c(v) be the third derivative of v**6/1440 - v**5/480 - v**3/2 + 2*v**2. Let r(f) be the first derivative of c(f). Factor r(h).
h*(h - 1)/4
Suppose 0 = 2*f + 9*a + 9, 4*a + 4 = 11*f - 10*f. Determine c so that f*c + 2/3*c**2 - 1/3*c**5 + 0 + 1/3*c**3 - 2/3*c**4 = 0.
-2, -1, 0, 1
Let r(z) be the first derivative of -z**8/672 + z**6/60 + 19*z**2 + 25. Let p(g) be the second derivative of r(g). What is b in p(b) = 0?
-2, 0, 2
Let t(r) be the second derivative of r**4/6 - 3*r**3 + 8*r**2 + 5*r + 10. Let t(c) = 0. What is c?
1, 8
Let w(t) be the second derivative of -t**6/6 - 2*t**5 - 85*t**4/12 - 25*t**3/3 - 19*t + 2. Let w(i) = 0. What is i?
-5, -2, -1, 0
Factor -14*v**2 + 96 + 82*v**2 + 4*v**3 + 2*v**3 + 13*v**2 + 156*v - 3*v**4 - 12.
-3*(v - 7)*(v + 1)*(v + 2)**2
Suppose -3*s = -5*z + 15, -4*z + 2 = 3*s - 10. Factor -32*o**z + 12*o**3 + 7*o + 13*o - 20 + 5*o**4 + 15*o**2.
5*(o - 2)**2*(o - 1)*(o + 1)
Let b(n) be the first derivative of 6*n**5/35 - 2*n**4 + 158*n**3/21 - 6*n**2 - 144*n/7 + 826. Suppose b(q) = 0. Calculate q.
-2/3, 3, 4
Let k be (62/(-124))/(7/(-2)). Let o(g) be the first derivative of -6 + 0*g + 3/7*g**2 - k*g**3. Solve o(j) = 0 for j.
0, 2
Let f(b) = 251*b**2 - 104*b + 16. Let x(t) = -253*t**2 + 103*t - 17. Let c(g) = 5*f(g) + 4*x(g). Factor c(u).
3*(9*u - 2)**2
Let p(u) be the first derivative of u**6/10 - 78*u**5/25 - 261*u**4/20 - 4. Factor p(i).
3*i**3*(i - 29)*(i + 3)/5
Let s(j) = -4*j**2 - 4*j - 6. Let b(r) = r**2 - 53*r + 27*r + 26*r. Let i(c) = -6*b(c) - s(c). Factor i(n).
-2*(n - 3)*(n + 1)
Solve 0 + 1/10*a**5 + 2/5*a**2 - 3/5*a**3 - 1/10*a**4 + 4/5*a = 0.
-2, -1, 0, 2
Let b(s) = 30*s - 448. Let i be b(15). Factor 4/3*f**4 - 8/3*f**3 - 4/3 + 8/3*f + 0*f**i.
4*(f - 1)**3*(f + 1)/3
Suppose 0 = 3*r - 42 - 12. Let x = r + -18. Factor 0*d**4 + x*d**2 + 0 + 2/11*d**5 + 0*d - 2/11*d**3.
2*d**3*(d - 1)*(d + 1)/11
Suppose -12*j + 5*k = -7*j + 10, 0 = j + 5*k - 34. Suppose -13/4*u**3 - 1/4*u**5 + 0 - 3/2*u**j - u - 3*u**2 = 0. Calculate u.
-2, -1, 0
Determine a so that -19 - 13 - 13*a**2 - 6*a + 8 + 16*a**2 = 0.
-2, 4
Factor -3/7 - 3/7*z**2 + 6/7*z.
-3*(z - 1)**2/7
Let o(r) be the first derivative of -r**6/27 + 2*r**5/15 + r**4/2 + 10*r**3/27 - 181. Suppose o(b) = 0. Calculate b.
-1, 0, 5
Let a(m) be the third derivative of 0*m + 0*m**4 + 0*m**3 + 0 - 20*m**2 - 1/360*m**6 - 1/180*m**5. Factor a(v).
-v**2*(v + 1)/3
Let q(a) = -a - 2*a + 3 + 4*a - 10. Let x be q(12). What is r in -6*r**2 + 5*r**3 - 2 - r**4 + 0*r**3 - x*r + 12*r - 3*r**2 = 0?
1, 2
Let t be 1 + 25/5 + -1. Let i(m) be the first derivative of 0*m**4 - 2/7*m - 2/35*m**t + 0*m**2 + 4/21*m**3 - 2. Factor i(j).
-2*(j - 1)**2*(j + 1)**2/7
Let x(z) be the third derivative of z**6/180 - z**5/20 + z**4/6 + 7*z**3/3 - 12*z**2. Let h(v) be the first derivative of x(v). Factor h(m).
2*(m - 2)*(m - 1)
Let 5*a**2 + 20*a**2 - 87656*a**3 + 87657*a**3 = 0. What is a?
-25, 0
Let j(a) be the third derivative of -5*a**8/336 - 4*a**7/21 + a**6/3 + 8*a**5 - 30*a**4 + 9*a**2 - 5*a. Let j(s) = 0. Calculate s.
-6, 0, 2
Let i(t) be the first derivative of t**4/34 - 20*t**3/51 - 23*t**2/17 - 24*t/17 + 20. Factor i(c).
2*(c - 12)*(c + 1)**2/17
Let b(o) = 8*o**3 - 32*o**2 + 28*o - 4. Let i(n) = 0 + 0 + 42*n**2 - 1 - 41*n**2. Let f(m) = b(m) + 4*i(m). Find k such that f(k) = 0.
1/2, 1, 2
Let q(w) be the third derivative of -16*w**2 + 0 + 3/16*w**4 + 1/2*w**3 + 0*w + 1/40*w**5. Let q(a) = 0. What is a?
-2, -1
What is m in 16/3*m**2 + 2/3*m**4 - 6 + 20/3*m - 20/3*m**3 = 0?
-1, 1, 9
Let i(k) = 4*k**3 - 8*k**2 - 7*k + 5. Let x(s) = -5*s**3 + 9*s**2 + 8*s - 6. Suppose 5*c + 5 = -20. Let y(n) = c*x(n) - 6*i(n). Find z, given that y(z) = 0.
-2, -1, 0
Let f(h) be the third derivative of -h**4/6 + 4*h**3/3 - 5*h**2. Let b be f(2). Factor l**4 + 0 - 1/2*l**3 + 0*l**2 + b*l - 1/2*l**5.
-l**3*(l - 1)**2/2
Let r = -17 + 17. Suppose -n - b + 8 = r, -2*n + 0*n - b + 13 = 0. Factor -1/5*f**n - 1/5*f**4 + 0 + 1/5*f**3 + 1/5*f**2 + 0*f.
-f**2*(f - 1)*(f + 1)**2/5
Let h = 80 + -70. Suppose 32*s - 27*s = h. Factor -2/3*g + 0 - 1/3*g**3 + g**s.
-g*(g - 2)*(g - 1)/3
Let h(o) be the first derivative of 2*o**3/9 + 13*o**2/3 - 28*o/3 - 74. Factor h(i).
2*(i - 1)*(i + 14)/3
Let o(z) be the first derivative of -15/2*z**2 + 9 + 5*z - 5/4*z**4 + 5*z**3. Factor o(b).
-5*(b - 1)**3
Let x(h) = 5*h - 5. Let v be x(3). Solve 4*q**4 - 84*q**4 - 4*q**5 - 16*q**5 - v*q - 105*q**3 - 55*q**2 = 0 for q.
-2, -1, -1/2, 0
Let y(w) be the third derivative of 0*w**3 - 4*w + 0 + 0*w**4 - 1/1512*w**8 + 1/945*w**7 + 3*w**2 + 0*w**5 + 0*w**6. Solve y(m) = 0 for m.
0, 1
Determine j, given that 0*j + 0 + 0*j**2 + 0*j**3 + 1/8*j**5 + 0*j**4 = 0.
0
Let k(m) = -m**3 - 122*m**2 + 205*m - 102. Let i(z) = 2*z**3 + 255*z**2 - 411*z + 204. Let s(u) = -2*i(u) - 5*k(u). Let s(t) = 0. What is t?
-102, 1
Determine r so that -2/3*r**2 + 404/3*r - 20402/3 = 0.
101
Let l(a) = -11*a - 33. Let q be l(-3). Let g(o) be the second derivative of 0*o**2 - 1/60*o**5 + q - 2*o + 1/90*o**6 + 0*o**3 + 0*o**4. Solve g(c) = 0 for c.
0, 1
Let t(h) = -4*h**4 - 86*h**3 + 8*h**2 + 260*h + 170. Let s(m) = -17*m**4 - 344*m**3 + 33*m**2 + 1039*m + 679. Let i(b) = -2*s(b) + 9*t(b). Solve i(j) = 0.
-43, -1, 2
Let k(a) be the first derivative of -4*a**5/45 - 2*a**4/3 + 64*a**2/9 + 6. Find f such that k(f) = 0.
-4, 0, 2
Let v(b) = -10*b + 5 + 9*b + b**2 - 4. Let k be (-2)/4 + (-15)/(-10). Let h(y) = 11*y**2 - 2*y - 1. Let c(g) = k*h(g) + v(g). Solve c(o) = 0.
0, 1/4
Let v(q) be the first derivative of -7*q**3/3 - 9*q**2/2 - 2*q - 154. Let v(i) = 0. Calculate i.
-1, -2/7
Let f(i) = 6*i**4 - i**3 - 12*i**2 + 33*i - 1. Let p(r) = r**4 - r**2 + 4*r + 1. Let n(k) = -f(k) + 5*p(k). Factor n(q).
-(q - 2)*(q - 1)**2*(q + 3)
Let d = 19 - 14. Factor -4*u**2 + 374*u**d - 4*u**3 - 4*u**2 - 370*u**5 + 8*u**4.
4*u**2*(u - 1)*(u + 1)*(u + 2)
Let p = -79 - -79. Suppose 4*v**2 - 9*v**2 - 5*v + 0 + p = 0. What is v?
-1, 0
Factor -5*n**2 + 25*n - 13*n + 33*n + 18 - 58.
-5*(n - 8)*(n - 1)
Let x be 98 - (-6 - (0 - 3)). What is a in 2*a**2 - 2 - x*a**4 + 1 + 100*a**4 = 0?
-1, 1
Let g(m) be the first derivative of 57/8*m**2 + 19 - 1/2*m**3 - 9/2*m - 9/16*m**4. Factor g(q).
-3*(q - 2)*(q + 3)*(3*q - 1)/4
Let k(n) be the first derivative of 13*n**6/1800 + n**5/40 + n**4/60 - n**3 - 10. Let x(q) be the third derivative of k(q). Suppose x(z) = 0. Calculate z.
-1, -2/13
Find c, given that -200/3*c - 2000 + 140*c**2 + 2/3*c**4 - 18*c**3 = 0.
-3, 10
Let a(q) be the second derivative of q**5/36 - 5*q**4/9 + 35*q**3/18 - 13*q**2/2 - 16*q. Let o(p) be the first derivative of a(p). Factor o(g).
5*(g - 7)*(g - 1)/3
Suppose -8*p = -30*p. Let t(g) be the third derivative of 0*g**4 - 1/840*g**7 - 3*g**2 + 0*g**5 + 0*g**6 + p*g**3 + 0*g - 1/1344*g**8 + 0. Factor t(s).
-s**4*(s + 1)/4
Let s(p) = -30*p**2 - 81*p - 78. Let h(i) = i**3 + 29*i**2 + 81*i + 79. Let q = -17 - -19. Let f(m) = q*s(m) + 3*h(m). Factor f(c).
3*(c + 3)**3
Let m(z) be the third derivative of -z**8/336 + 2*z**7/105 + z**6/160 - 13*z**5/240 + z**4/24 - 415*z**2. Determine x so that m(x) = 0.
-1, 0, 1/2, 4
Factor 2*v**4 + 3*v**4 + 5*v**3 - 15*v**2 - 2*v**4 - 5*v + 2*v**4 + 10.
5*(v - 1)**2*(v + 1)*(v + 2)
Factor -37/4*d + 6 + 9/4*d**3 + 1/4*d**4 + 3/4*d**2.
(d - 1)**2*(d + 3)*(d + 8)/4
Let g(u) be the third derivative of 3*u**7/35 - 43*u**6/80 + 13*u**5/20 + 7*u**4/4 - 2*u**3 + 97*u**2. Solve g(k) = 0 for k.
-2/3, 1/4, 2
Let u(d) be the second derivative of d**5/20 + d**4/2 + 4*d**3/3 + 4*d - 1. Factor u(a).
a*(a + 2)*(a + 4)
Suppose -108*t**2 - 26*t**2 + 891*t + 2*t**4 - 823*t + 64*t**3 = 0. What is t?
-34, 0, 1
Suppose -1 - 17 = -6*f. Solve q**2 + f*q**2 - 5*q**2 - 4*q**2 = 0 for q.
0
Let l = -287/195 - -20/13. Let y(x) be the second derivative of 0*x**2 - 2/9*x**3 - l*x**5 + x + 0 + 2/9*x**4. Suppose y(b) = 0. Calculate b.
0, 1
Let n(g) = -5*g**4 + 2*g**3 + 2*g + 1. Let k(j) = j**4 - j**3 + j**2 - j. Suppose -3*a = -9 - 9. Let q(l) = a*k(l) + n(l). Factor q(r).
(r - 1)**4
Let b(j) = -j**2 + 3*j - 4. Suppose -2*h = -7 - 5. Suppose -9 = 3*c + h. Let p(u) = 2*u**2 - 3*u + 5. Let l(s) = c*b(s) - 4*p(s). Factor l(x).
-3*x*(x + 1)
What is u in 152*u**4 - 75*u**4 - 5*u**2 - 11*u**3 - 30*u**2 - 25*u - 78*u**4 = 0?
-5, -1, 0
Let q(z) be the third derivative