 = -74 - -76. Let f(u) be the second derivative of -1/10*u**5 + 0 + 2*u**2 + z*u + 0*u**4 + u**3. Factor f(m).
-2*(m - 2)*(m + 1)**2
Let s = 47 - 26. Let c = s + -16. Factor 0*y + 2/9*y**3 + 0 - 2/9*y**c + 2/9*y**4 - 2/9*y**2.
-2*y**2*(y - 1)**2*(y + 1)/9
Let b(t) be the first derivative of t**3/5 - 3*t**2 + 15*t - 18. Determine k so that b(k) = 0.
5
Let q(b) = -b**3 + b**2 - 5. Let d be q(0). Let t = 7 + d. Let 4*p**4 + 4*p**t - 6*p**3 - 2*p**2 + 2*p**4 + 0*p**2 - 2*p**5 = 0. What is p?
0, 1
Let h(c) be the first derivative of 0*c**3 - 1/10*c**2 - 3 + 3/10*c**4 + 0*c + 8/25*c**5 + 1/10*c**6. Factor h(u).
u*(u + 1)**3*(3*u - 1)/5
Let l = 184 - 1286/7. Factor 0 + 8/7*j**5 + 0*j + 10/7*j**3 + l*j**2 + 16/7*j**4.
2*j**2*(j + 1)*(2*j + 1)**2/7
Let o be 8/12 + (-3)/18. Determine h, given that 0 - 1/4*h**4 - 1/4*h**2 + 0*h + o*h**3 = 0.
0, 1
Let n(l) be the third derivative of -l**8/672 - l**7/210 + l**6/320 + 3*l**5/160 + 11*l**2. Find y, given that n(y) = 0.
-3/2, 0, 1
Suppose -5*h + 19 - 9 = 0. Factor 0 - 1/2*g**4 - 1/2*g**h + 0*g + g**3.
-g**2*(g - 1)**2/2
Let p(f) = 12*f**3 - f**2. Let j be p(1). Suppose -j*a = -4*a. Factor -3/5*o**3 + 0*o + a*o**2 + 0.
-3*o**3/5
Let v(k) be the first derivative of k**5/100 - k**4/12 + 4*k**3/15 - 2*k**2/5 + 3*k - 3. Let w(h) be the first derivative of v(h). Factor w(f).
(f - 2)**2*(f - 1)/5
Let o = 2 + 2. Factor -8*b**o - 2*b + 15*b**3 - 7*b**3 + 6*b**3 - 4*b**2.
-2*b*(b - 1)**2*(4*b + 1)
Suppose 10*x**2 + 14/5*x**4 - 38/5*x**3 - 2/5*x**5 - 32/5*x + 8/5 = 0. Calculate x.
1, 2
Let p(k) = k**2 + k. Let u(f) be the first derivative of -f**3 - 7*f**2/2 + 5. Let j(n) = -4*p(n) - u(n). Factor j(a).
-a*(a - 3)
Factor -2*i**5 - 4/5*i**3 + 14/5*i**4 + 0 + 0*i + 0*i**2.
-2*i**3*(i - 1)*(5*i - 2)/5
Let u = -125 - -627/5. Factor 2/5 - 2/5*p**2 - 2/5*p**3 + u*p.
-2*(p - 1)*(p + 1)**2/5
Let q = -8 + 10. Factor -2*k**5 + q*k**4 + 6*k**3 - 7*k**5 - 5*k**4.
-3*k**3*(k + 1)*(3*k - 2)
Solve 12/7*m - 12/7*m**3 - 16/7*m**2 - 2/7 + 18/7*m**4 = 0.
-1, 1/3, 1
Let a(k) be the first derivative of k**3/3 - k**2/2 - 2*k - 4. Let l be a(2). Let -1/2*y + y**2 + l - 1/2*y**3 = 0. Calculate y.
0, 1
Let c(u) = -u - 3*u**2 - 2*u**2 + 0*u**2 + 1. Let g be (-2)/(-3 + 52/16). Let t(k) = 14*k**2 + 4*k - 2. Let f(q) = g*c(q) - 3*t(q). Factor f(j).
-2*(j + 1)**2
Let p = 4561/830 + 2/415. Factor -9/2*r**2 - p*r - 1.
-(r + 1)*(9*r + 2)/2
Solve -1/2*n - 1/6 - 1/3*n**2 = 0.
-1, -1/2
Solve 1/2*r**3 - 9/2*r - 3/2*r**2 - 5/2 = 0.
-1, 5
Let c be (-2)/(-8) + (-69)/(-12). Suppose 5*d - 3*l = 22, 0 = -l + 2 - c. Factor 0*m**d + 0 + 1/2*m - 1/2*m**3.
-m*(m - 1)*(m + 1)/2
Let z = 8/7 - 73/70. Let w(f) be the first derivative of 0*f + 2 + 1/2*f**2 + 0*f**4 + 1/2*f**3 - z*f**5. Factor w(n).
-n*(n - 2)*(n + 1)**2/2
Solve 2/3 + 3*d + 9*d**5 + 0*d**4 - 12*d**3 - 2/3*d**2 = 0.
-1, -1/3, 2/3, 1
Determine l so that 1 + 14*l + 115/4*l**2 = 0.
-2/5, -2/23
Let r = -43/4069 - -31553/142415. Let x = r + -1/91. Let 0 - 2/5*j - 3/5*j**2 - x*j**3 = 0. Calculate j.
-2, -1, 0
Suppose 1/5*u + 0*u**2 + 1/10*u**4 - 1/5*u**3 - 1/10 = 0. Calculate u.
-1, 1
Let a(r) = -r**2. Let f = 4 + -3. Let u(v) = -4*v**2 + 2*v. Suppose -2*h - h + 7 = 2*q, 5*h = 2*q + 33. Let k(d) = f*u(d) + h*a(d). Factor k(y).
-y*(9*y - 2)
Let m(y) be the second derivative of 4*y - 3/20*y**5 - 1/2*y**4 + 1/2*y**3 + 3*y**2 + 0. Solve m(p) = 0.
-2, -1, 1
Let r(c) be the second derivative of -c**4/12 - c**3/3 - 8*c. Factor r(z).
-z*(z + 2)
Let x = 22923/5 + -4626. Let a = -41 - x. Let 2/5*s**4 - 2/5*s + 2/5*s**3 - a*s**2 + 0 = 0. What is s?
-1, 0, 1
Let u(t) be the first derivative of t**6/360 - t**3/3 + 5. Let i(r) be the third derivative of u(r). Suppose i(q) = 0. What is q?
0
Suppose 6 = 5*g - 9. Suppose -12*i**2 + 11*i**2 - g*i + 0 - 2 = 0. Calculate i.
-2, -1
Let x(g) be the second derivative of g**6/135 - g**4/54 - 2*g. Determine h, given that x(h) = 0.
-1, 0, 1
Find n such that 1/3*n**3 + 1 + 1/3*n**2 - 5/3*n = 0.
-3, 1
Let l(q) = -2*q**4 - 4*q**3 + 4*q + 2. Let t(o) = 4*o**4 + 8*o**3 + o**2 - 8*o - 5. Let x(m) = -5*l(m) - 2*t(m). Factor x(n).
2*n*(n - 1)*(n + 1)*(n + 2)
Let t(n) = 187*n**3 - 37*n**2 - 20*n - 1. Let r(y) = -280*y**3 + 56*y**2 + 30*y + 2. Let l(a) = -5*r(a) - 8*t(a). Suppose l(b) = 0. What is b?
-1/3, 1/4
Let s(u) be the third derivative of 1/42*u**4 + 0*u**3 + 0 + 1/210*u**5 + 6*u**2 - 1/420*u**6 + 0*u. Solve s(t) = 0.
-1, 0, 2
Let a(w) be the third derivative of -1/90*w**7 + 0*w**3 + 0*w + 0 - 1/5*w**5 + 1/12*w**6 + 1/9*w**4 - w**2. Factor a(l).
-l*(l - 2)**2*(7*l - 2)/3
Find f, given that 0*f - 2*f**2 - 5*f + 3*f = 0.
-1, 0
Let b(z) be the first derivative of -1/4*z**4 - 1 + 2/9*z**3 + 1/6*z**2 + 0*z. Factor b(j).
-j*(j - 1)*(3*j + 1)/3
Let r be (-16)/(-72) + (25/9 - 1). Factor -4/11*w**3 + 2/11*w**5 + 2/11*w - 2/11*w**4 + 4/11*w**r - 2/11.
2*(w - 1)**3*(w + 1)**2/11
Let y = 274 + -272. Factor -1/4 - 3/4*a**y - 1/4*a**3 - 3/4*a.
-(a + 1)**3/4
Let l be (1 + -4)*(-24)/36. Let o = -1 - -4. Suppose -4*a**3 + 3*a**3 + l*a**4 - o*a**4 = 0. Calculate a.
-1, 0
Factor -i**4 - 4*i**2 + 3*i**4 - 3*i - 4*i**3 + 7*i + 2*i**4.
4*i*(i - 1)**2*(i + 1)
Suppose 2*q + 10 = -2*x, -3 = -4*q - 23. Let k be 2 - (x - 1) - 0. Solve -1/2 + 1/2*y**2 + y - y**k = 0 for y.
-1, 1/2, 1
Let p = -3/35 + 2/7. Find n such that 2/5*n**4 + 0 - p*n**5 - 2/5*n**2 + 0*n**3 + 1/5*n = 0.
-1, 0, 1
Let k(v) be the second derivative of v**5/36 - 2*v**4/27 + v**3/54 + v**2/9 - 12*v. Factor k(b).
(b - 1)**2*(5*b + 2)/9
Let r(z) be the second derivative of -z**8/10080 - z**7/1260 - z**6/360 - z**5/180 + z**4/12 - z. Let m(g) be the third derivative of r(g). Factor m(u).
-2*(u + 1)**3/3
Let v = -2 + 4. Determine c so that c + c + 2*c**3 - v*c = 0.
0
Let r = -148/3 + 50. Suppose r*v + 1/3 + 1/3*v**2 = 0. What is v?
-1
Let j(y) be the first derivative of -y**8/560 + y**7/175 - y**6/200 - 2*y**2 - 3. Let t(q) be the second derivative of j(q). Factor t(u).
-3*u**3*(u - 1)**2/5
Let u(p) be the third derivative of 7*p**6/120 - 31*p**5/90 + 11*p**4/18 - 4*p**3/9 - 4*p**2. Factor u(g).
(g - 2)*(3*g - 2)*(7*g - 2)/3
Let t(b) = 2*b. Suppose 3*r + 66 = -0*r. Let d = -13 - r. Let i(f) = -f**2 - 9*f. Let o(k) = d*t(k) + 2*i(k). Factor o(q).
-2*q**2
Let s(z) be the third derivative of z**8/20160 - z**7/5040 - z**6/360 + z**5/30 - 2*z**2. Let n(k) be the third derivative of s(k). Factor n(x).
(x - 2)*(x + 1)
Let z(h) be the third derivative of 0*h**4 - 3*h**2 + 0 - 1/2*h**3 + 1/180*h**6 + 1/60*h**5 + 0*h. Let p(q) be the first derivative of z(q). Factor p(l).
2*l*(l + 1)
Let d be ((-151)/302)/((0 - 3) + 1). Suppose v**2 + d*v**3 + 5/4*v + 1/2 = 0. What is v?
-2, -1
Let p(g) = -7*g + g**2 + 3*g + 5 + 7*g. Let n(x) = -8*x - 2*x**2 + 0*x**2 + 0*x**2 - 14. Let b(f) = -3*n(f) - 8*p(f). Factor b(d).
-2*(d - 1)*(d + 1)
Find s, given that 16*s + 12*s**4 - 2*s**5 - 8 - 2*s**2 - 14*s**3 - 2*s**4 + 0*s**4 = 0.
-1, 1, 2
Let h(v) be the third derivative of -v**5/15 + v**4/6 + 10*v**2. Determine u, given that h(u) = 0.
0, 1
Let h(x) = -4*x - 29. Let l be h(-8). Let q(s) be the first derivative of -2 + 3/8*s**2 + 0*s**l - 1/16*s**4 + 1/2*s. Solve q(k) = 0.
-1, 2
Let m(u) = -u**3 - 3*u**2 + 2*u. Let q(s) = -2*s**3 - 4*s**2 + 3*s. Suppose -h + 12 = -5*h. Let r(a) = h*m(a) + 2*q(a). Factor r(b).
-b**2*(b - 1)
Let w(t) be the third derivative of -7*t**5/30 - 13*t**4/48 + t**3/2 + 2*t**2. Determine j, given that w(j) = 0.
-3/4, 2/7
Suppose -53*d - 60 = -73*d. Factor 0*b + 0 - 2/15*b**2 + 2/15*b**d.
2*b**2*(b - 1)/15
Let l be -1*(2/(-6) + 2/6). Let f(p) be the first derivative of -1/4*p**2 + 1 + 1/12*p**3 + l*p. Factor f(s).
s*(s - 2)/4
Let r(a) be the third derivative of 3/28*a**8 + 4/15*a**5 + 0*a + 2/5*a**7 + 0*a**3 + 0 - a**2 + 0*a**4 + 8/15*a**6. Determine t so that r(t) = 0.
-1, -2/3, 0
Let k be -4 + 77/14 + (-13)/10. Let 1/5 - 2/5*j + k*j**2 = 0. What is j?
1
Let g(h) be the third derivative of 0*h + 1/210*h**5 + 0 - 1/84*h**4 + 0*h**3 - 2*h**2. Factor g(y).
2*y*(y - 1)/7
Let c(h) = 2*h**2 - 22*h. Suppose -5*t + 25 = 0, -2*s - 4*t + 240 = 3*s. Let v(z) = z. Let n(r) = s*v(r) + 2*c(r). Find p, given that n(p) = 0.
0
Let g be (-2 - (-12)/5)/((-160)/(-600)). Determine u, given that g*u**2 - 3*u + 0 = 0.
0, 2
Let h = 179581/5 + -35765. Let y = -148 + h. Factor y*v +