 + 0 - 1/60*p**5. Factor d(u).
-(u - 1)*(u + 1)
Let h(p) be the third derivative of -p**5/12 - 25*p**4/24 - 94*p**2. Let h(x) = 0. What is x?
-5, 0
Let s(u) be the third derivative of -u**6/24 + u**5/4 - 5*u**4/12 + 56*u**2. Factor s(g).
-5*g*(g - 2)*(g - 1)
Let g(v) be the second derivative of 0 + 5/3*v**3 - 5/12*v**4 - 5/2*v**2 - 10*v. Suppose g(b) = 0. What is b?
1
Suppose 178 = -152*p + 482. Solve -14/3*a**p + 4*a + 2/3 = 0 for a.
-1/7, 1
Let c(p) be the first derivative of -2*p**4/7 - 6*p**3 - 240*p**2/7 + 128*p/7 - 24. Factor c(t).
-2*(t + 8)**2*(4*t - 1)/7
Suppose -54*m = -232 + 70. Let x(o) be the third derivative of 1/15*o**m + 0*o**4 - 1/150*o**5 + 0*o + 0 + 8*o**2. Factor x(p).
-2*(p - 1)*(p + 1)/5
Let q(b) be the first derivative of -b**7/630 - b**6/180 + b**5/60 + 7*b**2 - 30. Let i(u) be the second derivative of q(u). Suppose i(k) = 0. Calculate k.
-3, 0, 1
Factor -2/9 + 2/9*t**2 + 0*t.
2*(t - 1)*(t + 1)/9
Let k(h) be the third derivative of h**6/64 - 87*h**5/160 - 5*h**4/64 + 87*h**3/16 + 3*h**2 - 80*h. Suppose k(o) = 0. Calculate o.
-1, 1, 87/5
Let w(v) be the second derivative of 0 - 1/48*v**4 - 2*v + 1/240*v**5 - v**2 + 1/24*v**3. Let z(c) be the first derivative of w(c). Factor z(n).
(n - 1)**2/4
Suppose 3*v - 9 = -s, 5*v - 20 + 7 = -s. Factor 0*w + 3/5*w**3 + 0 - 3/5*w**v.
3*w**2*(w - 1)/5
Suppose -3*j - 73 = -79. Suppose 0 = j*r + 2*r - 8. Let -1/5*u**r + 2/5*u + 0 = 0. Calculate u.
0, 2
Let x = -174 - -174. Let f(o) be the third derivative of 1/210*o**5 + 1/420*o**6 + 0*o**3 - 5*o**2 + 0*o**4 + 0 + x*o. Determine a so that f(a) = 0.
-1, 0
Let w(o) be the second derivative of 0*o**3 - 3/95*o**6 + 0 - 11/190*o**5 - 1/57*o**4 + 0*o**2 - 13*o. Find d such that w(d) = 0.
-1, -2/9, 0
Suppose 35 = v + 3*s, 2*s = v + 3*s - 27. Let h = -5 + 9. Determine k, given that -7*k - h*k**2 + v*k - 8*k = 0.
0, 2
Suppose 0*s = 2*z + 4*s - 16, 12 = 4*s. What is f in -25/4*f**3 + 0 - 5*f - 15*f**z = 0?
-2, -2/5, 0
Let d(y) be the first derivative of -3/10*y**2 - 1/15*y**3 + 0*y - 13. Factor d(r).
-r*(r + 3)/5
Let z(g) be the first derivative of g**7/4 - g**6/3 + g**5/10 + 8*g - 15. Let h(n) be the first derivative of z(n). Factor h(m).
m**3*(3*m - 2)*(7*m - 2)/2
Suppose -80*b + 35*b = -39*b. Find h such that 0*h**3 + b + 0*h**2 + 0*h - 1/7*h**4 = 0.
0
Let n(a) be the third derivative of -a**5/270 + 2*a**4/27 - 7*a**3/27 + 68*a**2. Solve n(d) = 0.
1, 7
Let z = -7727 + 7729. Factor 8/13 + 18/13*g**z + 2/13*g**3 + 22/13*g - 2/13*g**4.
-2*(g - 4)*(g + 1)**3/13
Let u be 1/(-4) - 15/(-28). Suppose -10*i + 60 - 30 = 0. Factor u*x + 0 - 2/7*x**i + 0*x**2.
-2*x*(x - 1)*(x + 1)/7
Let g be 17 - (-2 + 3 + -1). Let n = g + -9. Factor -8*o**3 - o + 11*o**3 - n*o + 6.
3*(o - 1)**2*(o + 2)
Let q(d) be the second derivative of -d**7/1440 - d**6/180 - d**5/120 - d**4/12 - 7*d. Let a(l) be the third derivative of q(l). Find s such that a(s) = 0.
-2, -2/7
Solve -466*b**2 + 148*b + 223*b**2 + 218 + 239*b**2 + 94 = 0.
-2, 39
Let n be -6*(6/(-4) + 1). Suppose -5*y = -c - 22, c = -n*y - 0*c + 10. Let 3*m**y + 6*m**3 - 2*m**2 + 0*m**2 + 5*m**2 = 0. What is m?
-1, 0
Suppose n + 72 - 75 = 0. Suppose -2*f + 2*q - 12 = -3*f, 3*f + n*q - 21 = 0. Factor 4/13*h**f - 2/13*h**3 + 2/13*h - 4/13.
-2*(h - 2)*(h - 1)*(h + 1)/13
Suppose 618*j + 516 = 790*j. Suppose 3/5 + 27/5*c + 72/5*c**2 + 48/5*c**j = 0. Calculate c.
-1, -1/4
Solve 4*j**2 - 219*j - 3*j**2 + 3*j**2 + 259*j = 0.
-10, 0
Let a(p) be the third derivative of 0*p + 7*p**2 - 8/525*p**7 + 1/50*p**6 + 0 + 4/75*p**5 - 2/15*p**4 + 1/420*p**8 + 0*p**3. Solve a(m) = 0 for m.
-1, 0, 1, 2
Let d(b) = -13*b - 104. Let o be d(-8). Let y(f) be the third derivative of 0*f**3 + 0 + o*f + 1/160*f**6 + 0*f**4 + 7*f**2 + 1/40*f**5. Factor y(x).
3*x**2*(x + 2)/4
Factor -51/5 - 9*k**2 + 99/5*k - 3/5*k**3.
-3*(k - 1)**2*(k + 17)/5
Factor l**2 + 422*l**4 + l - 12*l**3 + 11*l**3 - 423*l**4.
-l*(l - 1)*(l + 1)**2
Let c(m) be the first derivative of m**4/8 + 3*m**3 - 19*m**2/4 - 292. Factor c(x).
x*(x - 1)*(x + 19)/2
Solve 3*m**4 + 10*m**3 - 67*m - 36*m**2 + 23*m + m**4 - 14*m**3 - 16 = 0.
-1, 4
Let h(l) be the second derivative of -10*l**7/21 + 4*l**6/3 - l**5/4 - 25*l**4/12 + 5*l**3/6 + 5*l**2/2 + 28*l. Let h(j) = 0. What is j?
-1/2, 1
Solve -357*k**3 - 465*k**3 + 122*k**3 - 2707*k**4 + 2597*k**4 - 1000*k**2 - 5*k**5 = 0.
-10, -2, 0
Let p(g) be the second derivative of g**4/16 - 9*g**3/2 + 105*g**2/8 + 162*g. Factor p(r).
3*(r - 35)*(r - 1)/4
Let o(j) be the second derivative of -3*j**5/5 - 19*j**4/15 - 4*j**3/5 + 35*j. Factor o(r).
-4*r*(3*r + 2)*(5*r + 3)/5
Let l(m) = -m**2 - 7*m + 4. Let q be l(-6). Let d be q/5 - (2 - 3). Let 0*z**3 - 3*z**3 + 3*z**4 - d*z**3 + 3*z**2 = 0. What is z?
0, 1
Let m(z) = z**3 - 4*z**2 + 6*z - 4. Let o be m(3). Suppose g - v = -3*g + 11, -o*v = g - 8. Factor -i**3 + 4*i - 2*i**2 + 0*i + 7*i**g - 8*i**3.
-2*i*(i - 1)*(i + 2)
Let i(t) = -6*t**2 - 393*t - 206. Let n(p) = 39*p**2 + 2751*p + 1440. Let x(w) = -27*i(w) - 4*n(w). Suppose x(r) = 0. What is r?
-1/2, 66
Find y, given that -3*y - 1/2*y**4 - 1/2*y**2 + 0 + 2*y**3 = 0.
-1, 0, 2, 3
Let p be ((-18)/(-54))/(-2*3/(-12)). Let j(x) be the second derivative of 0*x**2 - p*x**3 + 7*x + 0 - 1/3*x**4. Let j(b) = 0. Calculate b.
-1, 0
Let w(f) be the first derivative of -12/5*f**2 - 36/25*f**5 + 32/15*f**3 + 4/5*f + 38 + 2/5*f**4 + 8/15*f**6. Determine g, given that w(g) = 0.
-1, 1/4, 1
Factor -7*n**2 + 31*n**2 + 59*n**3 - 63*n**3 - 4*n**4.
-4*n**2*(n - 2)*(n + 3)
Let d(c) be the first derivative of -c**3/12 - 25*c**2/4 - 24*c + 622. Let d(u) = 0. What is u?
-48, -2
Let s(r) be the third derivative of 0 - 9*r**2 + 0*r**6 + 1/45*r**5 + 0*r**3 + 1/36*r**4 - 1/504*r**8 + 0*r - 2/315*r**7. Determine l, given that s(l) = 0.
-1, 0, 1
Let j(g) = g**4 - 14*g**2 - 15*g - 5. Let v(o) = 4*o**4 - 57*o**2 - 59*o - 19. Let n(w) = 26*j(w) - 6*v(w). Factor n(l).
2*(l - 4)*(l + 1)**2*(l + 2)
Let k = 39/2 - 113/6. Suppose k*v + 0 - 2/9*v**2 = 0. What is v?
0, 3
Let x(m) be the third derivative of -1/48*m**4 - 1/12*m**3 + 0*m + 0 + 1/240*m**6 + 11*m**2 + 1/120*m**5. Factor x(p).
(p - 1)*(p + 1)**2/2
Let d(i) = 10*i**2 + 9*i - 18. Let f be d(4). Suppose 1792*m**4 - 424*m**2 + 826*m**5 - f*m**5 + 332*m**5 + 283*m**3 + 217*m**3 + 32 - 80*m = 0. Calculate m.
-1, -2/5, 2/7
Let y(c) be the third derivative of c**7/70 - c**6/20 - 7*c**5/20 + c**4 + 6*c**3 - 31*c**2. Find n, given that y(n) = 0.
-2, -1, 2, 3
Let z = 50 + -48. Factor -z + 12*c - 16*c**3 + 10 - 35*c**5 + 39*c**5 - 8*c**2.
4*(c - 2)*(c - 1)*(c + 1)**3
Let n(v) be the third derivative of 225*v**8/112 + 24*v**7 + 332*v**6/5 - 448*v**5/5 + 32*v**4 + 15*v**2 - 24. Factor n(z).
3*z*(z + 4)**2*(15*z - 4)**2
Let g be 8*(5 + 5 + 114/(-12)). Let s(j) be the second derivative of 0 + 1/70*j**5 - 7*j - 5/42*j**g + 8/21*j**3 - 4/7*j**2. Let s(h) = 0. Calculate h.
1, 2
Suppose 47*x**3 - 25*x**2 - 12*x + 66*x**4 + 11*x**3 - 157*x**3 + 85*x**2 - 15*x**5 = 0. What is x?
0, 2/5, 1, 2
Let y(h) be the first derivative of h**6/24 + 7*h**5/20 + 15*h**4/16 + 13*h**3/12 + h**2/2 - 53. Factor y(s).
s*(s + 1)**3*(s + 4)/4
Let b(q) be the first derivative of -5/3*q**3 + 11 + 0*q + 5*q**2. Solve b(w) = 0 for w.
0, 2
Let j(r) be the third derivative of r**7/490 - 5*r**6/56 + 69*r**5/140 - 67*r**4/56 + 11*r**3/7 + 377*r**2. Solve j(d) = 0 for d.
1, 22
Let r(y) = y**4 + 25*y**3 + 97*y**2 + 103*y + 38. Let l(q) = 2*q**2 - q - 1. Let u(z) = 12*l(z) - 3*r(z). Factor u(s).
-3*(s + 1)**2*(s + 2)*(s + 21)
Let k(h) be the first derivative of 3*h**5/80 - h**4/48 - h**3/8 + h**2/8 + h - 7. Let w(i) be the first derivative of k(i). Factor w(n).
(n - 1)*(n + 1)*(3*n - 1)/4
Suppose 0 = 26*z + 621 - 673. What is k in -1/2*k**z + 3/2*k - 1 = 0?
1, 2
Factor 8/5*k**2 + 4/5*k + 0 + 4/5*k**3.
4*k*(k + 1)**2/5
Suppose -20 = -f + 3*x, -38*f + 2*x = -40*f. Factor -1/5*q**2 + 2*q - f.
-(q - 5)**2/5
Let t = -1 + -7. Let i be (-1)/((-28)/t)*-7. Suppose 2 - v + 3*v - 4*v**i - 9*v = 0. Calculate v.
-2, 1/4
Let f(n) be the first derivative of -n**4/46 + 14*n**3/69 - 6*n**2/23 - 142. Find i, given that f(i) = 0.
0, 1, 6
Let p = 183 - 180. Suppose -2*n - 15 = -p*c, -4*n - 10 - 17 = -5*c. Suppose -v**4 + 0 + 0*v**2 + 2/3*v**c + 0*v + 1/3*v**5 = 0. Calculate v.
0, 1, 2
Let n(s) be the sec