d derivative of r**7/70 + 3*r**5/20 + 5*r**4/24 - r**3/3 + 2*r**2. Let b(n) = -5*a(n) + i(n). Factor b(j).
-2*(j - 1)**2*(j + 1)**2
Let b(s) = 2*s**3 + 10*s**2 - 4*s - 36. Let y(n) = n**3 + n**2. Let f(m) = -3*b(m) + 3*y(m). Find o such that f(o) = 0.
-9, -2, 2
Let 3/2*q**5 + 9*q**2 - 9/2 - 9/2*q**4 + 3/2*q - 3*q**3 = 0. Calculate q.
-1, 1, 3
Let j(t) be the second derivative of 0*t**2 + 19*t + 0 + 13/30*t**5 - 7/90*t**6 - 1/3*t**3 - 13/36*t**4. Determine k, given that j(k) = 0.
-2/7, 0, 1, 3
Let g(m) = -m + 13. Let w be g(9). Factor 2*x**w - 5*x**2 + x**2 - x**4.
x**2*(x - 2)*(x + 2)
Solve 0*g**2 - 12/5*g**3 + 0 + 4*g**4 - 3/5*g**5 + 0*g = 0 for g.
0, 2/3, 6
Let k(w) be the first derivative of 0*w + 4/5*w**5 + 5*w**4 + 32/3*w**3 + 8*w**2 + 7. Factor k(g).
4*g*(g + 1)*(g + 2)**2
Suppose 155*p = 82*p + 77*p. Let j(m) be the second derivative of -1/36*m**4 + p - 3/40*m**5 - 2*m + 1/6*m**2 + 1/4*m**3. Factor j(c).
-(c - 1)*(c + 1)*(9*c + 2)/6
Let n be (-1 + (-86)/6)*(-42)/(-8). Let t = n + 81. Find v, given that 0 + 1/2*v + t*v**2 - 1/2*v**4 - 1/2*v**3 = 0.
-1, 0, 1
Find v such that 0 + 0*v + 1/6*v**4 + 1/6*v**2 - 1/3*v**3 = 0.
0, 1
Let l(w) = 9*w**3 - 5*w**2 - 9*w - 2. Let f(g) = g**3 - g**2 - g. Let q(p) = -p**2 - p + 6. Let a be q(-5). Let h(k) = a*f(k) + 2*l(k). Factor h(u).
4*(u - 1)*(u + 1)**2
Find i, given that 108/7*i + 2916/7 + 1/7*i**2 = 0.
-54
Factor 9/5*q**3 + 0 + 18/5*q**2 - 24/5*q - 3/5*q**4.
-3*q*(q - 4)*(q - 1)*(q + 2)/5
Let f = 172 + -135. Let s be 31 - f - 168/(-22). Let 2/11*b**4 + s*b**2 - 10/11*b**3 - 14/11*b + 4/11 = 0. Calculate b.
1, 2
Let c(p) = p**5 + 4*p**4 + 2*p**3 - 4*p**2 - 6*p. Let j(v) = -2*v**5 - 7*v**4 - 3*v**3 + 7*v**2 + 10*v. Let g(h) = -5*c(h) - 3*j(h). Factor g(s).
s**2*(s - 1)*(s + 1)**2
Solve 18*a - 1/2*a**2 - 162 = 0 for a.
18
What is c in 1/2*c**2 - 3/2*c + 1 = 0?
1, 2
Let o(z) be the third derivative of z**6/480 - z**5/48 - z**4/96 + 5*z**3/24 - 15*z**2 - 2. Suppose o(a) = 0. What is a?
-1, 1, 5
Let x = -56 + 65. Let c = 12 - x. Factor 0 + 2/5*r**4 + 0*r**c + 0*r**2 + 4/5*r**5 + 0*r.
2*r**4*(2*r + 1)/5
Determine d, given that -59/6*d**3 + 140*d**2 + 1/6*d**4 + 150*d + 0 = 0.
-1, 0, 30
Let b(j) be the third derivative of 0*j**3 - 1/30*j**6 + 0*j + 0 + 29*j**2 + 2/15*j**5 + 1/2*j**4. Factor b(o).
-4*o*(o - 3)*(o + 1)
Let h(w) = -w - 24. Let u(x) = x**2 + 6*x - 27. Let y be u(-6). Let z be h(y). Find d, given that 0*d + 0 - 1/3*d**z + 2/3*d**2 = 0.
0, 2
Let z be (-13)/(-3) - 6/18. Factor 5*x**z + 16*x - 12*x**3 - 4*x**4 + 3*x**4.
4*x*(x - 2)**2*(x + 1)
Suppose 28*g = 157 - 73. Let z(m) be the first derivative of 11 - 2/7*m + 0*m**4 + 0*m**2 + 4/21*m**g - 2/35*m**5. What is k in z(k) = 0?
-1, 1
Let b(g) be the third derivative of g**6/72 + g**5/3 + 10*g**4/3 + g**3/3 + 5*g**2. Let o(w) be the first derivative of b(w). Let o(j) = 0. Calculate j.
-4
Let p(g) be the third derivative of 0*g + 0*g**4 + 16/27*g**3 - 4/135*g**5 + 0*g**6 + 0 + 1/945*g**7 + 25*g**2. Factor p(k).
2*(k - 2)**2*(k + 2)**2/9
Let l(i) be the third derivative of i**8/392 + 29*i**7/735 + 31*i**6/210 + i**5/5 - i**4/84 - i**3/3 + 216*i**2. Find r such that l(r) = 0.
-7, -1, 1/3
Let a be -1 + 13/4 + (-36)/24. Let s = -43/10 + 24/5. Factor a*k + 1/4*k**2 + s.
(k + 1)*(k + 2)/4
Let h(m) be the first derivative of m**4/14 + 2*m**3/21 - m**2/7 - 2*m/7 + 10. Factor h(u).
2*(u - 1)*(u + 1)**2/7
Let j = 88 + -70. Let 1 + 43*v - v**2 + 6*v**2 - j*v + 19 = 0. Calculate v.
-4, -1
Let p(q) = q**2 + q. Let o(v) be the first derivative of -3/4*v**4 - 9 + 0*v + v**2 + 2/3*v**3. Let g(w) = o(w) - 2*p(w). Find c, given that g(c) = 0.
0
Let c = 720 - 720. Let t(v) be the second derivative of v + 0*v**3 - 1/10*v**6 + 0*v**2 + 3/20*v**5 + 1/4*v**4 - 1/14*v**7 + c. Let t(z) = 0. What is z?
-1, 0, 1
Let a(z) = -2*z**2 + 34*z - 64. Let u(c) = -c**2 + 17*c - 34. Let j(w) = -4*a(w) + 10*u(w). Let j(n) = 0. Calculate n.
3, 14
Let n(t) be the first derivative of -27 + 5/3*t**3 - 25*t**2 + 125*t. Factor n(l).
5*(l - 5)**2
Let t be 2 + 1 - -3 - -1. Suppose -4*h + t = 5*z, 4*h + 7*z - 9 = 4*z. Solve 3*w - 1 - 3*w**3 + 6*w**4 + w**5 - 2*w**2 + w**3 - 2*w**5 - h*w**4 = 0 for w.
-1, 1
Let o(f) be the first derivative of f**5/3 + 5*f**4/12 - 5*f**3/9 - 5*f**2/6 + 437. Determine d so that o(d) = 0.
-1, 0, 1
Let y(k) be the third derivative of -k**10/15120 + k**9/22680 + k**8/5040 - 5*k**4/12 + 7*k**2. Let t(x) be the second derivative of y(x). Factor t(b).
-2*b**3*(b - 1)*(3*b + 2)/3
Let o(t) be the second derivative of -t**6/10 + 9*t**5/10 - 13*t**4/4 + 6*t**3 - 6*t**2 - 29*t - 2. Suppose o(y) = 0. Calculate y.
1, 2
Let l(u) be the first derivative of u**5/90 + 5*u**4/18 + 25*u**3/9 - 17*u**2 - 16. Let i(y) be the second derivative of l(y). Factor i(a).
2*(a + 5)**2/3
Let n = -203 + 209. Let o(m) be the first derivative of -12*m + 8*m**3 + n - 5/2*m**4 + 11*m**2. Find z such that o(z) = 0.
-1, 2/5, 3
Let x(t) be the first derivative of t**3/6 + 5*t**2 - 21*t/2 - 588. What is w in x(w) = 0?
-21, 1
Let c(f) = -408*f**3 + 179*f**2 - 16*f. Let k(q) = -204*q**3 + 90*q**2 - 8*q. Suppose 4*u + 20 = -0*u. Let i(j) = u*k(j) + 2*c(j). Factor i(z).
4*z*(3*z - 1)*(17*z - 2)
Let m be 38/18 - (1/1 + 1). Let i(k) be the third derivative of 0 + 0*k + 1/3*k**3 - k**2 + 1/90*k**5 + m*k**4. Factor i(n).
2*(n + 1)*(n + 3)/3
Let s be (-13)/(520/(-64))*(-5)/(-2). Factor -1/5*x**s + 1/5*x**5 + 0*x - 1/5*x**3 + 0 + 1/5*x**2.
x**2*(x - 1)**2*(x + 1)/5
Solve 88*i + 4/3*i**2 - 2/3*i**3 + 336 = 0 for i.
-6, 14
Let m(d) = -24*d - 4 - 13 + d**2 + 28*d. Let o be m(-7). Suppose 20*n**4 + 4*n**3 - n - 39*n**4 + 21*n**o - 3*n**5 - 2*n**2 = 0. What is n?
-1, -1/3, 0, 1
Let h(n) be the second derivative of 0*n**6 + 2/5*n**5 - 1/21*n**7 - 2*n**2 - n**3 + 0 + 2*n + 1/3*n**4. Find r, given that h(r) = 0.
-1, 1, 2
Let q(z) be the first derivative of 2*z**3/15 + 13*z**2/5 - 42. Factor q(u).
2*u*(u + 13)/5
Let j(k) be the third derivative of -k**6/150 + 101*k**5/75 - 260*k**4/3 + 1000*k**3/3 + k**2 + 192*k. Factor j(a).
-4*(a - 50)**2*(a - 1)/5
Let w(s) be the third derivative of -s**9/15120 + s**7/420 - s**6/90 - s**5/12 - 12*s**2. Let d(n) be the third derivative of w(n). Factor d(z).
-4*(z - 1)**2*(z + 2)
Let j be 5 + 1426/(-115) + 8. Factor 4/5*k + 0 - j*k**3 - 1/5*k**4 + 0*k**2.
-k*(k - 1)*(k + 2)**2/5
Let p(w) be the third derivative of -1/1785*w**7 + 0 + 1/255*w**5 + 0*w**4 + 0*w + 0*w**6 - 4*w**2 - 1/51*w**3. Factor p(f).
-2*(f - 1)**2*(f + 1)**2/17
Let c(a) = 2*a**2 - 14*a + 12. Let n be c(6). Let u be 36/4 - (0 - n). Find y such that 2*y**4 - 3*y - y**4 - u*y**2 - 9*y**3 - 4*y**4 = 0.
-1, 0
Let c(g) = g**2 + g. Let p = 49 - 51. Let t(a) = -2*a**3 - 16*a**2 - 14*a. Let v(w) = p*t(w) - 36*c(w). Find z, given that v(z) = 0.
-1, 0, 2
Suppose 0*z + 7*z = 0. Let q(s) be the first derivative of -2 + 0*s + 0*s**2 - 1/6*s**6 + z*s**4 - 3/5*s**5 + 4/3*s**3. What is b in q(b) = 0?
-2, 0, 1
Let 2/7*y**2 + 0 - 26/7*y = 0. Calculate y.
0, 13
Factor -21/4 - 3/8*t**2 - 45/8*t.
-3*(t + 1)*(t + 14)/8
Let d = -183/43 - -1087/215. Find u, given that d*u**3 + 4*u**2 + 0 + 0*u = 0.
-5, 0
Let f(l) be the third derivative of l**7/70 - 3*l**6/40 + l**5/10 + 253*l**2. Factor f(c).
3*c**2*(c - 2)*(c - 1)
Let y(s) = -s - 1. Let p be y(-4). Suppose 2*q - 15 = -3*q. Suppose 3*v**q + 5*v**p - 5*v**3 - 3*v = 0. What is v?
-1, 0, 1
Let h = 32 - 23. Factor h*c**2 - 14*c**3 + 10*c**2 - 174*c**4 + 178*c**4 + 2 - c**2 - 10*c.
2*(c - 1)**3*(2*c - 1)
Let s = -1146 - -2293/2. Let -1 + 5*l**2 + 2*l**3 - 4*l**4 + s*l - 5/2*l**5 = 0. Calculate l.
-1, 2/5, 1
Let i(y) be the first derivative of y**5/20 + 9*y**4/16 + 2*y**3 + 2*y**2 - 83. Suppose i(m) = 0. Calculate m.
-4, -1, 0
Let n(q) = -15*q**2 - 48 + 26 + 2 - 40*q. Let k(o) = -15*o**2 - 40*o - 20. Let a(d) = 2*k(d) - 3*n(d). Factor a(y).
5*(y + 2)*(3*y + 2)
Let n = 330 - 327. Factor -5/4*l - 5/4 + 5/4*l**2 + 5/4*l**n.
5*(l - 1)*(l + 1)**2/4
Let i(u) be the third derivative of -1/180*u**5 - 5*u**2 + 0*u + 7/18*u**3 + 1/12*u**4 + 0. Factor i(j).
-(j - 7)*(j + 1)/3
Let t(j) be the second derivative of j**9/10584 + j**8/2940 - j**6/630 - j**5/420 + 7*j**3/6 - 7*j. Let h(v) be the second derivative of t(v). Factor h(f).
2*f*(f - 1)*(f + 1)**3/7
Suppose 24 = -2*q - 2*q. Let n(d) = -d**3 - 7*d**2 -