 of n**8/6480 - n**7/378 + 2*n**6/405 + 11*n**5/20 - 5*n**2. Let f(a) be the third derivative of y(a). Solve f(b) = 0 for b.
2/7, 4
Let d(c) be the third derivative of 0*c**6 + 0*c + 0*c**3 - 1/224*c**8 + 1/20*c**5 + 5*c**2 - 1/70*c**7 + 0 + 1/16*c**4. Suppose d(u) = 0. What is u?
-1, 0, 1
Let a(v) = -21*v**3 - 15*v**2 + 12*v + 6. Let h(k) = 20*k**3 + 14*k**2 - 11*k - 5. Let b be 9/4*(-24)/(-9). Let j(d) = b*h(d) + 5*a(d). Factor j(r).
3*r*(r + 1)*(5*r - 2)
Let r(v) be the third derivative of v**7/840 + v**6/480 - v**5/20 + v**4/24 + 2*v**3/3 + 7*v**2. Factor r(d).
(d - 2)**2*(d + 1)*(d + 4)/4
Let h(s) be the first derivative of 0*s - 1/3*s**4 + 7 - s**2 + 1/30*s**5 + s**3. Let b(x) be the second derivative of h(x). Factor b(i).
2*(i - 3)*(i - 1)
Solve 18*p**2 + 4096 + 256*p + 15*p**2 - 29*p**2 = 0 for p.
-32
Let u(x) be the third derivative of -x**5/270 - x**4/12 - 20*x**3/27 + 116*x**2. Factor u(w).
-2*(w + 4)*(w + 5)/9
Suppose 10*n = 5*n. Let 3/4*u + 3/4*u**3 + n - 3/2*u**2 = 0. Calculate u.
0, 1
Suppose -3*x = -3*q - 3, 0*x - 4*q - 4 = -5*x. Suppose -2*t + 21 - 15 = x. Determine j so that 10 + 9*j**t + 2*j**2 - 11*j**3 - 10 + 4*j = 0.
-1, 0, 2
Find u such that 2079*u**3 - 1962*u**3 - 2*u**4 + 243*u**2 + 123*u - u**4 = 0.
-1, 0, 41
Suppose -50 = -i - 2*n, -100 = -3*i + 2*n + 34. What is g in 5*g**5 - i*g**3 - 8*g**2 - 5*g**4 + 15*g**4 - 2*g**2 + 41*g**3 = 0?
-2, -1, 0, 1
Suppose -111*y = -154*y + 43. Let x(t) be the first derivative of 5/2*t**4 + y + 2/3*t**3 + 0*t + 6/5*t**5 - t**2. What is i in x(i) = 0?
-1, 0, 1/3
Suppose 5*v - 11*v - 48 = 0. Let d(j) = -4*j**2 - 36*j - 24. Let b(r) = -r**2 - 12*r - 8. Let g(h) = v*b(h) + 3*d(h). Factor g(z).
-4*(z + 1)*(z + 2)
Suppose 24 = 11*w - 3*w. Find a such that 8*a**5 - a**4 - 9*a**5 + 2*a**w - a**2 + a**2 = 0.
-2, 0, 1
Let l(i) be the third derivative of 0*i**3 + 0 - 1/7*i**5 + 5/84*i**6 + 3/28*i**4 + 12*i**2 + 0*i. Factor l(j).
2*j*(5*j - 3)**2/7
Let r(t) be the third derivative of -t**8/30240 + t**7/11340 + 3*t**4/8 + t**2. Let u(i) be the second derivative of r(i). Suppose u(s) = 0. Calculate s.
0, 1
Let d = -375 + 22501/60. Let t(p) be the third derivative of 0*p + d*p**6 + 3*p**2 - 3/50*p**5 + 0 - 1/525*p**7 - 2/15*p**3 + 7/60*p**4. Factor t(g).
-2*(g - 2)*(g - 1)**3/5
Suppose 1288 = 4*h + 1304, 0 = -3*x - 2*h - 2. Factor 3/2*f - 1/4*f**3 + 0 - 1/4*f**x.
-f*(f - 2)*(f + 3)/4
Let r(j) be the third derivative of -j**2 + 0*j + 0 + 1/4*j**4 - 1/2*j**3 + 3/20*j**5. Factor r(s).
3*(s + 1)*(3*s - 1)
Let o(a) be the first derivative of -1/3*a**4 + 0*a + 0*a**2 - 8/15*a**5 + 0*a**3 - 2/9*a**6 + 5. Factor o(h).
-4*h**3*(h + 1)**2/3
Factor 0*z + z**2 - 1/4*z**4 + 0 + 3/4*z**3.
-z**2*(z - 4)*(z + 1)/4
Let w = 114 - 112. Let 3*n**2 - 2*n**2 - 12 - 40*n + 3*n**2 + 3*n**w = 0. Calculate n.
-2/7, 6
Solve -21*f**2 - 1377*f + 3*f**4 - 18*f**3 + 9*f**2 + 3*f**5 + 1401*f = 0.
-2, 0, 1, 2
Solve -2/3*j**3 + 0*j + 0 + 46/3*j**2 = 0 for j.
0, 23
Let v(x) be the second derivative of -x**7/525 - x**6/150 - x**5/150 + 23*x**2/2 + 18*x. Let u(q) be the first derivative of v(q). Find g, given that u(g) = 0.
-1, 0
Determine k so that k - 1/5*k**3 - 3/5*k**2 + 1/5*k**4 - 2/5 = 0.
-2, 1
Let f(s) be the first derivative of -s**5/100 - s**4/40 - 7*s**2 - 12. Let h(k) be the second derivative of f(k). Factor h(c).
-3*c*(c + 1)/5
Let a(c) be the third derivative of c**6/40 - c**5/30 + c**4/24 - 6*c**2. Let u be a(1). Factor n - 4*n**4 + 6*n**4 - 4*n**2 - 3*n - 2*n**5 + u + 4*n**3.
-2*(n - 1)**3*(n + 1)**2
Let d(n) be the first derivative of -n**6/2700 + n**5/150 - n**4/20 + 11*n**3/3 + 13. Let p(g) be the third derivative of d(g). Factor p(x).
-2*(x - 3)**2/15
Let h(o) = o**3 - 4*o**2 - 4*o - 8. Let u be h(5). Let m be -5*(25/9 + u). Solve 4/9*a + m*a**3 + 0 - 14/9*a**2 = 0.
0, 2/5, 1
Factor 6*v + 9*v + 2*v**2 + 2 + 11 - 3*v**2 - 3*v.
-(v - 13)*(v + 1)
Let v = 17 + -38. Let l be (-45)/(-60)*(-8)/v. Factor 3/7*h + 1/7*h**2 + l.
(h + 1)*(h + 2)/7
Let p(g) be the first derivative of -1/18*g**4 + 0*g**3 - 1/2*g**2 + 3 + 0*g - 1/90*g**5. Let u(d) be the second derivative of p(d). Factor u(t).
-2*t*(t + 2)/3
Find r such that 4*r**2 - 15*r - 1 + 26*r**3 + r**2 - 9 + 5*r**4 - 11*r**3 = 0.
-2, -1, 1
Let h(g) = -17*g**2 - 186*g + 8637. Let a(o) = 20*o**2 + 186*o - 8635. Let w(t) = 6*a(t) + 7*h(t). Factor w(p).
(p - 93)**2
Suppose -t - 19 = -5*o, 4*o + 0*t - 11 = 5*t. Factor 4/3*f**2 - 2/3*f**o - 4/3*f**3 - 2/3 + 2/3*f + 2/3*f**5.
2*(f - 1)**3*(f + 1)**2/3
Let m = 33 + -39. Let l be -2 + (m/(-3) - 0). Factor l*i**2 + 0 - 1/4*i**3 + 0*i.
-i**3/4
Let x(o) be the third derivative of -o**8/336 + o**7/35 - 13*o**6/120 + o**5/5 - o**4/6 + 21*o**2 - 2. Factor x(l).
-l*(l - 2)**2*(l - 1)**2
Suppose 0 = -3*v + 5*m + 29, -4*m - m = -2*v + 26. Find p, given that -v*p**2 + 19*p**3 - 11*p**3 - 4*p**4 - p**2 = 0.
0, 1
Let h = 71 - 51. Suppose -1414 + 5*y**3 + h*y**2 + 1414 = 0. Calculate y.
-4, 0
Let l be (1168/4530)/((-14)/(-21)). Let u = l + 2/151. Solve -1/5*m**3 - u - 1/5*m**4 + 1/5*m + 3/5*m**2 = 0 for m.
-2, -1, 1
Suppose -k = -2*v - 4*k + 96, 4*v = 3*k + 192. Suppose -v*g + 44*g = -16. Determine r so that -8/5*r**2 + 0 + 4/5*r + 0*r**3 + 8/5*r**g - 4/5*r**5 = 0.
-1, 0, 1
Suppose 0 = -7*l + 61 - 5. Solve -550*m**2 + 4*m + m**3 + l + m**3 + 542*m**2 - 6*m**3 = 0 for m.
-2, -1, 1
Let n be -61*(-6)/9 + (-4)/6. Suppose 51*w - 22 = n*w. Solve 2 + 6*t + 13/2*t**w + 1/2*t**4 + 3*t**3 = 0.
-2, -1
Let j(f) be the second derivative of -f**8/1120 - f**7/180 - f**6/180 + 2*f**4/3 - 5*f. Let d(g) be the third derivative of j(g). Factor d(a).
-2*a*(a + 2)*(3*a + 1)
Factor -87/7*x**2 - 48/7 + 18*x + 9/7*x**3.
3*(x - 8)*(x - 1)*(3*x - 2)/7
Let l = 4929/8638 - -1/1234. Let -l*s**2 + 0 - 2/7*s - 2/7*s**3 = 0. What is s?
-1, 0
Let m(r) = -32*r**2 + 21*r - 11. Let c(b) = 6*b**2 - 4*b + 2. Suppose 0 = 76*j - 72*j + 44. Let o(f) = j*c(f) - 2*m(f). Determine n, given that o(n) = 0.
0, 1
Suppose 8 = -y - 8*l, -1 + 2 = -4*y - l. Factor 2*d**3 + 1/2*d**2 - d - 3/2*d**4 + y.
-d*(d - 1)**2*(3*d + 2)/2
Let r be 282/423 - 8/(-42). Factor 8/7*x**2 - 2/7*x**3 - r*x + 0.
-2*x*(x - 3)*(x - 1)/7
Solve -288/7 - 1/7*g**3 - 132/7*g - 20/7*g**2 = 0 for g.
-8, -6
Let i(d) be the third derivative of 0 - 1/360*d**6 + 0*d - 1/9*d**3 + 1/90*d**5 + 16*d**2 + 1/72*d**4. What is x in i(x) = 0?
-1, 1, 2
Let h(z) = -2*z**2 + 9*z - 4. Let k be h(4). Let q = 937/91 - 132/13. Let 0 - 2/7*l**4 + k*l + 1/7*l**2 - q*l**3 = 0. Calculate l.
-1, 0, 1/2
Let 5/2*w**2 - 1/4*w**3 - 7/4*w - 9/2 = 0. What is w?
-1, 2, 9
Let s(b) = -b**2 + 8*b + 30. Let z be s(9). Let w be (-165)/(-84) - (-6)/z. Determine q, given that -1/4*q**4 + 7/4*q**3 - 15/4*q**2 + 0 + w*q = 0.
0, 1, 3
Let w(k) = -7*k**3 + 20*k**2 - 11*k - 2. Let f(o) = -27*o**2 + 14*o**3 - 6*o**2 + 6 - 1 + 22*o - 8*o**2. Let y(t) = 4*f(t) + 9*w(t). Factor y(r).
-(r - 1)**2*(7*r - 2)
Suppose -m - 5 = 4*k - 2, 3*m + 9 = -5*k. Let a be 1 + k + 65/(-15) + 4. Solve 2/3*c**3 - 7/3*c**2 + c**4 + 0 + a*c = 0 for c.
-2, 0, 1/3, 1
Let a(q) = -36*q**2 - 140*q - 32. Let r(f) = 7*f**2 + 28*f + 6. Let k(z) = 3*a(z) + 16*r(z). Determine y so that k(y) = 0.
-7, 0
Suppose -3*z - i + 18 = 0, 3*z - 3*i - i - 3 = 0. Factor 7*h**2 + h**3 - z*h**2 - 2*h**3 - 2*h + h**2.
-h*(h - 2)*(h - 1)
Let b(a) be the third derivative of -a**7/70 + a**6/40 + 69*a**2. Factor b(r).
-3*r**3*(r - 1)
Let l(w) be the third derivative of 0*w - 1/4*w**5 - 25/24*w**4 - 12*w**2 + 1/24*w**6 - 5/3*w**3 + 0 + 1/42*w**7. Factor l(c).
5*(c - 2)*(c + 1)**3
Let g(p) = 16*p**3 + 159*p**2 + 98*p - 39. Let k(z) = 32*z**3 + 319*z**2 + 194*z - 79. Let y(x) = 7*g(x) - 3*k(x). Suppose y(l) = 0. Calculate l.
-9, -1, 1/4
Let u(q) = -17*q**2 - 71*q + 11. Let d(h) = -9*h**2 - 36*h + 6. Let s(k) = -11*d(k) + 6*u(k). Factor s(r).
-3*r*(r + 10)
Let n = 243 + -728/3. Let m(a) be the second derivative of -1/5*a**5 - n*a**3 + 1/2*a**2 - 12*a - 7/12*a**4 + 0. Factor m(z).
-(z + 1)**2*(4*z - 1)
Let t = 803 + -12847/16. Let y(r) be the second derivative of -t*r**4 + 1/2*r**2 + 1/120*r**6 - 1/6*r**3 + 0 + 1/40*r**5 + 10*r. Factor y(s).
(s - 1)**2*(s + 2)**2/4
Let a(q) be the first derivative of -q**3/21 - q**2 - 24*q/7 - 155. Let a(t) = 0. Calculate t.
-12, -2
Factor 0 + 6/5*h**3 + 1/5*h**4 - 14/5*h - 9/5*h**2.
h*(h - 2