(n + 1)**3
Let s(k) be the third derivative of 11/42*k**7 + 0*k**4 + 121/48*k**6 + 0 + 5/672*k**8 - 26*k**2 + 0*k**5 + 0*k + 0*k**3. Factor s(u).
5*u**3*(u + 11)**2/2
Let d(w) be the second derivative of 2/35*w**5 + 6/7*w**2 + 0 - 23/21*w**3 - 12*w - 5/42*w**4. Suppose d(n) = 0. Calculate n.
-2, 1/4, 3
Let v(s) be the first derivative of -5/7*s**3 + 2/7*s + 1 - 13/14*s**2. Factor v(r).
-(r + 1)*(15*r - 2)/7
Factor 55 + 30*m**4 - 720*m**2 - 820 + 1755*m + 50*m**3 - 671 + 86 - 5*m**5.
-5*(m - 3)**3*(m - 2)*(m + 5)
Factor 7*t**2 - 2*t - 28 + 1/2*t**3.
(t - 2)*(t + 2)*(t + 14)/2
Suppose -5*o + j = -2*j - 338, -o - 2*j = -65. Let k = o - 65. Let 32/3 + 2/3*p**k - 16/3*p = 0. Calculate p.
4
Let y(f) be the first derivative of 8*f**3/21 + 9*f**2/7 + 4*f/7 + 69. Find x, given that y(x) = 0.
-2, -1/4
Let v(i) be the third derivative of i**6/180 - i**5/18 - 2*i**4/9 + 4*i**3/3 + 12*i**2 - 1. Solve v(z) = 0 for z.
-2, 1, 6
Factor 8*h**2 - 3821*h + 16 + 3849*h + h**3 - 5*h**3.
-4*(h - 4)*(h + 1)**2
Let u(h) = h**3 - 6*h**2 - 6*h - 16. Let q be u(7). Let k be (-10)/45 + (-2)/q. Let k - 1/4*s**2 - 1/4*s = 0. What is s?
-1, 0
Let u(p) be the first derivative of p**5 - 5*p**4/4 - 5*p**3/3 + 5*p**2/2 - 104. Factor u(m).
5*m*(m - 1)**2*(m + 1)
Let g(z) = z**2 - 11*z - 17. Let j be 8 + (-3)/(-4 + 5). Let d(n) = 2*n**2 - 16*n - 25. Let o(y) = j*d(y) - 7*g(y). Suppose o(a) = 0. What is a?
-1, 2
Let v(q) = 13 + 12*q + q**3 - 2*q**3 + 9*q**2 - 11*q + 8*q. Let t be v(10). Find y such that -4/3 + 2*y + 1/6*y**4 - 1/3*y**2 - 1/2*y**t = 0.
-2, 1, 2
Suppose -5*b - 3*b - 160 = 0. Let x be (-6)/(-8) + 5/b. Factor -1/2*g**3 - g**2 + 1 + x*g.
-(g - 1)*(g + 1)*(g + 2)/2
Let x(v) = v**2. Let r(o) be the second derivative of -7*o**5/4 + 19*o**4/6 + 4*o**3/3 - 2*o**2 + o. Let f(n) = 5*r(n) - 35*x(n). Suppose f(q) = 0. What is q?
-2/5, 2/7, 1
Let x(p) = -p**3 + 5*p**2 - 3*p - 2. Let o be x(3). Suppose 8*t + o - 23 = 0. Suppose 0 - 2/7*z**t + 6/7*z = 0. Calculate z.
0, 3
Let q be (-78)/(-13) - 9 - -6. Find v, given that 32 + 56*v + 30*v**2 + 1/2*v**4 + 13/2*v**q = 0.
-4, -1
Suppose -3447*m = -3434*m - 39. Factor 0 + 2/5*g**2 + 4/15*g**m + 2/15*g.
2*g*(g + 1)*(2*g + 1)/15
Let x = -55889 - -55889. Factor 18/13*f**4 + 88/13*f**2 + 48/13*f + x + 60/13*f**3 + 2/13*f**5.
2*f*(f + 2)**3*(f + 3)/13
Let u(t) be the first derivative of -t**6/15 - 4*t**5/25 + 2*t**4 - 16*t**3/5 - 133. Factor u(o).
-2*o**2*(o - 2)**2*(o + 6)/5
Let f be 24/240*(-25)/(-10). Factor 0 - 1/4*o - f*o**2.
-o*(o + 1)/4
Let a(z) = 5*z**2 - 50*z. Let g(u) = 60*u**2 - 600*u. Suppose 0 = 3*b - 7*b - 140. Let r(l) = b*a(l) + 3*g(l). Factor r(i).
5*i*(i - 10)
Suppose 0 = 2*n + 4 - 14. Let u be (n - -1)*1/2. Suppose -7*b**u - 2*b**4 + b**3 + 0*b**4 - b**4 = 0. Calculate b.
-2, 0
Factor 7/3*r**2 - 7/3 + 1/3*r - 1/3*r**3.
-(r - 7)*(r - 1)*(r + 1)/3
Let a(r) be the second derivative of -r**7/504 + r**6/36 - r**5/6 + r**4/3 - 8*r. Let j(i) be the third derivative of a(i). Determine x so that j(x) = 0.
2
Let q(g) be the first derivative of g**6/165 + g**5/110 - g**4/66 - g**3/33 + 11*g - 13. Let y(c) be the first derivative of q(c). Factor y(a).
2*a*(a - 1)*(a + 1)**2/11
Let r(z) be the third derivative of -4/3*z**3 + 1/330*z**5 - 9*z**2 + 0*z + 0 - 1/220*z**6 + 0*z**4. Let c(x) be the first derivative of r(x). Factor c(g).
-2*g*(9*g - 2)/11
Let b be (-2)/5 + 13*(-4)/(-120). Let y(l) be the second derivative of b*l**4 + 4/5*l**2 + 0 - 4*l + 4/15*l**3. Find z, given that y(z) = 0.
-2
Let k(x) = x**3 - 27*x**2 + 29*x - 7. Let s be k(26). Let w = s + -69. Solve -1/2*q**2 + w + 1/4*q**3 - q = 0 for q.
-2, 2
Let w be (-3510)/297 + (3 - -9). Factor -w*q**2 - 4/11 - 6/11*q.
-2*(q + 1)*(q + 2)/11
Let l(q) = q**3 - 4*q**2 + 3*q - 10. Let m be l(4). Suppose 2*t - 8 = -m*s, t + 21 = 5*s + 1. Factor 2/13*g**5 + 0 + 2/13*g**3 + 0*g**2 - 4/13*g**4 + t*g.
2*g**3*(g - 1)**2/13
Factor -43*k**3 + 3*k**2 + 8*k**4 - 7*k**4 + 15*k**2 + 63*k**3 + k**4.
2*k**2*(k + 1)*(k + 9)
Suppose -3*f + t = 76, -2*f = -3*t + 3 + 57. Let d be (19/(-76))/(2*1/f). Factor -10/7*p**d - 18/7*p**2 - 2/7*p**4 - 2*p - 4/7.
-2*(p + 1)**3*(p + 2)/7
Determine r so that 35/3*r**4 + 0*r - 5*r**5 + 20/3 - 55/3*r**2 + 5*r**3 = 0.
-1, -2/3, 1, 2
Let z(y) be the third derivative of y**6/210 - 136*y**5/105 + 1495*y**4/14 + 6348*y**3/7 + 8*y**2 - 19. Factor z(b).
4*(b - 69)**2*(b + 2)/7
Let n(m) be the second derivative of -m**7/420 + 4*m**6/75 + 9*m**5/100 - 2*m**4/15 - 17*m**3/60 + 169*m. Determine c so that n(c) = 0.
-1, 0, 1, 17
Let o(u) = -8*u**2 - 450*u - 16870. Let f(r) = -r**2 + 1. Let n(l) = 5*f(l) - o(l). Factor n(t).
3*(t + 75)**2
Suppose 9 = 4*r - 23. Let p(j) = 7 + 13*j - 3 - 8*j**2 - 3*j - 6*j**3. Let l(c) = -c**3 + 1. Let h(n) = r*l(n) - p(n). Determine y so that h(y) = 0.
1, 2
Let g(p) = -8*p**4 - 87*p**3 - 10*p**2 + 78*p. Let r(j) = -4*j**4 - 44*j**3 - 4*j**2 + 40*j. Let d(k) = 4*g(k) - 9*r(k). Solve d(x) = 0.
-12, -1, 0, 1
Let h(i) be the second derivative of -i**6/30 + 7*i**5/4 + 223*i. Factor h(y).
-y**3*(y - 35)
Solve -4374 - 2/3*g**3 - 4482*g - 326/3*g**2 = 0.
-81, -1
Let g(t) be the first derivative of 2*t**4 + t**3 - t**2/2 + 11*t + 8. Let i(m) = 8*m**3 + 2*m**2 - 2*m + 10. Let p(l) = -6*g(l) + 7*i(l). Factor p(y).
4*(y - 1)*(y + 1)*(2*y - 1)
Let h(q) be the second derivative of 1849*q**4/120 - 43*q**3/30 + q**2/20 - 97*q + 1. Find t such that h(t) = 0.
1/43
Let c(z) = 85*z**2 - 767*z + 22. Let g be c(9). Let 3*u**3 - 3/2*u**5 + 0 + 0*u**g + 0*u**2 - 3/2*u = 0. Calculate u.
-1, 0, 1
Let y(j) be the second derivative of -j**5/18 + j**4/6 - j**3/9 - j**2/9 + 135*j. Factor y(h).
-2*(h - 1)**2*(5*h + 1)/9
Let z = -3008/6405 - -24/61. Let a = 1/15 - z. Suppose 1/7*d**2 + 0*d - a = 0. Calculate d.
-1, 1
Let j(x) be the third derivative of x**6/75 + 3*x**5/50 + x**4/12 + 99*x**2. Suppose j(n) = 0. What is n?
-5/4, -1, 0
Let l(h) be the first derivative of h**5 - 15*h**4 + 260*h**3/3 - 240*h**2 + 320*h + 293. Find v such that l(v) = 0.
2, 4
Let y be 14/3 + 4/(-6). Factor 8*m**2 + 2*m + 3*m - 20*m**2 + 3*m + 4*m**y.
4*m*(m - 1)**2*(m + 2)
Let h(a) be the second derivative of 0 - 5*a**2 + 1/4*a**5 + 5/6*a**4 - 5/6*a**3 - 18*a. Determine q, given that h(q) = 0.
-2, -1, 1
Let k(s) be the first derivative of s**3/5 - 9*s**2/10 + 6*s/5 - 7. Suppose k(x) = 0. What is x?
1, 2
Let f = -25 - -38. Let p = f + -8. Factor 8*j + p*j**3 - 16*j**3 + j**2 + 7*j**3 + 3*j**2.
-4*j*(j - 2)*(j + 1)
Suppose 36*c**2 - 8/5*c - 48 + 2/5*c**4 + 66/5*c**3 = 0. What is c?
-30, -2, 1
Let o(p) be the first derivative of 4 - 2/9*p - 2/27*p**3 + 2/9*p**2. Determine v, given that o(v) = 0.
1
Suppose -4/15*r**4 + 0 - 8/15*r - 2/5*r**3 + 16/15*r**2 + 2/15*r**5 = 0. What is r?
-2, 0, 1, 2
Let n be 21/6 + 553/(-316) + 2/8. Find d, given that -10/7*d**n + 40/7 + 96/7*d = 0.
-2/5, 10
Suppose 311*q - 48 = 305*q. Let r(n) be the third derivative of 0*n**4 + 0*n**3 + 0*n - 1/100*n**6 + 1/525*n**7 + 0 + q*n**2 + 1/75*n**5. Solve r(j) = 0 for j.
0, 1, 2
Solve 5/3*h**5 - 65/3*h**4 + 880/3*h + 95/3*h**3 + 320/3 + 725/3*h**2 = 0 for h.
-1, 8
Let z be (3 + -14 + 11)*(-1 - 0). Let l(g) be the third derivative of z - 4*g**2 - 1/36*g**4 - 1/90*g**5 + 2/9*g**3 + 0*g. Factor l(w).
-2*(w - 1)*(w + 2)/3
Suppose 4 + 3811*u**4 - 8*u**2 - 1264*u**4 + 0 - 1270*u**4 - 1273*u**4 = 0. Calculate u.
-1, 1
Let s(l) be the third derivative of 0 - 11*l**2 + 37/60*l**4 + 7/600*l**6 + 8/15*l**3 + 13/60*l**5 + l. Factor s(v).
(v + 1)*(v + 8)*(7*v + 2)/5
Factor 0*p**4 + 0*p**2 + 1/3*p**5 - 1/3*p**3 + 0*p + 0.
p**3*(p - 1)*(p + 1)/3
Find w, given that 38*w + 8333 - 3*w**3 - 72*w**2 - 8333 + 205*w = 0.
-27, 0, 3
Let 37*z**2 - 4*z - 38*z + 3*z**2 + 2*z**3 = 0. What is z?
-21, 0, 1
Let a(g) be the third derivative of g**5/120 - g**4/8 + 2*g**3/3 - 7*g**2 - 31. Factor a(k).
(k - 4)*(k - 2)/2
Factor 150*w + 42 + 21/2*w**2.
3*(w + 14)*(7*w + 2)/2
Let a = 1873 - 7533/4. Let m = -10 - a. Factor 0*y - 1/4*y**2 + 0 + m*y**4 + 0*y**3.
y**2*(y - 1)*(y + 1)/4
Factor -1/2*a**4 + 0*a**3 + 0 + 1/2*a**5 + 0*a + 0*a**2.
a**4*(a - 1)/2
Let d = -64 + 66. Factor -12*a**d + 127*a + 256 + 34*a**2 + 65*a + 26*a**2 + 4*a**3.
4*(a + 4)**3
Let m = -21 + 25. Suppose -4*c - m = 4*u, 8*c - 3*c - 7 = -2*u. Factor c*w**4 - 75 - 12*w**2 + 75.
3*w**2*(w - 2)*(w + 2)
