 0
Let w(j) be the third derivative of j**6/480 + 91*j**5/120 + 361*j**4/96 + 15*j**3/2 + j**2 + 172*j. Factor w(x).
(x + 1)**2*(x + 180)/4
Factor -2*d**2 + 34*d + 0 - 17/2*d**3 + 1/2*d**4.
d*(d - 17)*(d - 2)*(d + 2)/2
Let j be (7 + 93/(-9))*12/10. Let a be 3*(j + 7 + -2). Let -2*u**4 - u**4 - 254*u - 39*u**2 - 108 + 434*u - 30*u**a = 0. Calculate u.
-6, 1
Suppose -74*t - 3619 - 10811 = 0. Let k be (-611)/t + (-2)/15. Determine f, given that 26/5*f - 44/5*f**k + 24/5*f**2 + 4/5 - 6*f**5 - 76/5*f**4 = 0.
-1, -1/5, 2/3
Let k(g) = g**3 + 40*g**2 - 90*g - 27. Let l be k(-42). Let m be ((-3)/(-2))/(-12 - l/(-18)). Factor -6/5*a**2 - 12/5 + 21/5*a - 3/5*a**m.
-3*(a - 1)**2*(a + 4)/5
Let y be (5 - 17/3)/((16 - 17)/(-3 + 11)). Factor y*x + 1/3*x**2 + 64/3.
(x + 8)**2/3
Let d(s) be the first derivative of s**7/280 - s**6/24 - s**5/5 + 3*s**4/2 + 26*s**3/3 - s**2/2 + 184. Let b(y) be the third derivative of d(y). Factor b(r).
3*(r - 6)*(r - 1)*(r + 2)
Let d(n) be the first derivative of -n**4/26 + 1406*n**3/39 - 123200*n**2/13 - 247808*n/13 + 6209. Determine v so that d(v) = 0.
-1, 352
Determine x, given that 13*x**2 + 155*x**2 + 48*x**2 - 9*x**4 - 43*x**3 - 21*x**4 - 60*x - 146*x**3 + 63*x**5 = 0.
-2, 0, 10/21, 1
Let m(h) be the first derivative of 6*h**6 + 96*h**5/5 + 73*h**4/4 + h**3 - 9*h**2/2 + h + 694. Factor m(x).
(x + 1)**3*(6*x - 1)**2
Let p(s) be the first derivative of -s**5 - 175*s**4/2 + 240*s**3 + 243. Factor p(w).
-5*w**2*(w - 2)*(w + 72)
Let d = 45 - 51. Let x = d - -28. Factor -17*a + 9*a**3 + 3*a**5 - 12*a**4 + 12*a**2 + x*a - 17*a.
3*a*(a - 2)**2*(a - 1)*(a + 1)
Let x(n) be the second derivative of -n**6/75 - 6*n**5/25 - 9*n**4/10 + 4*n**3/15 + 36*n**2/5 - 2*n + 23. Determine b so that x(b) = 0.
-9, -2, 1
Suppose 4*q - 60 = -16*q. Find t such that -85*t + 94*t - 10*t**3 - 33*t**2 - 2*t**q = 0.
-3, 0, 1/4
Let w = 179 + -523/3. Suppose 0 = 3*l + 9*o + 99, 4*l + 2*o - 41624 = -41636. Factor -4/3 - 2/3*g**5 + 4/3*g**4 + 4/3*g**l + w*g - 16/3*g**2.
-2*(g - 1)**4*(g + 2)/3
Let q(j) = 2263 - 3*j - 2262 + 5*j + 2*j**2. Let r(m) = 3*m**2 - 513*m - 148. Let b(p) = 6*q(p) + 3*r(p). Let b(h) = 0. What is h?
-2/7, 73
Let v(a) be the first derivative of -2*a**5/5 + 8*a**4 + 36*a**3 + 56*a**2 + 38*a + 363. Factor v(u).
-2*(u - 19)*(u + 1)**3
Let q be (-6)/(-1) - 3/3. Factor -2*s**4 + q*s**3 + 144 - 27*s**3 + 120*s - 186*s**2 + 142*s**2.
-2*(s - 2)*(s + 1)*(s + 6)**2
Let x be (-4)/(-14)*19/(-285)*-70. Factor -1/6*k**3 + x - 2*k + k**2.
-(k - 2)**3/6
Let q(v) be the third derivative of v**8/2184 + v**7/455 - 11*v**6/780 - 9*v**5/130 + 5*v**4/78 + 8*v**3/13 - 7*v**2 - 2*v + 95. Find l such that q(l) = 0.
-4, -2, -1, 1, 3
Let i(z) be the first derivative of z**6/6 - z**5/2 - 35*z**4/12 - 10*z**3/3 - 80*z + 97. Let y(u) be the first derivative of i(u). Factor y(o).
5*o*(o - 4)*(o + 1)**2
Suppose -10*b - 46 = -3*b - 6*b + 8*u, 0 = 3*b + 5*u + 24. Let s = -12 + 99/7. Let 9/7*z**b + s*z**3 + 3/7*z**4 - 15/7*z - 12/7 = 0. Calculate z.
-4, -1, 1
Let g(x) = -23*x + 3. Let s be g(0). Determine c, given that 3*c**2 + 6*c**2 - c**3 + 22*c + 7*c**s - 7*c**3 = 0.
-2, 0, 11
Find f, given that -50*f**2 + 6*f**3 + 484/3 - 2/9*f**4 + 946/9*f = 0.
-1, 6, 11
Let u be 10/2 - 423/(-47). Determine z so that -u*z**2 - 18 + 14*z**2 - 3*z + 3*z**2 = 0.
-2, 3
Let b(k) = 532*k**2 - 205*k + 13. Suppose 94*g + 32 = 93*g. Let v(l) = -5852*l**2 + 2256*l - 144. Let r(h) = g*b(h) - 3*v(h). Factor r(z).
4*(7*z - 2)*(19*z - 2)
Let v be -1*(13 + -2)*(-3 + (-899)/(-319)). Solve 18/5 - 3/5*c**v + 3*c = 0.
-1, 6
Let c(k) be the first derivative of 2*k**5/15 + 2*k**4 + 92*k**3/9 + 20*k**2 + 50*k/3 - 433. Factor c(n).
2*(n + 1)**2*(n + 5)**2/3
Let x(q) be the third derivative of -q**7/630 - q**6/180 + 13*q**5/180 - 5*q**4/36 + 3*q**2 - 273*q - 3. Determine n so that x(n) = 0.
-5, 0, 1, 2
Suppose 4*x**3 + 0 - 1/2*x**4 + 0*x - 7/2*x**2 = 0. What is x?
0, 1, 7
Let z(d) be the third derivative of d**7/3780 + 7*d**6/360 + 19*d**5/90 + 61*d**4/12 - 10*d**2 + 2. Let m(x) be the second derivative of z(x). Factor m(v).
2*(v + 2)*(v + 19)/3
Let v(k) = 61*k**3 + 2658*k**2 + 6186*k - 3750. Let t(p) = 195*p**3 + 8505*p**2 + 19795*p - 12000. Let m(y) = -11*t(y) + 35*v(y). Factor m(o).
-5*(o + 3)*(o + 50)*(2*o - 1)
Suppose -22*n - 3020 = 7342. Let s = n + 473. Factor 0*g**s + 2/5*g**3 + 0 + g**4 - 7/5*g**5 + 0*g.
-g**3*(g - 1)*(7*g + 2)/5
Let o = 139 - 126. Let c = 30 - 27. Factor -4*n**4 - 20*n**3 - o*n**3 + 4*n**5 + 4*n**2 + 29*n**c.
4*n**2*(n - 1)**2*(n + 1)
Let g(n) be the second derivative of 1/6*n**4 + 0*n**2 + 2 + 3*n - 2/3*n**3. Factor g(h).
2*h*(h - 2)
Let t(o) = o**3 - 7*o**2 - 101*o + 99. Let c(a) = -a**3 + 8*a**2 + 102*a - 99. Let n(z) = 4*c(z) + 5*t(z). Find f such that n(f) = 0.
-9, 1, 11
Let d(x) be the first derivative of 4*x**4 + 2812*x**3/3 + 10400*x**2 - 5376*x - 10302. Factor d(c).
4*(c + 8)*(c + 168)*(4*c - 1)
Solve 2/7*j**3 - 18/7*j**2 - 194/7*j + 30 = 0.
-7, 1, 15
Let h(s) be the first derivative of -1/15*s**5 - 10/3*s**2 + 0*s + 16/9*s**3 - 1/12*s**4 - 189. Factor h(d).
-d*(d - 2)**2*(d + 5)/3
Let t = 51 - 49. Factor 72 - 10*i - t*i**3 + 70*i**2 - 70*i - 32*i**2 - 12*i**2.
-2*(i - 9)*(i - 2)**2
Determine p so that 163 + 136*p**2 - 380*p + 10 + 2*p**3 - 14*p**3 - 61 = 0.
1/3, 4, 7
Find c, given that 2/9*c**4 + 350/9 - 20/3*c**3 + 212/3*c + 224/9*c**2 = 0.
-1, 7, 25
Let v(c) = -5*c - 42. Let x be v(-9). Factor 9*u + 30*u**3 + 10*u**2 + 25*u**x - 54*u**3.
u*(u + 1)*(u + 9)
Suppose 163*p - 56 = 156*p. Solve -68*w - 2*w**2 - p*w**2 + 14*w**2 = 0 for w.
0, 17
Let z(d) = -312*d**2 - 28*d - 36. Let m(b) = -47*b**2 - 4*b - 5. Let v(n) = 20*m(n) - 3*z(n). Suppose v(i) = 0. Calculate i.
-1, 2
Determine f, given that 1/6*f**2 - 22/3 + 10/3*f = 0.
-22, 2
Let h(i) = -930*i**3 + 926*i**3 - 11*i + 1 + 9*i**2 + 36*i + 6. Let q(m) = 2*m**3 - 4*m**2 - 12*m - 4. Let c(t) = -2*h(t) - 5*q(t). Factor c(v).
-2*(v - 3)*(v + 1)**2
Let m(a) = a**3 + 2*a**2 - 6*a - 4. Let y be m(-3). Factor 10*r - 14*r**2 + 18*r**2 + y*r**4 - 3*r**2 - 16*r**2.
5*r*(r - 1)**2*(r + 2)
What is l in -667/6*l**2 + 49/6*l**3 + 529/2*l + 0 - 1/6*l**4 = 0?
0, 3, 23
Suppose -85 + 70 + 57 = 14*x. Let b(i) be the first derivative of -52 - 2/3*i - 1/18*i**x + 1/3*i**2. Find m such that b(m) = 0.
2
Let j(w) be the first derivative of -w**3/21 + 220*w**2/7 - 48400*w/7 - 863. Determine f so that j(f) = 0.
220
Suppose -37*u = -15*u - 4*u - 47 + 11. Factor 1/5*k**3 + 133/5*k - 4*k**u - 294/5.
(k - 7)**2*(k - 6)/5
Suppose -415 + 415 = -74*h. Factor -6/5*m + h - 2/5*m**2.
-2*m*(m + 3)/5
Factor 2/3*b**3 + 20/3*b**2 - 18*b - 24.
2*(b - 3)*(b + 1)*(b + 12)/3
What is o in 18 + 3 + 9 + 2 - 12*o**2 + 16*o - 4*o**3 + 16 = 0?
-3, -2, 2
Let j(i) = 6*i**4 - 70*i**3 + 366*i**2 - 542*i + 224. Let w(y) = -47*y**4 + 560*y**3 - 2928*y**2 + 4333*y - 1794. Let a(f) = 31*j(f) + 4*w(f). Solve a(z) = 0.
1, 4, 29
Let l(a) = -292*a**2 - 2004*a - 13144. Let o(p) = -22*p**2 - 154*p - 1011. Let x(q) = -3*l(q) + 40*o(q). Let x(b) = 0. Calculate b.
-28, -9
Let f(z) be the first derivative of -16*z**6/3 - 336*z**5/5 - 81*z**4/2 - 20*z**3/3 + 681. Factor f(q).
-2*q**2*(q + 10)*(4*q + 1)**2
Let s(q) be the first derivative of 5*q**3/3 - 85*q**2/2 + 300*q - 832. Factor s(p).
5*(p - 12)*(p - 5)
Let f(v) be the first derivative of -3*v**4/4 - 49*v**3 + 312*v**2 - 636*v + 10690. Factor f(n).
-3*(n - 2)**2*(n + 53)
Let m = 1795/22 + -749/11. Let w be (266/4)/7 + 1. Determine d, given that w*d**2 - m*d + 3 = 0.
2/7, 1
Let b be -3*(4 + 17/(-3)). Solve 18 + 3*a - 3 - 3*a**3 - 20*a**2 + b*a**2 = 0 for a.
-5, -1, 1
Let a(y) be the second derivative of -y**5/4 - 95*y**4/12 - 40*y**3 - 417*y. Factor a(l).
-5*l*(l + 3)*(l + 16)
Suppose 0 = 287*w - 291*w + 132. Suppose -w*s - 21 + 87 = 0. Factor 1/10*z**3 + 1/10*z + 0 + 1/5*z**s.
z*(z + 1)**2/10
Factor 8 - 11/8*u**3 - 97/2*u + 25*u**2.
-(u - 16)*(u - 2)*(11*u - 2)/8
Let w be (4/(48/9))/(11/44). Let h(b) = 2*b**3 - 9*b**2 + 3*b - 1. Let y be h(6). Factor -20*i**2 - 2*i**4 + 7*i**4 + 110*i**3 - y*i**w.
5*i**2*(i - 4)*(i + 1)
Let r be 87/(-12)*-2 + (369/(-9) - -37). Let -3/2*c**3 - 15/2 - 33/2*c - r*c**2 = 0. Calculate c.
-5, -1
Let l(c) = -2*c**3 + 5*c**2 - 19*c - 35. Let w be l(10). Let n = 1729 + w. Find t such that 4/15*t + 0*t**2 - 