c) + d(c). Solve u(f) = 0.
1
Suppose 3*q + 2 + 1 = 0, 3*q + 6 = t. Factor u**3 - 4*u**2 + 0*u**t + 3*u**2 - u**2 + u.
u*(u - 1)**2
Let v(c) be the third derivative of c**7/10080 - c**6/1440 + c**5/480 + c**4/24 - c**2. Let i(l) be the second derivative of v(l). Factor i(t).
(t - 1)**2/4
Let j(k) be the third derivative of k**5/60 - 7*k**3/6 - 3*k**2. Let w be j(3). Factor -2/3 + 1/3*i + i**w.
(i + 1)*(3*i - 2)/3
Let u(y) be the first derivative of y**5/240 + y**4/96 + 3*y**2/2 - 2. Let j(i) be the second derivative of u(i). Factor j(l).
l*(l + 1)/4
Let n be (2 + -2)*(-3 + 2). Suppose -4 = -z + d, n = 2*z - d - 3 - 3. Let 2*r**3 - z*r + 5 - 2*r**2 - 2 - 1 = 0. What is r?
-1, 1
Let h(t) be the second derivative of -2*t + 0*t**2 + 1/10*t**5 + 0*t**4 + 1/14*t**7 + 0*t**3 - 1/6*t**6 + 0. Factor h(m).
m**3*(m - 1)*(3*m - 2)
Let c be 5 + 2 + -1 + -2. Suppose -v - 3*x + 12 = -0*v, -2*x = c*v - 18. Find d, given that 4/3*d**v + 0*d + 0 - 2*d**4 + 0*d**2 - 10/3*d**5 = 0.
-1, 0, 2/5
Determine q so that 1/5 - 12/5*q**5 + 0*q + 13/5*q**4 - 14/5*q**2 + 12/5*q**3 = 0.
-1, -1/4, 1/3, 1
Suppose l - 3*z = 17, -4*l + z = -2*z - 23. Suppose 0 = -c - l*x - 6, -3*x - 5 = 7. Determine o, given that 3*o + 0*o + 16 - c*o**3 - 27*o + 12*o**2 = 0.
2
Let i(n) = 9*n - 3. Let t be i(2). Suppose 2*h = -3*h + t. Factor h*w - 2*w**2 + w + 8*w**2.
2*w*(3*w + 2)
Let i(u) be the first derivative of u**3/5 + 9*u**2/5 + 27*u/5 - 4. Factor i(r).
3*(r + 3)**2/5
Let p(y) be the first derivative of 9*y**4/10 - 4*y**3/15 + 5. Determine s, given that p(s) = 0.
0, 2/9
Suppose 14/9*z**2 + 4/3 - 46/9*z = 0. What is z?
2/7, 3
Let l be ((-6)/10)/(2/(-40)). Suppose 5*s**5 + 10*s**2 - l*s**3 - 18*s**2 - s**5 = 0. Calculate s.
-1, 0, 2
Let u(n) be the first derivative of -n**6/9 - 4*n**5/15 - n**4/6 - 5. Suppose u(q) = 0. Calculate q.
-1, 0
Let b(k) be the second derivative of -7*k**5/180 - k**4/36 + 2*k**2 - 5*k. Let s(h) be the first derivative of b(h). Factor s(r).
-r*(7*r + 2)/3
Let f(j) be the first derivative of -j**6/33 + 3*j**4/22 + 4*j**3/33 - 37. Factor f(l).
-2*l**2*(l - 2)*(l + 1)**2/11
Let t(f) be the first derivative of f**8/224 - f**7/70 + f**6/80 - f**2/2 - 2. Let r(s) be the second derivative of t(s). Suppose r(g) = 0. Calculate g.
0, 1
Let h(i) be the second derivative of -4*i**6/105 + 3*i**5/70 + i**4/42 + 7*i. Determine s, given that h(s) = 0.
-1/4, 0, 1
Let n(g) = -4*g**5 - 16*g**3 - 20*g**2 + 14*g - 14. Let j(a) = -a**5 - 3*a**3 - 4*a**2 + 3*a - 3. Let c(i) = 14*j(i) - 3*n(i). Factor c(p).
-2*p**2*(p - 2)*(p + 1)**2
Suppose h + 5 + 5 = 3*z, 3*h + 5*z = 26. Determine i, given that -1/4*i**h - 1/2 + 3/4*i = 0.
1, 2
Let n(b) = 7*b**2 - 8*b + 6. Let z(h) = 14*h**2 + 2 + 0 + 9 - 15*h. Let s(a) = 11*n(a) - 6*z(a). Solve s(d) = 0 for d.
0, 2/7
Factor 0*v - 1/6*v**4 + 0*v**3 + 0 + 1/6*v**2.
-v**2*(v - 1)*(v + 1)/6
Let u = 5 + -1. Suppose 3*b = -3*b + 6. Factor -3*g - 2*g**3 + u*g - g**2 + 0*g + b + g**3.
-(g - 1)*(g + 1)**2
Let u(f) be the third derivative of -f**6/360 + f**5/60 - f**4/36 + 17*f**2. Factor u(l).
-l*(l - 2)*(l - 1)/3
Suppose -91 = 3*k - 100. Suppose 0*c**2 + 0 - 1/5*c + 2/5*c**k + 0*c**4 - 1/5*c**5 = 0. What is c?
-1, 0, 1
Let h(g) be the third derivative of -g**6/20 + 11*g**5/30 - 5*g**4/12 - g**3 - 11*g**2 + 3*g. Find y such that h(y) = 0.
-1/3, 1, 3
Let d = 1/15 + 3/5. Let w = 1 - 1. Factor d*i**4 - 2/3*i**2 + w*i**3 + 0*i + 0.
2*i**2*(i - 1)*(i + 1)/3
Let u be (((-12)/(-3))/2)/4. Let o(s) be the first derivative of 1 - 1/2*s**2 + 1/6*s**3 + u*s. Let o(z) = 0. Calculate z.
1
Let y = 3 + -2. Let m(o) = -o**2 - o. Let j(w) = -4*w**2 - 6*w - 2. Let p(h) = y*j(h) - 2*m(h). Factor p(k).
-2*(k + 1)**2
Let d(g) be the second derivative of 0 - 1/12*g**3 + 0*g**4 + 0*g**6 - g + 1/20*g**5 + 0*g**2 - 1/84*g**7. Factor d(o).
-o*(o - 1)**2*(o + 1)**2/2
Factor 1/2*t**3 + 2*t**2 + 5/2*t + 1.
(t + 1)**2*(t + 2)/2
Factor 14*k**2 + 3*k + 0*k - k + 2*k + 6*k**3.
2*k*(k + 2)*(3*k + 1)
Let p(z) be the first derivative of 0*z**2 - 1/2*z**3 + 3/10*z**5 + 1/4*z**6 + 0*z - 3/8*z**4 - 3. Let p(b) = 0. Calculate b.
-1, 0, 1
Let t(y) be the second derivative of y**4/8 - 3*y**3 + 27*y**2 - 4*y. Factor t(a).
3*(a - 6)**2/2
Let j(y) be the second derivative of -1/4*y**4 - 4*y - 1/2*y**3 + 0 + 3*y**2. Suppose j(t) = 0. Calculate t.
-2, 1
Let g(t) be the second derivative of 1/120*t**6 + 0 - 1/40*t**5 + 0*t**2 + 0*t**3 + 3*t + 1/48*t**4. Find k, given that g(k) = 0.
0, 1
Let h(p) be the second derivative of 7*p**5/10 + p**4/3 - 7*p**3/3 - 2*p**2 + 57*p. What is r in h(r) = 0?
-1, -2/7, 1
Let d = 14 - 22. Let h be (d/32)/(1/(-16)). Suppose 1/3*y**2 - 1/3*y**h + 1/3*y - 1/3*y**3 + 0 = 0. Calculate y.
-1, 0, 1
Let b = 1 + 4. Let q(y) be the third derivative of 1/270*y**b + 0*y**3 + 0*y - 1/108*y**4 + y**2 + 0. Let q(g) = 0. What is g?
0, 1
Let a(o) = o**2 - 7. Let h be a(-3). Factor -1/2*d - 4*d**h + 0 - 8*d**4 - 10*d**3.
-d*(2*d + 1)**2*(4*d + 1)/2
Let f(n) be the third derivative of -8*n**2 + 0*n + 0*n**5 + 1/168*n**8 + 0 + 0*n**4 + 1/105*n**7 + 0*n**3 + 0*n**6. Factor f(s).
2*s**4*(s + 1)
Let w(i) = 45*i**5 - 275*i**4 + 335*i**3 + 185*i**2 + 5*i. Let c(f) = -68*f**5 + 413*f**4 - 502*f**3 - 277*f**2 - 7*f. Let s(k) = 5*c(k) + 7*w(k). Factor s(x).
-5*x**2*(x - 3)**2*(5*x + 2)
Let c = -98/3 + 33. Find t such that -1/3*t**2 - 1/3*t + 1/3 + c*t**3 = 0.
-1, 1
Let v = -4 + 19. Let f be 2/(-6) + 10/v. Factor 2/3*w - 2/3*w**3 + 0*w**2 - 1/3 + f*w**4.
(w - 1)**3*(w + 1)/3
Let o(f) be the third derivative of -f**8/80640 - f**7/5040 - f**6/720 - f**5/20 - f**2. Let k(y) be the third derivative of o(y). Factor k(w).
-(w + 2)**2/4
Let u be (10/14 - 1)*-7. Factor -2/9 - 2/9*y**4 + 0*y + 0*y**3 + 4/9*y**u.
-2*(y - 1)**2*(y + 1)**2/9
Find y such that -7/12*y**5 - 1/6 + 1/3*y**3 + 1/4*y + 7/6*y**2 - y**4 = 0.
-1, 2/7, 1
Suppose -v + 4*u = 10, -4*v - 6 = -u + 4. Let l be 3/v + (-28)/(-8). Factor 3 - 3 + i**l.
i**2
Let v(n) be the first derivative of n**5/120 + n**4/72 - n**3/36 - n**2/12 - 9*n + 7. Let t(f) be the first derivative of v(f). Factor t(g).
(g - 1)*(g + 1)**2/6
Let r(y) be the second derivative of -y**7/3780 + y**6/540 - y**5/180 + y**4/6 - 3*y. Let q(d) be the third derivative of r(d). Factor q(m).
-2*(m - 1)**2/3
Let y be (-2)/8 + 2 + (-4)/(-16). Let f(z) be the second derivative of 0 - 3/110*z**5 + y*z - 2/33*z**4 + 2/11*z**2 + 1/33*z**3. Factor f(h).
-2*(h + 1)**2*(3*h - 2)/11
Let t(g) be the second derivative of -5*g**6/3 - 12*g**5 - 92*g**4/3 - 32*g**3 - 16*g**2 + 26*g. Factor t(x).
-2*(x + 2)**2*(5*x + 2)**2
Let z(x) = 25*x**2 - 27*x + 9. Let m(l) = -25*l**2 + 26*l - 9. Let d(k) = -3*m(k) - 4*z(k). Factor d(v).
-(5*v - 3)**2
Let w be (-1)/(-1) - 176/(-3). Let s = w + -59. Let -s*r**3 + 0 - 5/3*r**5 + 7/3*r**4 + 0*r**2 + 0*r = 0. Calculate r.
0, 2/5, 1
Let l(r) = -3*r**4 - r**3 + 9*r**2 - 11*r + 6. Let j(q) = 3*q**4 - 9*q**2 + 12*q - 6. Let n(a) = 4*j(a) + 3*l(a). Factor n(c).
3*(c - 1)**3*(c + 2)
Factor -3*d**2 - d**2 + 459*d - 439*d.
-4*d*(d - 5)
Let c(k) be the first derivative of -k**5/10 + k**4/6 - 3*k + 2. Let s(n) be the first derivative of c(n). Factor s(j).
-2*j**2*(j - 1)
Let k(l) be the second derivative of l**6/15 + 2*l**5/5 + 5*l**4/6 + 2*l**3/3 - 10*l + 1. Let k(h) = 0. Calculate h.
-2, -1, 0
Let x be 15/(-20)*(-8)/3. Determine p so that 2/3*p + 0 - 1/3*p**x = 0.
0, 2
Let i(c) be the first derivative of -4*c**3/3 - 10*c**2 - 28. Let i(h) = 0. Calculate h.
-5, 0
Let w(u) = -287*u**2 + 175*u - 17. Let x(l) = 144*l**2 - 87*l + 9. Let a(m) = m**3 - 6*m**2 + 7. Let y be a(6). Let z(k) = y*x(k) + 3*w(k). Factor z(q).
3*(7*q - 2)**2
Determine v so that 4/5*v**5 - 1/5 - 1/5*v**4 + 2/5*v**2 - 8/5*v**3 + 4/5*v = 0.
-1, 1/4, 1
Factor -2*l**2 + 10*l - 6*l + 0 + 2 - 4*l**3.
-2*(l - 1)*(l + 1)*(2*l + 1)
Let q(v) be the third derivative of 1/5*v**3 + 0*v + 0 - 3/40*v**4 + 2*v**2 + 1/100*v**5. Factor q(i).
3*(i - 2)*(i - 1)/5
Suppose -2*w - w + 53 = 4*u, -4*u = 2*w - 42. Suppose 4*v + 11 - w + 4*v**2 + v**3 = 0. Calculate v.
-2, 0
Let f(q) be the second derivative of 2*q**6/15 - q**5/5 + q. Let f(n) = 0. What is n?
0, 1
Let h(j) be the second derivative of -j**4/16 + j**3/4 + 9*j**2/8 + 8*j. What is f in h(f) = 0?
-1, 3
Let w(c) be the first derivative of c**7/840 - c**6/360 - c**5/60 + 2*c**