4760)*317. Let b = -70/17 - d. Determine z so that 12/7 + b*z**2 - 24/7*z - 3/7*z**3 = 0.
1, 2
Let s(b) be the third derivative of -b**6/360 + b**5/40 + b**4/6 - 89*b**3/2 - 50*b**2. Let n(r) be the first derivative of s(r). What is u in n(u) = 0?
-1, 4
Let z(b) be the second derivative of 2*b**6/75 + 3*b**5/5 + 71*b**4/15 + 86*b**3/5 + 144*b**2/5 - 4036*b. Solve z(r) = 0 for r.
-8, -3, -1
Let c(r) = -19*r**3 + 3988*r**2 + 416*r + 844. Let j be c(210). Factor -8/5*n**3 + 24/5*n**2 + 16/5 - 32/5*n + 1/5*n**j.
(n - 2)**4/5
Let s(z) be the third derivative of z**6/280 - 39*z**5/70 - 241*z**4/56 - 81*z**3/7 + 804*z**2. Factor s(x).
3*(x - 81)*(x + 1)*(x + 2)/7
Let z(i) be the third derivativ