r) be the third derivative of -1/8*r**4 + 0*r**3 + 10*r**2 - 1/20*r**5 + 0 + 0*r. Solve x(s) = 0 for s.
-1, 0
Suppose -j = 5 - 10. Let d = -3 + j. Factor -4*o - 4*o**2 + o - d*o**3 + o.
-2*o*(o + 1)**2
Let n(b) = b**3 - 2*b**2 - b + 1. Let l(o) = 4*o**3 + 4*o**2 + 18*o - 282. Let z(p) = l(p) - 6*n(p). Let z(y) = 0. Calculate y.
-4, 6
Let c(s) be the third derivative of s**8/3360 + s**7/1680 - s**6/720 - s**5/240 + 7*s**3/2 - 20*s**2. Let m(p) be the first derivative of c(p). Factor m(u).
u*(u - 1)*(u + 1)**2/2
Let z(v) be the first derivative of -7*v**4/18 - 592*v**3/27 - 371*v**2/9 - 164*v/9 + 543. Let z(y) = 0. Calculate y.
-41, -1, -2/7
Factor 0*t - 1/3*t**2 - 1/3*t**3 + 0.
-t**2*(t + 1)/3
Let i(d) = -3*d + 55. Let q(k) = -k + 18. Let v(w) = 2*i(w) - 7*q(w). Let y be v(18). Factor m + 2*m + 3*m**2 - 3*m - y*m.
m*(3*m - 2)
Let z = -37 - -25. Let q = z + 21. Factor -2*c**2 + 6*c**2 - c**2 + q*c + 6.
3*(c + 1)*(c + 2)
Let a(z) be the second derivative of z**4/6 + 5*z**3/21 - 12*z**2/7 + z + 159. Let a(j) = 0. What is j?
-12/7, 1
Let h(i) be the first derivative of -1/12*i**4 + 1/180*i**5 - 5/2*i**2 + 0*i + 8 + 1/2*i**3. Let v(w) be the second derivative of h(w). Solve v(x) = 0 for x.
3
Find f such that -306*f - 162*f + 240 - 11*f**2 + 89*f**2 - 60*f**3 + 5*f**4 + 28*f + 177*f**2 = 0.
1, 3, 4
Factor 675*d + 2*d**3 + 185*d**2 + 773*d - 1268*d + 3*d**3.
5*d*(d + 1)*(d + 36)
Let n(b) be the third derivative of -b**8/1008 - 2*b**7/315 + 7*b**5/90 + 17*b**4/72 + b**3/3 + 55*b**2. Suppose n(k) = 0. Calculate k.
-3, -1, 2
Let c = 16 - 8. Let j be (-13 - -10) + 2*c. Solve -t**3 - 75*t - 4*t**3 + j + 32 + 35*t**2 = 0.
1, 3
Let l(t) be the third derivative of -t**7/840 + t**5/10 + t**4/2 + 14*t**2. Let u(v) be the second derivative of l(v). Find a, given that u(a) = 0.
-2, 2
Let q(y) = -y + 17. Let a be (12/(-7))/((-5)/35). Let w be q(a). Factor j**2 - j**4 + j**w - 2*j**4 - 3*j**5 + 0*j**2.
-j**2*(j + 1)**2*(2*j - 1)
Let k be 10 + 0/(-2) - 5. Suppose k*v - 4*u - 6 - 4 = 0, -3*v + 6 = 5*u. Factor 1/3 + d + d**v + 1/3*d**3.
(d + 1)**3/3
Suppose -9/2*l - 1/2*l**2 + 5 = 0. What is l?
-10, 1
Let y(i) be the second derivative of i**4/32 - 3*i**3/16 - 21*i**2/4 + 17*i - 7. Factor y(b).
3*(b - 7)*(b + 4)/8
Let d = -17 - -17. Factor -3*o**3 + 2*o**2 - 5*o**2 + d*o**2.
-3*o**2*(o + 1)
Let c(p) be the second derivative of 0 + 1/3*p**2 - 1/18*p**3 - 26*p + 1/60*p**5 - 1/12*p**4 + 1/90*p**6. Let c(w) = 0. Calculate w.
-2, -1, 1
Suppose -2*y + 6*y + 2*s - 20 = 0, -4*y + 5*s = -34. Determine g, given that -4*g - 6*g**5 + 10*g**5 - y*g**2 + 6*g**4 + 2*g**3 - 2*g**5 = 0.
-2, -1, 0, 1
Let s(v) = 13*v**2 - 72*v + 15. Let i(l) = -6*l**2 + 36*l - 6. Let o(a) = 5*i(a) + 2*s(a). Solve o(m) = 0 for m.
0, 9
Let j = 38125 - 724373/19. Determine u so that 0 - 6/19*u + j*u**2 = 0.
0, 3
Let g(r) be the third derivative of -1/420*r**6 - 2/7*r**3 - 2/105*r**5 + 11/84*r**4 + 0 + 0*r + 18*r**2. Factor g(c).
-2*(c - 1)**2*(c + 6)/7
Suppose b - c - 12 = -4*c, -3*b - 3*c = -12. Suppose b = -6*o + 4*o + 4. Find g such that -4/3 - 2*g + 10/3*g**o = 0.
-2/5, 1
Let z(m) be the third derivative of -m**5/180 + 5*m**4/72 - 2*m**3/9 + 121*m**2. Factor z(f).
-(f - 4)*(f - 1)/3
Determine a so that 44 - 106/5*a - 2/5*a**2 = 0.
-55, 2
Let p(s) be the second derivative of 3*s**5/100 + 13*s**4/2 + 257*s**3/10 + 192*s**2/5 - 23*s + 4. Factor p(t).
3*(t + 1)**2*(t + 128)/5
Factor 3*n**4 - 12*n + 6*n**2 + 7*n**3 - 108*n + 12*n**2 + 17*n**3 + 75.
3*(n - 1)**2*(n + 5)**2
Let j = 9 - 3. Factor 4*a - j*a**2 - 6*a + 3*a**4 - 5*a**4 - 6*a**3.
-2*a*(a + 1)**3
Determine l so that 5/6*l**2 - 115/3*l + 0 = 0.
0, 46
Let w(o) = -4*o + 16*o**2 + 29*o + 39*o + 40 + 15. Let m(u) = -4*u**2 - 16*u - 14. Let k(j) = -9*m(j) - 2*w(j). Determine a, given that k(a) = 0.
-2
Let l be (-1 - -1)/(-159 - -160). Let s(t) be the third derivative of 1/180*t**5 + 0*t**6 + l*t**4 - 1/1260*t**7 + 0*t + 0 - 1/36*t**3 + 5*t**2. Factor s(f).
-(f - 1)**2*(f + 1)**2/6
Find k, given that -8/5 + 0*k - 2/5*k**3 + 6/5*k**2 = 0.
-1, 2
Determine l, given that 161*l - 184*l**2 + 512 - 244*l**3 + 479*l + 42*l**4 - 4*l**5 + 22*l**4 = 0.
-1, 2, 8
Let h = -1840 + 1842. Suppose 3*v = 11 - 2. Factor 0*n - 1/3*n**v + 0*n**h + 0.
-n**3/3
Let q be (3888/(-1215))/(14/(-15)). Factor -2/7*i**2 - 72/7 - q*i.
-2*(i + 6)**2/7
Let d be (156/(-728))/(2 + (-88)/42). Let i(w) be the second derivative of 1/24*w**4 + d*w**2 - 1/2*w**3 + 0 + w. Solve i(g) = 0.
3
Let c = -960 + 1921/2. Factor 0 - c*r - 1/2*r**2.
-r*(r + 1)/2
Find v such that -23*v - 5*v**2 - 230*v**2 - 5*v**3 - 2645 - 2852*v = 0.
-23, -1
Find j such that 143 + 153 + 8*j + 142 - 426 + j**2 = 0.
-6, -2
Let f(x) be the second derivative of -x**7/147 - 2*x**6/105 + 3*x**5/70 + 4*x**4/21 + 4*x**3/21 - 2*x - 104. Let f(w) = 0. Calculate w.
-2, -1, 0, 2
Let m(s) = 24*s**5 - 20*s**4 + 16*s**3 + 12*s**2 - 48*s. Let o(c) = -c**5 + c**4 - c**3 - c**2 + 2*c. Let y(j) = 2*m(j) + 44*o(j). Find k, given that y(k) = 0.
-1, 0, 2
Let d(u) be the third derivative of u**5/20 - 31*u**4/4 - 63*u**3/2 + 7*u**2 - 22. Let d(n) = 0. Calculate n.
-1, 63
Suppose -129*o - 3 = -130*o. Let j be (2 - 27/12)/(o/(-6)). Factor 0 - 1/2*y**3 + y - j*y**2.
-y*(y - 1)*(y + 2)/2
Let k(o) be the second derivative of 2*o**6/15 + 2*o**5/5 + o**4/3 - o - 77. Factor k(m).
4*m**2*(m + 1)**2
Factor 0 + 0*s - 6/11*s**2 - 10/11*s**3.
-2*s**2*(5*s + 3)/11
Let p(u) = u**3 - 12*u**2 + 36*u - 37. Let t(m) = m**2 + 1. Let z(f) = p(f) + t(f). Factor z(h).
(h - 6)*(h - 3)*(h - 2)
Let l(j) be the third derivative of j**7/525 + j**6/75 - 11*j**5/150 + j**4/10 + j**2 + 25. Factor l(t).
2*t*(t - 1)**2*(t + 6)/5
Let f(d) be the first derivative of -d**3/12 + d**2/8 + d/2 - 124. Factor f(s).
-(s - 2)*(s + 1)/4
Let d(h) be the third derivative of -h**7/560 - h**6/80 - h**5/40 - 49*h**2 + h. Factor d(m).
-3*m**2*(m + 2)**2/8
Let h be -63 + (4 - 1 - 1). Let f = h - -63. Factor -5/6*u - 1/3 - 1/2*u**f + 1/6*u**3 + 1/6*u**4.
(u - 2)*(u + 1)**3/6
Let y be (46/(-1771)*11)/((-18)/21). Find n, given that -y*n**4 + 0 - 1/3*n - n**2 - n**3 = 0.
-1, 0
Let s(u) be the third derivative of -2*u**7/63 + 17*u**6/180 - 2*u**5/45 - u**4/12 - 225*u**2. Determine d so that s(d) = 0.
-3/10, 0, 1
Let f(v) = v**2 + 12*v + 38. Let m be f(-6). Solve 2*z**3 - 18 - 24*z**2 + 44*z**2 - 10*z**m + 6*z = 0.
-3, 1
Let z(t) be the first derivative of 2*t**6/3 - 8*t**5/5 - 3*t**4 + 32*t**3/3 - 8*t**2 - 82. Determine a so that z(a) = 0.
-2, 0, 1, 2
Let q(w) = -w**3 + 21*w**2 - 32*w - 111. Let i be q(19). Let r(t) be the first derivative of 0*t + 1/10*t**2 - 1/15*t**i + 1. Let r(y) = 0. Calculate y.
0, 1
Let x(a) be the first derivative of -a**6/2 + 6*a**4 - 6*a**3 - 21*a**2/2 + 18*a - 110. Solve x(y) = 0 for y.
-3, -1, 1, 2
Suppose 7 + 5 = -4*i + 4*w, -2*i + 3*w = 9. Factor 28*g - 18*g + 4 + 6*g**2 + i*g - 2*g**4 - 2*g**3.
-2*(g - 2)*(g + 1)**3
Let b(r) be the first derivative of -2*r**3/39 - 8*r**2/13 + 96*r/13 - 514. Factor b(y).
-2*(y - 4)*(y + 12)/13
Solve 6*q**2 + 12*q**4 - 4*q**5 + 12 - 4*q + 8*q**3 + 3*q**2 - 20*q**2 - 13*q**2 = 0.
-1, 1, 3
Suppose 0 = -5*t + 112 + 78. Let l = t + -33. Factor 6*f**5 + 26*f**3 + 37*f**3 + l*f**4 - 39*f**4 + 40*f + 11*f**3 - 8 - 78*f**2.
2*(f - 2)*(f - 1)**3*(3*f - 2)
Let x be 4/(4 + -8) - -28. Suppose 0 = v - 5*g - x, 0 = -2*v + g + 4*g + 29. Suppose -27*j**3 + 17*j + 15*j + 20*j**v + 31*j**3 + 5 + 11 = 0. What is j?
-2, -1
Let x(j) be the third derivative of j**5/360 + 17*j**4/72 + 11*j**3/12 - 134*j**2. Let x(w) = 0. Calculate w.
-33, -1
Let m(u) be the second derivative of -3/160*u**5 + 1/16*u**3 + 0 - 17*u + 0*u**2 + 0*u**4. Factor m(n).
-3*n*(n - 1)*(n + 1)/8
What is y in 96/13*y + 0 - 2/13*y**3 - 2*y**2 = 0?
-16, 0, 3
Let y = 437 - 437. Let v(k) be the second derivative of 1/168*k**7 + 0*k**6 + 0*k**4 + y - 1/40*k**5 + 1/24*k**3 + 0*k**2 + 6*k. Factor v(m).
m*(m - 1)**2*(m + 1)**2/4
Let h(w) be the first derivative of 0*w - 1/16*w**4 + 7 + 1/12*w**3 + 1/4*w**2. Determine i so that h(i) = 0.
-1, 0, 2
Let p(w) be the third derivative of -w**5/30 + w**4/2 + 7*w**3/3 + 52*w**2. Factor p(a).
-2*(a - 7)*(a + 1)
Let l(v) be the first derivative of -7*v**4/20 - v**3/5 + v**2 + 441. Find f such that l(f) = 0.
-10/7, 0, 1
Let m(g) be the first derivative of 2*g