 + 1/3*a**5.
(a - 1)*(a + 1)**4/3
Let f = 11/29 + 3/145. Factor 1/5*i**2 - 3/5*i + f.
(i - 2)*(i - 1)/5
Let y(d) be the second derivative of 3*d**5/40 - d**4/4 - 3*d**3/4 - 17*d - 1. Factor y(p).
3*p*(p - 3)*(p + 1)/2
Suppose 12 = 13*i - 14. Factor 13 - 10*v**2 + 16*v + 19 - 2*v**3 - 2*v**3 + i*v**2.
-4*(v - 2)*(v + 2)**2
Factor 62/7*p + 961/7 + 1/7*p**2.
(p + 31)**2/7
Let p be (30/(-27))/(-5) + 50/18. Suppose 59 - p*j**3 - 35 - 36 + 9*j**2 = 0. Calculate j.
-1, 2
Let z(w) be the third derivative of w**5/240 + 3*w**4/8 + 27*w**3/2 - 5*w**2 + 2*w. Factor z(v).
(v + 18)**2/4
Let v(w) be the first derivative of -3*w**5/20 - 7*w**4/2 - 293*w**3/12 - 53*w**2 + 44*w + 83. Suppose v(k) = 0. Calculate k.
-11, -4, 1/3
Let f(l) be the first derivative of 2/15*l**5 + 1/6*l**4 - 2/9*l**3 + 0*l - 1/3*l**2 - 7. Determine h so that f(h) = 0.
-1, 0, 1
Let l(x) be the third derivative of 7 - 5*x**2 + 7/6*x**5 - 5/12*x**6 - 11/12*x**4 + 0*x + 1/3*x**3. Factor l(w).
-2*(w - 1)*(5*w - 1)**2
Let a be (9 + -8)/((-2)/(-1548)). Let 126*z + 500 + 214*z**2 + a*z - 90*z**3 + 91*z**2 + 5*z**4 = 0. Calculate z.
-1, 10
Let s(n) be the third derivative of -n**8/40320 + n**7/1680 - n**6/288 - n**5/6 + 5*n**2. Let f(g) be the third derivative of s(g). Suppose f(t) = 0. What is t?
1, 5
Let k(i) = i**2 - 5*i + 1. Let m be k(6). Factor -1 + 12*w - m - 2*w**2 + 0 - 2*w**2.
-4*(w - 2)*(w - 1)
Solve 2/7*j**2 + 8/7*j**5 + 0 + 4/7*j**3 + 0*j - 2*j**4 = 0 for j.
-1/4, 0, 1
Let q(x) be the third derivative of -34*x**2 - 1/84*x**7 - 5/16*x**4 + 1/16*x**6 + 0 + 1/24*x**5 + 0*x + 0*x**3. What is m in q(m) = 0?
-1, 0, 1, 3
Let v be 24187/11725 + (-6)/(-75). Factor -9/7*s**2 + 3/7*s**4 + 3/7*s**3 - 6/7 - v*s.
3*(s - 2)*(s + 1)**3/7
Let i = 1638 - 1635. Suppose -9/2*p**i - 7/4*p**2 + 0 + 1/2*p + 63/4*p**4 = 0. Calculate p.
-1/3, 0, 2/7, 1/3
Let k(c) = c**2 - 66*c + 132. Let l be k(64). Let 0*v + 0*v**2 + 0*v**3 + 0 + 1/8*v**l = 0. Calculate v.
0
Factor -2*d**2 + 3*d**2 + 573*d + 18 - 564*d.
(d + 3)*(d + 6)
Factor -5*u**4 + 37*u**3 - 90 - 5*u**3 + 13*u**3 + 507*u**2 - 492*u**2 - 125*u.
-5*(u - 9)*(u - 2)*(u + 1)**2
Suppose -97 - 129 = -3*u + c, 379 = 5*u - 4*c. Let l be (-5)/(u/6) - 54/(-60). Determine z, given that 0 + l*z**3 + 1/2*z + z**2 = 0.
-1, 0
Find r, given that 3/7*r**4 - 27/7*r**2 - 9/7*r**3 + 0 + 81/7*r = 0.
-3, 0, 3
Suppose m - 5*u + 3 = 26, -3*u + 46 = 2*m. Suppose -m*o + 4 = -22*o. Factor -4/3*q**3 - 14/3*q + 4/3*q**o - 16/3*q**2 + 2/3*q**5 - 4/3.
2*(q - 2)*(q + 1)**4/3
Let k = -2948/21 - -992/7. Let g(t) be the first derivative of 4*t**2 + 4 + k*t**3 + 0*t - t**4. Factor g(m).
-4*m*(m - 2)*(m + 1)
Suppose 105*c + 18 - 113 = 220. Suppose 0*y - 4/7*y**4 + 32/7*y**2 + 4*y**c + 0 = 0. What is y?
-1, 0, 8
Let p(c) be the first derivative of -13 + 4*c - 3/2*c**4 + 5*c**2 - 8/3*c**3. Factor p(k).
-2*(k - 1)*(k + 2)*(3*k + 1)
Let h = 49027/5 + -9805. Find a, given that -6/5*a**2 - h*a**3 + 0 + 8/5*a = 0.
-4, 0, 1
Let z(x) be the second derivative of -2*x**7/63 + 2*x**6/5 - 32*x**5/15 + 56*x**4/9 - 32*x**3/3 + 32*x**2/3 - x - 64. Factor z(n).
-4*(n - 2)**4*(n - 1)/3
Let d be ((-9)/(135/12))/((-1)/5). Suppose -4*h = -4*m - d, -1 = -0*h - 5*h + m. Find o such that h - 6/5*o + 3/5*o**2 = 0.
0, 2
Let a(p) be the first derivative of -p**6/216 + p**5/12 - 25*p**4/72 + 6*p**3 + 27. Let z(k) be the third derivative of a(k). Factor z(w).
-5*(w - 5)*(w - 1)/3
Let f(r) be the first derivative of 0*r + 0*r**4 + 0*r**2 - 15 + 8/9*r**3 - 2/5*r**5 + 1/9*r**6. Find g, given that f(g) = 0.
-1, 0, 2
Let p = -78 - -69. Let n be (-2)/(-5) - p/90. Factor -j**3 + 0*j**2 + 3/2*j**4 + 0 + 0*j - n*j**5.
-j**3*(j - 2)*(j - 1)/2
Determine x so that 0 + 0*x**2 + 2/5*x**5 - 8/5*x**4 + 0*x + 6/5*x**3 = 0.
0, 1, 3
Let g(m) be the first derivative of -m**6/10 + 21*m**5/40 - m**4/2 - m**3 + 21*m - 7. Let o(q) be the first derivative of g(q). Determine s so that o(s) = 0.
-1/2, 0, 2
Let i(f) be the third derivative of f**8/3360 - f**7/1680 - f**6/360 - 5*f**3/3 - 7*f**2. Let w(z) be the first derivative of i(z). Find n, given that w(n) = 0.
-1, 0, 2
Let l(h) be the third derivative of 2*h**6/15 - 7*h**5/15 - 17*h**4/3 - 16*h**3/3 - 58*h**2. Solve l(u) = 0.
-2, -1/4, 4
Let p(y) be the second derivative of -5*y**4/12 - 95*y**3/3 + 195*y**2/2 - 264*y. Let p(u) = 0. What is u?
-39, 1
Let c(h) be the second derivative of -h**4/24 + 7*h**3/6 - 49*h**2/4 - 8*h + 4. Factor c(b).
-(b - 7)**2/2
Let r be (-1)/2 - 735/(-882). Factor -r*c**3 + 0*c - 1/3*c**2 + 0.
-c**2*(c + 1)/3
Let i(h) = 3*h**2 + 143. Let m(o) = -o**2 + 4*o - 71. Let g(d) = -2*i(d) - 5*m(d). Factor g(y).
-(y - 3)*(y + 23)
Let i = -157145/9 + 17461. Let n(u) = -u**3 + 6*u**2 - u + 8. Let b be n(6). Solve 2/9 + i*z + 2/9*z**b = 0 for z.
-1
Suppose -3*i + 3*g + 408 = 0, -5*i - 2*g = -343 - 337. Find v, given that -3*v**4 + i*v**2 - 4*v**3 + 2*v**4 - 139*v**2 = 0.
-3, -1, 0
Let q(g) be the first derivative of -160*g**6/3 + 176*g**5/5 + 39*g**4/20 - 44*g**3/15 - 2*g**2/5 + 588. Factor q(d).
-d*(5*d - 2)**2*(8*d + 1)**2/5
Let n be (16/(-6))/(-3*(-6)/27). Let w be -4 + ((-25)/3)/(n/3). Solve 3/4*b**5 - 15/4*b**4 + 0*b + 27/4*b**2 + 0 + w*b**3 = 0 for b.
-1, 0, 3
Let l = -2 + -2. Let s be 2/l + 5/2. Solve -4*a + 2*a**4 - s*a**2 + 4*a**3 + a - a = 0 for a.
-2, -1, 0, 1
Find p such that -64/21 - 104/21*p**2 - 20/21*p**3 + 2/7*p**4 + 2/21*p**5 - 48/7*p = 0.
-2, -1, 4
Let z(n) be the third derivative of -1/70*n**7 + 1/32*n**6 + 0 + 1/448*n**8 - 1/40*n**5 + 0*n - 11*n**2 + 0*n**3 + 0*n**4. Factor z(g).
3*g**2*(g - 2)*(g - 1)**2/4
Suppose -4*k = 5*g - 12, 16 = -2*g - 2*g. Suppose 3*j + 2*j = 50. Factor -d**4 + k*d**2 + 4*d**5 - 12*d + 8*d**3 - d**4 - j*d**4 + 4.
4*(d - 1)**4*(d + 1)
Let n(v) be the second derivative of -v**5/80 - v**4/12 - 5*v**3/24 - v**2/4 - 2*v - 109. Suppose n(p) = 0. Calculate p.
-2, -1
Let v be (70/10)/((-14)/(-4)). Let x(q) be the third derivative of 1/9*q**6 - 11/36*q**4 + 0*q + 2/9*q**3 + 0 + 7/90*q**5 + 10*q**v. What is u in x(u) = 0?
-1, 1/4, 2/5
Suppose 0 = 4*l - 3*q - 22, 6*l - 2*q - 8 = 5*l. Find m, given that 5*m - 5*m**3 + 5/4*m**2 + 1 - 9/4*m**l = 0.
-2, -1, -2/9, 1
Let i = -26 + 53. Factor -24*y**2 - 33*y**3 - 32*y**3 + i + 53*y**3 + 9*y.
-3*(y - 1)*(2*y + 3)**2
Let z(c) be the first derivative of c**6/15 + 19*c**5/10 + 21*c**4 + 108*c**3 + 216*c**2 - 43*c + 38. Let t(f) be the first derivative of z(f). Factor t(r).
2*(r + 1)*(r + 6)**3
What is u in -40/13*u**2 + 2/13*u**5 - 112/13*u + 20/13*u**3 - 64/13 + 14/13*u**4 = 0?
-4, -2, -1, 2
Let w(t) be the second derivative of t**7/315 + t**6/75 - 7*t**5/150 - 7*t**4/90 + 2*t**3/5 - 8*t**2/15 - 331*t. Suppose w(j) = 0. Calculate j.
-4, -2, 1
Suppose -36 = -0*g - 18*g. Factor -3*n**g + 0 + 1/2*n + 5/2*n**3.
n*(n - 1)*(5*n - 1)/2
Let u be 15/(-10)*10*(-12)/30. Let f(y) be the first derivative of 3/8*y**2 + u + 0*y + 1/12*y**3. Factor f(t).
t*(t + 3)/4
Let j be 23 + 4 + 0 + 3. Let a be (j/(-270))/((-2)/4). Factor -a*b**2 + 4/9 - 2/9*b.
-2*(b - 1)*(b + 2)/9
Let p(w) be the first derivative of w**5/10 - 4*w**4/15 + w**3/15 + 2*w**2/5 - 19*w - 7. Let m(a) be the first derivative of p(a). Factor m(k).
2*(k - 1)**2*(5*k + 2)/5
Suppose -12*f = -89*f + 308. Let l(j) be the third derivative of 25/72*j**f + 1/9*j**5 + 4*j**2 + 5/9*j**3 + 0*j + 0 + 1/72*j**6. Factor l(w).
5*(w + 1)**2*(w + 2)/3
Let c(k) be the second derivative of -2/25*k**5 + 0*k**4 + 2/5*k**2 - 2/75*k**6 - 13*k + 0 + 4/15*k**3. Factor c(a).
-4*(a - 1)*(a + 1)**3/5
What is v in 0 - 47/4*v - 1/4*v**2 = 0?
-47, 0
Let n = -17599/7 + 2515. What is c in -n*c + 0 + 2/7*c**3 - 4/7*c**2 = 0?
-1, 0, 3
Let a(d) be the second derivative of -d**8/2240 + d**6/480 - 23*d**3/6 + 9*d. Let g(m) be the second derivative of a(m). Factor g(l).
-3*l**2*(l - 1)*(l + 1)/4
Let v(h) be the third derivative of 0*h + 4 + 2*h**2 + 135/2*h**3 - 15/4*h**4 + 1/12*h**5. Factor v(r).
5*(r - 9)**2
Let h = -83213/191 + 1307/3. Let p = 376/1719 - h. Find r such that -2/9*r**2 - p*r**3 + 0 + 0*r = 0.
-1, 0
Let t be ((-90)/5)/(-9) + (0 - -2). Suppose 0 = -t*p + 5*r + 13, -5*p + 4*p = -r - 3. Determine s so that -2/5 - 12/5*s - 2*s**p = 0.
-1, -1/5
Determine o, given that 2/9*o**3 - 4/9*o**2 - 8/9 - 14/9*o = 0.
-1, 4
Let p(h) be the first derivative of h**9/9072 - h**8/1680 -