d**8/12600 - d**7/3150 + d**6/2700 - 5*d**3/6 + 8*d. Let f(m) be the second derivative of c(m). Factor f(x).
2*x**2*(x - 1)**2/15
Suppose -5*x + 14*x - 27 = 0. Let f(j) be the second derivative of 0*j**x + 0 - 4*j - 1/66*j**4 + 1/11*j**2. Let f(o) = 0. What is o?
-1, 1
Let v(w) be the first derivative of -w**6/30 + 3*w**5/25 + 7*w**4/20 - w**3 - 9*w**2/5 - 136. Suppose v(h) = 0. What is h?
-2, -1, 0, 3
Suppose -21 = -6*f - f. Let 15*x**5 + 65*x**2 + 17*x - 5*x**f + 56*x**4 + 2 - 11*x**2 - 10*x**3 + 95*x**3 = 0. Calculate x.
-1, -2/5, -1/3
Suppose 0 = -g - 4*f - 3, -f = -3*g - 2*f + 13. Let t(h) be the second derivative of 1/8*h**4 + 0 + h + 0*h**3 - h**2 - 1/40*h**g. Factor t(u).
-(u - 2)**2*(u + 1)/2
Let g(h) = -16*h - 222. Let q be g(-14). Suppose 5/4*x - 5/2*x**q + 5/4*x**3 + 0 = 0. Calculate x.
0, 1
Let q(k) be the first derivative of -k**4/12 + 5*k**3/9 + 13*k**2/6 + 7*k/3 - 287. Determine z so that q(z) = 0.
-1, 7
Suppose 51*j = 68*j - 3060. Factor 5/4*f**2 + j + 30*f.
5*(f + 12)**2/4
Let j(l) = -2*l**3 - l - 6. Let y(z) = -9*z**3 - 11*z**2 - 9*z - 18. Let b(s) = -6*j(s) + 2*y(s). Factor b(a).
-2*a*(a + 3)*(3*a + 2)
Let t = 310/3 + -106. Let v = -5/12 - t. Factor -v*h + 0 + 3/2*h**2 - 1/4*h**3.
-h*(h - 3)**2/4
Let l(a) be the second derivative of a**8/8960 + a**7/3360 - a**6/160 + 11*a**4/12 + 21*a. Let k(i) be the third derivative of l(i). Let k(u) = 0. What is u?
-3, 0, 2
Let w(a) = -a**3 - 9*a**2 + 3. Let s be w(-9). Suppose 4*h + 16 = 5*p, 5*p + 0*h - 12 = s*h. Factor -2/7 + 2/7*d**2 + p*d.
2*(d - 1)*(d + 1)/7
Let p(t) be the first derivative of 2*t**7/147 - 4*t**6/105 + 2*t**4/21 - 2*t**3/21 - 2*t + 42. Let s(x) be the first derivative of p(x). Factor s(y).
4*y*(y - 1)**3*(y + 1)/7
Let h(o) be the third derivative of o**6/60 + o**5/15 - 13*o**4/12 + 10*o**3/3 + 360*o**2. Factor h(j).
2*(j - 2)*(j - 1)*(j + 5)
Suppose 7*m = 31 - 31. Let j(g) be the second derivative of 0*g**4 + m - 1/30*g**5 + g + 1/63*g**7 + 0*g**3 + 0*g**6 + 0*g**2. Suppose j(t) = 0. Calculate t.
-1, 0, 1
Let b be 546/468 + 46/(-60). Let n(h) be the first derivative of 1/15*h**3 - 1 - b*h + 1/10*h**2. Factor n(j).
(j - 1)*(j + 2)/5
Let b(r) be the first derivative of -4 + 6/25*r**5 + 1/15*r**6 + 0*r**2 + 0*r + 2/15*r**3 + 3/10*r**4. Factor b(v).
2*v**2*(v + 1)**3/5
Let p(x) be the first derivative of x**5 + 25*x**4 + 500*x**3/3 + 30. Find a, given that p(a) = 0.
-10, 0
Let d be 6*4/24 - 1. Let k(a) be the second derivative of 0*a**3 + 0*a**2 + 1/30*a**4 + 2*a + d - 1/75*a**6 + 0*a**5. Find t, given that k(t) = 0.
-1, 0, 1
Let t(p) = -17*p - 33. Let f be t(-10). Factor f*h - 5*h**2 - h**4 - 2*h**3 - 135*h + 6*h**3.
-h*(h - 2)*(h - 1)**2
Factor -5/2*l**3 + 33/4*l**2 - 10*l + 1/4*l**4 + 4.
(l - 4)**2*(l - 1)**2/4
Let m(v) be the second derivative of 0 - 1/6*v**4 + 7*v + 4*v**2 + 0*v**3. Solve m(n) = 0.
-2, 2
Let s = 13882 + -41642/3. Solve -2/3*w**4 + w**3 + 4/3*w**2 + 0 - s*w - 1/3*w**5 = 0 for w.
-2, 0, 1
Let s(g) = g**3 - 2*g**2 - 7*g + 6. Let t(b) = -3*b**3 + 3*b**2 + b - 1. Let r be t(-1). Let o be s(r). Factor 10*v**2 - o*v + 5*v**3 - 4*v**2 + 13*v - 2*v**3.
3*v*(v + 1)**2
Let l(j) be the first derivative of 4*j**5/35 + 6*j**4/7 - 4*j**3/7 - 40*j**2/7 - 48*j/7 + 111. Factor l(b).
4*(b - 2)*(b + 1)**2*(b + 6)/7
Let v = -205 - -221. Suppose 6 + v = 11*o. Factor 2/7*a**3 + 0*a + 0 + 4/7*a**o.
2*a**2*(a + 2)/7
Let z be -21*((-1687)/(-189) - 9). Factor -z*p**2 + 2/9*p**3 - 2 + 10/3*p.
2*(p - 3)**2*(p - 1)/9
Let g(a) be the first derivative of 3/4*a**4 + 27*a + 7*a**3 + 45/2*a**2 - 10. Factor g(i).
3*(i + 1)*(i + 3)**2
Let z(o) be the first derivative of -19 + 3/10*o**2 + 0*o + 1/15*o**3. Let z(x) = 0. What is x?
-3, 0
Let t(m) be the first derivative of -6 + 1/4*m**2 + 0*m - 1/6*m**3. Let t(h) = 0. What is h?
0, 1
Let z(b) be the first derivative of b**4/16 + b**3/4 - b**2/2 - 3*b + 57. Factor z(u).
(u - 2)*(u + 2)*(u + 3)/4
Let k(x) = x**2 + x. Let z(t) = -728*t - 4*t**2 + 719*t - 4*t**2. Let q(m) = -18*k(m) - 2*z(m). Let q(i) = 0. Calculate i.
0
Suppose -8 + 63 = 11*n. Let u(y) be the second derivative of -1/10*y**n + 1/21*y**7 + 0 + 0*y**3 - 1/15*y**6 + 1/6*y**4 + 0*y**2 - 5*y. Factor u(v).
2*v**2*(v - 1)**2*(v + 1)
Suppose 0 = -2*m - 2 + 4. Let v(d) = 2*d**3 + 7*d**2 - 8. Let c(t) = t**2. Let i(q) = m*v(q) - c(q). Determine j, given that i(j) = 0.
-2, 1
Let a(v) = -3*v - 35. Let d be a(-14). Let r be (-24)/20*(d + -15). Factor -r*p - 2/5*p**3 + 32/5 + 18/5*p**2.
-2*(p - 4)**2*(p - 1)/5
Let l(r) = -16*r**3 - 60*r**2 - 12*r + 28. Let g(x) = -x**3 - 3*x**2 + 1. Let k(u) = -20*g(u) + l(u). Factor k(n).
4*(n - 1)**2*(n + 2)
Let g(z) be the first derivative of -z**4/8 + 28*z**3/3 + 29*z**2 + 623. What is u in g(u) = 0?
-2, 0, 58
Let t = 63 - 503/8. Let d(y) be the first derivative of -1/2*y - 1/2*y**3 - 3 + t*y**4 + 3/4*y**2. Factor d(q).
(q - 1)**3/2
Let s(x) be the first derivative of -x**6/9 + 11*x**4/3 - 40*x**3/9 - 7*x**2 + 40*x/3 - 335. Determine b so that s(b) = 0.
-5, -1, 1, 4
Let -9/5*r**3 + 3/5*r**4 + 0*r + 0 - 12/5*r**2 = 0. What is r?
-1, 0, 4
Suppose 139*j - 130*j = 0. Let g(u) be the second derivative of -3/70*u**5 + 1/42*u**4 + 2*u + j*u**2 + 2/21*u**3 + 0. Let g(m) = 0. What is m?
-2/3, 0, 1
Let y = 2174/3 + -713. Let q(s) be the first derivative of -10*s - 3 + y*s**3 + 25/2*s**2. Factor q(k).
5*(k + 1)*(7*k - 2)
Let w(z) be the first derivative of 22*z**3/7 - 31*z**2/7 - 4*z/7 + 63. Let w(t) = 0. What is t?
-2/33, 1
Suppose 0 = 2*b + 2*b - 16. Factor -33*j**3 + 12*j**b - 7*j + 15*j**2 - 3*j - 7*j + 23*j.
3*j*(j - 2)*(j - 1)*(4*j + 1)
Let h = 6487/9726 - 1/3242. Find w, given that 4*w - 28/3*w**2 - 6*w**4 + 4/3*w**5 - h + 32/3*w**3 = 0.
1/2, 1
Factor 6*m**2 - 187 - 5*m**3 + 89 + 68 + 14*m**2 - 5*m.
-5*(m - 3)*(m - 2)*(m + 1)
Let k(v) be the third derivative of 5*v**8/336 + 2*v**7/21 - 11*v**6/24 + v**5/2 - 10*v**2 - 3*v. Determine b so that k(b) = 0.
-6, 0, 1
Let f(u) be the second derivative of 0 - 12*u - 1/3*u**4 - 7/10*u**5 - 11/21*u**7 + 0*u**3 + 0*u**2 + 4/3*u**6. What is z in f(z) = 0?
-2/11, 0, 1
Let y(k) be the third derivative of 0 + 0*k + 1/5*k**4 - 8/15*k**3 - 33*k**2 - 3/100*k**5 + 1/600*k**6. Factor y(t).
(t - 4)**2*(t - 1)/5
Let c(k) be the third derivative of 1/30*k**5 + 0 - 2/3*k**3 + 0*k - 1/12*k**4 - 22*k**2. Solve c(s) = 0 for s.
-1, 2
Let r(y) be the second derivative of 1/10*y**6 + 0 - 1/4*y**4 + 3/2*y**3 + 22*y + 0*y**2 - 9/20*y**5. Let r(q) = 0. What is q?
-1, 0, 1, 3
Find j such that 0 + 18/7*j + 3/7*j**3 - 15/7*j**2 = 0.
0, 2, 3
Let q(c) be the second derivative of 5*c**3/6 - 7*c**2/2 - 10*c. Let a be q(5). Find o, given that 36*o**2 + 2*o**4 + 0*o**4 - 2 - 14*o**3 + a - 40*o = 0.
1, 2
Let g(y) be the third derivative of y**6/540 - 31*y**5/270 - 881*y**2. Factor g(s).
2*s**2*(s - 31)/9
Suppose -10 = -8*f + 6*f. Let m(q) be the third derivative of 7/120*q**f + 0 + 7*q**2 + 0*q + 0*q**3 - 1/24*q**4 - 1/48*q**6. Let m(z) = 0. Calculate z.
0, 2/5, 1
Suppose -c = 2*n - 7, -4*n + 2 = -4*c - 6. Suppose n*f + 4 = 4*f. Solve 1/4*g - 1/4*g**3 + 0 + 1/4*g**f - 1/4*g**2 = 0 for g.
-1, 0, 1
Let w(z) be the third derivative of z**8/336 + 2*z**7/105 - 13*z**6/60 + 11*z**5/15 - 31*z**4/24 + 4*z**3/3 + 38*z**2. Factor w(h).
(h - 1)**4*(h + 8)
Let g(h) be the second derivative of 0 - 4*h - 1/5*h**5 - 1/6*h**4 + 2/3*h**3 + h**2. Determine j so that g(j) = 0.
-1, -1/2, 1
Suppose -5*g = -27 - 18. Suppose 5*v = 3*a - 0*a + 27, 4*v - 2*a - 20 = 0. Factor 8*z**2 - 2*z**2 - g*z - 6*z**4 + 12*z - v*z**5.
-3*z*(z - 1)*(z + 1)**3
Suppose -60*s + 73*s - 1690 = 0. Let g = -126 + s. Determine o so that 9*o**5 + 21*o**3 + 27*o**g + 2/3*o + 19/3*o**2 + 0 = 0.
-2, -1/3, 0
Let n(i) be the first derivative of 5*i**6/4 + 33*i**5/8 - 3*i**4/4 - 7*i**3 + 6*i**2 + 10*i - 7. Let b(v) be the first derivative of n(v). Solve b(z) = 0.
-2, -1, 2/5
Let q(r) = -r - 1. Let m(w) be the third derivative of w**5/60 - 7*w**4/12 + 5*w**3/3 + 3*w**2. Let h(z) = -5*m(z) + 30*q(z). Factor h(v).
-5*(v - 4)**2
Let m = -388/9 + 394/9. Let u(d) be the first derivative of 3 + m*d**3 + 8*d**2 + 32*d. Factor u(s).
2*(s + 4)**2
Let n(g) = -g**4 - g**3 + 4*g - 1. Let r(x) = 9*x**4 + 21*x**3 + 46*x**2 + 16*x + 8. Let v(k) = -24*n(k) - 3*r(k). Factor v(a).
-3*a*(a + 2)*(a + 3)*(a + 8)
Let 