 d(r) = 0.
-1, 0, 1
Let r(u) = 2*u**5 - 3*u**3 - 257*u**4 - u**5 + 261*u**4. Let n(c) = 4*c**4 - 4*c**3. Let p(f) = -3*n(f) + 4*r(f). Find i such that p(i) = 0.
-1, 0
Let m(i) = -4*i**2 + 1. Let a(u) = 25*u**2 - 80*u + 315. Let x(j) = -a(j) - 5*m(j). Let x(w) = 0. Calculate w.
8
Let x = 502303/42 + -11959. Let s(p) be the second derivative of 10/21*p**3 + 1/7*p**2 + x*p**4 + 0 + 6*p. Factor s(m).
2*(5*m + 1)**2/7
Let d(j) be the first derivative of j**4/22 + 14*j**3/11 + 135*j**2/11 + 486*j/11 - 396. Factor d(s).
2*(s + 3)*(s + 9)**2/11
Suppose 8 = 5*m + c - 3, -3*m = -3*c - 21. Suppose -o - 2*o = -81. Factor 0*v - 6*v + o*v**2 - 22*v**m + v**3.
-3*v*(v - 1)*(7*v - 2)
Let w = 11/13 - 163/208. Let c(l) be the second derivative of 2*l + 0 + 1/2*l**3 + 3/2*l**2 + w*l**4. Factor c(k).
3*(k + 2)**2/4
Let j(v) = -1 - 7*v + v**2 - 11 + 0*v + 0. Let h be j(9). Suppose 20/3*u - h*u**2 + 4/3*u**3 - 2 = 0. What is u?
1/2, 1, 3
Let d(g) be the third derivative of g**8/12096 - g**7/756 + g**6/144 - g**5/4 + 31*g**2. Let t(f) be the third derivative of d(f). Factor t(j).
5*(j - 3)*(j - 1)/3
Let q = -2152 - -2156. Let j be 0/1 - (-1 - 1). Determine m, given that 4/3 - 8/3*m**j + 4/3*m**q + 4/3*m + 4/3*m**5 - 8/3*m**3 = 0.
-1, 1
Solve 120*j - 109 + 0 - 28 + 0*j**2 + 13 + 4*j**2 = 0 for j.
-31, 1
Let n be (-4)/(-7)*(-28)/(-8). Let c be ((-65)/10)/((-1)/n). Factor -15*v**3 + 13 + 20*v**2 - 4*v - c - v.
-5*v*(v - 1)*(3*v - 1)
Let l = 491 - 488. Let q(h) be the second derivative of 0 + 3/2*h**2 + 1/4*h**4 - 2*h - h**l. Determine y, given that q(y) = 0.
1
Let c(k) be the third derivative of -9*k**2 + 0*k + 3/20*k**6 + 3/2*k**4 + 2*k**3 + 13/20*k**5 + 0 + 1/70*k**7. Suppose c(d) = 0. Calculate d.
-2, -1
Let p(f) be the third derivative of 2*f**7/105 + 5*f**6/12 - 41*f**5/30 + 7*f**4/6 - f**2 - 23. Determine c, given that p(c) = 0.
-14, 0, 1/2, 1
Suppose 0*l = -2*s + 2*l, -l = 2*s - 3. Suppose 4*w - q = -5 + 18, -s = -w - 2*q. Factor 2/3*z - 2/9 - 4/9*z**2 - 2/9*z**5 - 4/9*z**w + 2/3*z**4.
-2*(z - 1)**4*(z + 1)/9
Suppose -3*u - 7 = -4*u. Let h(q) = 15*q**2 + 3*q - 5. Let n(d) = 14*d**2 + 4*d - 4. Let z(w) = u*n(w) - 6*h(w). What is p in z(p) = 0?
-1, -1/4
Let g(q) be the first derivative of 0*q**5 + q**2 + 1/15*q**6 - 5*q + 4 - 1/3*q**4 + 0*q**3. Let c(z) be the first derivative of g(z). Factor c(r).
2*(r - 1)**2*(r + 1)**2
Suppose -4*o - 3*j - 27 = 0, 163 - 109 = -4*o - 6*j. Factor -50/7*k**5 + 0 + o*k**2 - 8/7*k**3 + 0*k + 40/7*k**4.
-2*k**3*(5*k - 2)**2/7
Let t(z) = -2*z**3 - 4*z**2 - 4*z - 3. Let r be t(-2). Let b be (-1 + 2)/((r - 2)/6). Factor 0*l + 3/2*l**3 + 0 - 3/2*l**b.
3*l**2*(l - 1)/2
Let k(q) = q**3 + 34*q**2 - 106*q + 189. Let n be k(-37). Let 243*f**2 + n + 729/2*f**3 + 54*f = 0. Calculate f.
-2/9
Let f(a) = -a**3 + 2*a**2 - 9. Let m be -7 - -4 - (-1 - 0). Let i = -5 - m. Let s(d) = d**2 - d. Let k(g) = i*s(g) - f(g). Factor k(j).
(j - 3)**2*(j + 1)
Let f(d) be the second derivative of 3/10*d**5 - 1/2*d**3 + 0 - 1/10*d**6 - 1/14*d**7 + 1/2*d**4 - 3/2*d**2 + 21*d. Let f(g) = 0. What is g?
-1, 1
Suppose -9*u + 15 = -4*u. Let x(w) = -3*w**3 - 1. Let a be x(-1). Factor 2/9*d**u - 2/9*d - 2/9*d**4 + 2/9*d**a + 0.
-2*d*(d - 1)**2*(d + 1)/9
Let j(u) be the third derivative of -u**8/784 - 53*u**7/490 - 727*u**6/280 - 89*u**5/20 + 13*u**4 + 338*u**3/7 - 85*u**2 - 2. Determine k so that j(k) = 0.
-26, -1, 1
Let r(g) = -4*g**3 - 54*g**2 + 64*g - 20. Let v(y) = -19*y**2 - y**3 + 1 + 8*y**2 - 5 + 13*y. Let q(n) = 6*r(n) - 28*v(n). Factor q(j).
4*(j - 2)*(j - 1)**2
Suppose 122/13*p - 12/13 + 42*p**3 - 32*p**2 - 272/13*p**4 + 32/13*p**5 = 0. What is p?
1/4, 1, 6
Let y(k) be the third derivative of -15/8*k**4 - 25/6*k**3 + 1/24*k**6 + 0 - 1/4*k**5 + 0*k + 44*k**2. Solve y(q) = 0 for q.
-1, 5
Let v(y) be the third derivative of y**6/60 - 52*y**5/45 - 37*y**4/9 + 16*y**3 - 472*y**2 - 2. Solve v(r) = 0 for r.
-2, 2/3, 36
Factor -45*q**3 - 2*q - 36*q - 49*q**3 + 96*q**3 - 36*q**2.
2*q*(q - 19)*(q + 1)
Let d(l) be the third derivative of -l**5/60 - l**4/3 - 5*l**2. Let o be d(-8). Find n, given that n**2 - 1 + 0 + o + 0 = 0.
-1, 1
Let t be -24 + 23 - 48/(-18). Factor -1/3*d**3 + 5/3*d**2 - t + 1/3*d.
-(d - 5)*(d - 1)*(d + 1)/3
Let n be -2 - 2 - (3 - -1). Let u be 2*((-10)/(-25) - n/5). Factor 1/2*j**5 + 3/2*j**3 + 1/2*j**2 + 0*j + 3/2*j**u + 0.
j**2*(j + 1)**3/2
Factor 38/9*m - 2/9*m**3 + 40/9 - 4/9*m**2.
-2*(m - 4)*(m + 1)*(m + 5)/9
Let w(b) be the first derivative of b**6/240 + b**5/80 + 2*b**3/3 + 12. Let s(c) be the third derivative of w(c). Factor s(q).
3*q*(q + 1)/2
Let k(b) be the first derivative of 2*b**6/15 - b**5/5 - 2*b**4/3 - 3*b - 23. Let q(a) be the first derivative of k(a). Factor q(n).
4*n**2*(n - 2)*(n + 1)
Let u = 17 - 12. Suppose -4*s = 4*v - 3 - 9, -v = u*s - 15. Solve 2*k - 4*k**2 + 0*k**5 + 2*k**4 + 6 + 2*k**5 - 4*k**s - 4 = 0.
-1, 1
Let u(z) be the first derivative of z**4/8 - 8*z**3/3 + 29*z**2/4 - 7*z + 15. Find t, given that u(t) = 0.
1, 14
Let i(l) be the first derivative of 4*l**5/5 + 14*l**4 - 80*l**3/3 - 156*l**2 - 180*l - 26. What is v in i(v) = 0?
-15, -1, 3
Suppose 4*b + n - 10 = 0, 5*n = -4*b + 2*b + 14. Let r be 1/3 - (-4)/(-12). Let r + 0*m**b + 1/7*m - 1/7*m**3 = 0. What is m?
-1, 0, 1
Let n = -1299 + 9095/7. What is x in n*x**2 + 0 + 4/7*x = 0?
-2, 0
Suppose 0 = 4*j - 13 + 5. Let u = -237/2 - -122. Suppose -u*a**3 - 1/2*a - 5/2*a**j - 3/2*a**4 + 0 = 0. What is a?
-1, -1/3, 0
Let j(d) be the third derivative of -d**8/2520 + d**7/1575 + d**6/30 + 37*d**5/225 + 67*d**4/180 + 7*d**3/15 - 53*d**2 - 2*d. Determine f so that j(f) = 0.
-3, -1, 7
Let o = 7/2 + -3. Factor 1/2*p**4 + 0 - o*p**3 - 3/2*p - 5/2*p**2.
p*(p - 3)*(p + 1)**2/2
Let w(d) be the third derivative of 9/16*d**3 + 0 - 3/32*d**4 - 11*d**2 + 1/160*d**5 + 0*d. Suppose w(z) = 0. What is z?
3
Suppose 4*b = -150 + 158. Let -71*y**2 + 143*y**2 - 77*y**b + 5*y**3 = 0. Calculate y.
0, 1
Factor -1/2*o**2 + 1/6*o**3 - 2/3*o + 2.
(o - 3)*(o - 2)*(o + 2)/6
Let s(x) be the first derivative of -x**4/6 + 70*x**3/9 - 247*x**2/3 - 722*x + 242. Factor s(b).
-2*(b - 19)**2*(b + 3)/3
Solve -3/4*u**2 + 21/8*u - 3/8*u**3 - 3/2 = 0.
-4, 1
Let o(c) = -2*c**4 + c**3 - c**2 + 1. Let i(n) = 3*n**4 - 10*n**3 + 26*n**2 - 27*n + 9. Let z(h) = 4*i(h) + 4*o(h). Factor z(l).
4*(l - 5)*(l - 2)*(l - 1)**2
Let u(i) be the second derivative of -i**4/18 - 8*i**3/9 + 2*i + 29. Find o such that u(o) = 0.
-8, 0
Suppose 20*p = -1430 + 1470. Factor -8/9 - 2/3*f + 2/9*f**p.
2*(f - 4)*(f + 1)/9
Let t(o) be the first derivative of -o**8/168 - 2*o**7/105 - o**6/60 - 5*o**2 + 3. Let f(l) be the second derivative of t(l). Factor f(q).
-2*q**3*(q + 1)**2
Suppose -9*o**2 + 22*o + 36*o - 2*o**3 + 0*o**2 - 36*o + o**3 = 0. What is o?
-11, 0, 2
Let o(m) = 11*m**2 + 17*m + 2. Let c(w) = 23*w**2 + 36*w + 3. Let t(g) = 2*c(g) - 5*o(g). Solve t(f) = 0.
-1, -4/9
Let d(l) be the second derivative of -289*l**7/840 - 17*l**6/90 - l**5/30 + 11*l**3/2 + 26*l. Let q(w) be the second derivative of d(w). Factor q(u).
-u*(17*u + 2)**2
Let f = -224087/23 + 9743. Suppose 10/23*n**2 + f*n + 0 + 6/23*n**3 - 10/23*n**4 - 8/23*n**5 = 0. What is n?
-1, -1/4, 0, 1
Let r be (-80)/(-6) + (-32)/24. What is y in 4 + 2*y**5 + 2*y**3 - 12*y**4 + 3*y**5 + 8*y**2 - r*y + 6*y**3 - y**5 = 0?
-1, 1
Let c(r) = -3*r**4 - 300*r**3 - 290*r**2 + 302*r + 283. Let v(j) = -2*j**4 - 300*j**3 - 290*j**2 + 303*j + 277. Let z(n) = 3*c(n) - 2*v(n). Factor z(h).
-5*(h - 1)*(h + 1)**2*(h + 59)
Let z(n) be the second derivative of -40/3*n**3 + 13*n + 85/12*n**4 + 15/2*n**2 - n**5 + 0. Find x, given that z(x) = 0.
1/4, 1, 3
Let f(p) be the second derivative of -3*p**2 - 7/18*p**4 + 5/3*p**3 + 1/30*p**5 + 2*p + 0. Determine j so that f(j) = 0.
1, 3
Let l = -449 + 452. Let t(x) be the second derivative of 1/6*x**4 + 4*x**2 - l*x - 4/3*x**3 + 0. Find a, given that t(a) = 0.
2
Suppose -338*n = -291*n - 235. Factor 160/9*x**2 - 2/9*x**n - 160/9*x + 64/9 - 80/9*x**3 + 20/9*x**4.
-2*(x - 2)**5/9
Let z = 19 + -17. Factor 6*s - 3*s + 22*s**2 - z + 0*s + 17*s.
2*(s + 1)*(11*s - 1)
Let x(q) be the first derivative of q**4/3 + q**3/2 - q**2/2 + 7*q - 5. Let n(b) be the first derivative of x(b). Factor n(y).
(y + 1)*(4*y - 1)
Let q(p) = -3*p**5 + p**4 + 3*p**3 - p**2 - 7*p. Let w(o) = 