, -1/5, 0, 1/4
Let u(d) be the first derivative of -7*d**6/660 - d**5/165 - 3*d**2/2 - 6. Let i(m) be the second derivative of u(m). Determine t so that i(t) = 0.
-2/7, 0
Let -39 - 6*m**3 + 8*m**3 + 16*m - 10*m**2 + 31 = 0. What is m?
1, 2
Let k = -8543/7 - -1221. What is f in 20/7*f + k + 37/7*f**2 + 30/7*f**3 + 9/7*f**4 = 0?
-1, -2/3
Let h(u) be the third derivative of -u**6/320 + 3*u**5/160 + u**4/64 - 3*u**3/16 - 7*u**2. Factor h(y).
-3*(y - 3)*(y - 1)*(y + 1)/8
Let g(j) = -2*j**3 - 2*j**2 + 8*j - 22. Let q(m) = 4*m**3 + 5*m**2 - 16*m + 45. Let y(b) = -13*g(b) - 6*q(b). Solve y(o) = 0.
-2, 2
Let h(m) = m + 5. Let y be h(-8). Let l be (y/(63/(-12)))/1. Factor -8/7*c + 2/7*c**4 + 8/7 - 6/7*c**2 + l*c**3.
2*(c - 1)**2*(c + 2)**2/7
Let q(o) = -7*o - 2*o**2 + 3 + 2 + 0. Let k(i) = -i**2 - 4*i + 3. Let z(p) = -5*k(p) + 3*q(p). Determine f, given that z(f) = 0.
-1, 0
Let b(a) be the second derivative of a**3/6 + 4*a**2 + a. Let y be b(-5). Let -2/3 - 4/3*f**5 + 8/3*f**y - 4/3*f - 2/3*f**4 + 4/3*f**2 = 0. Calculate f.
-1, -1/2, 1
Let x(i) be the third derivative of i**7/840 - i**6/120 - i**4/24 + i**2. Let d(p) be the second derivative of x(p). Factor d(k).
3*k*(k - 2)
Let i(n) be the third derivative of -2/3*n**3 + 1/120*n**6 - 1/70*n**7 + 0*n + 0 + 0*n**4 + 7/60*n**5 - 1/336*n**8 + n**2. What is v in i(v) = 0?
-2, -1, 1
Factor 0*d + 0*d**3 + 2/3*d**4 + 0 - 2/3*d**2.
2*d**2*(d - 1)*(d + 1)/3
Suppose 2*o + 4*o = 942. Let 42*x + 280*x**3 - 72*x**3 + 96*x**4 - 7*x**2 + 4 + o*x**2 = 0. Calculate x.
-1, -2/3, -1/4
Let n(s) be the second derivative of -s**7/7 + s**6/10 + 3*s**5/20 + 11*s. Factor n(z).
-3*z**3*(z - 1)*(2*z + 1)
Let z(a) be the third derivative of -3*a**2 + 0*a + 1/30*a**4 + 0 + 1/75*a**6 + 7/150*a**5 - 1/15*a**3. Let z(i) = 0. What is i?
-1, 1/4
Let n(i) be the third derivative of -i**6/30 + i**5/15 - 4*i**2 - 1. Factor n(j).
-4*j**2*(j - 1)
Let m(a) = -a + 2. Let r be m(-4). Let f(s) = -s + r*s + 7*s**2 + s**3 + 6 - 3. Let c(d) = d**3 + 14*d**2 + 10*d + 7. Let g(i) = -4*c(i) + 10*f(i). Factor g(u).
2*(u + 1)**2*(3*u + 1)
Let u(t) = t**2 - 32*t - 75. Let o(m) = -18*m**2 + 513*m + 1200. Let s(j) = 2*o(j) + 33*u(j). Factor s(k).
-3*(k + 5)**2
Let s(i) = -15*i**3 - 44*i**2 + 18*i. Let y(k) = -30*k**3 - 87*k**2 + 36*k. Let p(l) = -9*s(l) + 5*y(l). Factor p(n).
-3*n*(n + 3)*(5*n - 2)
Let a = -158/3 - -647/12. Factor -1/2 - 1/4*u**4 - 9/4*u**2 + 7/4*u + a*u**3.
-(u - 2)*(u - 1)**3/4
Let u(x) be the second derivative of x**6/2 + x**5 + 5*x**4/12 - 9*x. Factor u(p).
5*p**2*(p + 1)*(3*p + 1)
Let r = -198 - -596/3. Factor 0*m + 8/3 - 2*m**2 - r*m**3.
-2*(m - 1)*(m + 2)**2/3
Let g(p) = -p**2 - 10*p - 6. Let u be g(-10). Let t = u + 15. Factor 6*k**3 + t*k**5 - 1 - 2*k**2 - 15*k - 14*k**4 + 20*k**2 + 4 - 7*k**4.
3*(k - 1)**3*(k + 1)*(3*k - 1)
Let h(f) = f. Let q be h(5). Suppose -2*r + 4 = -s, -20 = -0*r + 3*r + q*s. Factor 1/2*d**2 - 1/2*d**4 + 1/2*d**5 + r*d - 1/2*d**3 + 0.
d**2*(d - 1)**2*(d + 1)/2
Let q(a) be the second derivative of -7*a**6/180 + a**5/5 + a**4/3 - 5*a**3/6 - 8*a. Let u(d) be the second derivative of q(d). What is t in u(t) = 0?
-2/7, 2
Let t(a) be the third derivative of -a**10/90720 + a**8/20160 - a**4/12 - 3*a**2. Let i(x) be the second derivative of t(x). Solve i(s) = 0.
-1, 0, 1
Factor 6*l**2 - 3 + 4*l - 8*l**3 + 0 + 4*l - 3.
-2*(l - 1)*(l + 1)*(4*l - 3)
Let w(x) be the second derivative of x**6/180 - x**5/60 + 5*x**3/6 + 4*x. Let h(g) be the second derivative of w(g). Factor h(o).
2*o*(o - 1)
Suppose 92 = -2*k - 5*g - 88, 4*g = -4*k - 384. Let s be (-20)/15 - k/66. Solve 0*c**4 + 4/11 - s*c**5 - 4/11*c**2 + 8/11*c**3 - 6/11*c = 0 for c.
-2, -1, 1
Suppose -5*n = -10*n - 120. Let t be 5/(-2)*n/30. Factor 0 - 3/5*x - 3/5*x**t.
-3*x*(x + 1)/5
Let l(s) = -s**3 - s**2 - 4*s - 3. Let v be l(-2). Suppose v*f - 5*f = 0. Factor -2/5*h**2 + f - 4/5*h.
-2*h*(h + 2)/5
Solve -2/3*r**2 + 0 - 20/3*r**4 + 0*r + 3*r**5 + 13/3*r**3 = 0 for r.
0, 2/9, 1
Let d(p) be the third derivative of -p**5/180 + p**4/24 - p**3/9 - 16*p**2. Factor d(b).
-(b - 2)*(b - 1)/3
Let g(p) be the second derivative of p**8/840 - p**7/210 - p**6/180 + p**5/30 + p**3/3 + 4*p. Let f(d) be the second derivative of g(d). Solve f(l) = 0 for l.
-1, 0, 1, 2
Let t = -169 + 511/3. Factor 5/3*k**3 + 4/3 + t*k - 13/3*k**2.
(k - 2)*(k - 1)*(5*k + 2)/3
Suppose s - 2 = -0. Let -5*f**3 + 6*f - 11*f**2 + 8*f**3 + 2*f**s = 0. Calculate f.
0, 1, 2
Let g be 2 - (-2 + (-60)/(-16)). Determine w so that -1/4*w**3 + g*w + 1/4 - 1/4*w**2 = 0.
-1, 1
Factor 1 + 5/4*q**2 + 1/4*q**3 + 2*q.
(q + 1)*(q + 2)**2/4
Let t(i) be the first derivative of i**7/210 - i**6/120 + 5*i**2/2 - 2. Let a(g) be the second derivative of t(g). Factor a(r).
r**3*(r - 1)
Let h(f) be the second derivative of -5*f**4/12 + 25*f**3/6 - 10*f**2 - 18*f. Factor h(o).
-5*(o - 4)*(o - 1)
Let c(a) be the first derivative of -a**5/20 + a**4/16 + a**3/4 - 5*a**2/8 + a/2 - 8. Determine n, given that c(n) = 0.
-2, 1
Suppose 2*v = -20 - 20. Let n be v/(-21) + (-10)/15. Solve 4/7 + 2/7*s - n*s**3 - 4/7*s**2 = 0.
-2, -1, 1
Let k be ((-20)/(-15))/(2/3). Solve 3*m + 5*m**k - 4*m**2 - m = 0.
-2, 0
Let x = 1/60 + 11/15. Solve -x*c**2 + 1/4 + 1/2*c = 0.
-1/3, 1
Let l(r) = -r**3 - 39*r**2 + 49*r. Let u(w) = -w**3 - 19*w**2 + 24*w. Let h(b) = -4*l(b) + 9*u(b). Determine x, given that h(x) = 0.
-4, 0, 1
Let s = 8957/11 - 813. Let 6/11*q + s*q**3 + 24/11*q**2 - 4/11 = 0. What is q?
-1, 2/7
Let l(c) be the third derivative of 0*c**3 + 2*c**2 + 0*c + 0*c**5 + 1/72*c**4 - 1/360*c**6 + 0. Factor l(f).
-f*(f - 1)*(f + 1)/3
Let h(c) be the second derivative of 7/78*c**4 + 0*c**2 + 0 + 10*c - 1/26*c**5 - 2/39*c**3. Factor h(x).
-2*x*(x - 1)*(5*x - 2)/13
Factor -6/13 + 16/13*k + 0*k**3 - 12/13*k**2 + 2/13*k**4.
2*(k - 1)**3*(k + 3)/13
Let b(l) = l**2 - 2*l - 8. Let t be b(4). Let m(o) = o**2 - 8*o + 9. Let z be m(7). Suppose -32/7*s**z + 6*s**3 + t - 18/7*s**4 + 8/7*s = 0. Calculate s.
0, 2/3, 1
Let o = -182 - -934/5. Let k = -1946/5 + 392. Find b, given that -o*b - 8/5 + k*b**3 + 18/5*b**2 = 0.
-2, -2/7, 1
Let c(j) = -3*j**2 - 2*j - 2. Let m(r) = 4*r**2 + 2*r + 2. Let l(s) = -3*c(s) - 2*m(s). Let d be l(-2). Let -2*a**2 - a - a**3 + 4*a**d + 0*a = 0. What is a?
0, 1
Let d(a) be the second derivative of -1/90*a**6 - 1/126*a**7 + 0*a**2 + 0 + 0*a**3 + 6*a + 1/60*a**5 + 1/36*a**4. Find x such that d(x) = 0.
-1, 0, 1
Factor 2 + 140*i + 5 - 3 + i**2 - 136*i.
(i + 2)**2
Let f(u) be the third derivative of -1/1050*u**7 + 1/300*u**6 + 0*u**4 + 3*u**2 + 0 - 1/300*u**5 + 0*u + 0*u**3. Factor f(j).
-j**2*(j - 1)**2/5
Let z(v) be the third derivative of v**4/24 - v**3/3 - v**2. Let r be z(4). Factor -25*p**2 - 63*p**r - 117*p**3 + 24*p**3 - 16*p - 63*p**3 - 90*p**4.
-2*p*(3*p + 2)**2*(5*p + 2)
Let x(p) be the third derivative of -p**7/420 - p**6/120 + p**5/30 + p**4/24 - p**3/4 - 7*p**2. Solve x(y) = 0 for y.
-3, -1, 1
Let x(a) = -2*a**3 - 3*a**2 + 15*a - 13. Let r(v) = -5*v**3 - 5*v**2 + 30*v - 25. Let t(i) = -3*r(i) + 5*x(i). Factor t(o).
5*(o - 1)**2*(o + 2)
Let x(y) be the third derivative of 1/3*y**3 + 1/540*y**6 - 1/60*y**5 + 0 - 3*y**2 + 0*y + 1/18*y**4. Let d(c) be the first derivative of x(c). Factor d(m).
2*(m - 2)*(m - 1)/3
Let m = -5 - -7. Suppose i = 5*v - 5, i + 5 = m*v + v. Factor 0*o + 6/5*o**3 + v - 4/5*o**2.
2*o**2*(3*o - 2)/5
Suppose 80*n + 24 = 88*n. Factor -2*f + 2/3*f**4 + 2*f**n - 4/3 + 2/3*f**2.
2*(f - 1)*(f + 1)**2*(f + 2)/3
Let a(p) be the third derivative of -p**2 + 1/135*p**7 + 1/108*p**6 - 5/108*p**4 + 0*p + 0 + 2/27*p**3 - 1/30*p**5. What is t in a(t) = 0?
-1, 2/7, 1
Let t = 1860707/14452 - 3/3613. Let p = t + -125. Let -405/4*s**4 + p*s + 135/2*s**3 + 243/4*s**5 - 1/4 - 45/2*s**2 = 0. Calculate s.
1/3
Factor -2/3*t**3 + 0*t + 0*t**2 + 0*t**4 + 2/3*t**5 + 0.
2*t**3*(t - 1)*(t + 1)/3
Determine q so that -1/6 - q**2 + 2/3*q**3 - 1/6*q**4 + 2/3*q = 0.
1
Let c = 99 - 95. Let u(k) be the third derivative of 0*k**3 - 1/180*k**6 - 1/120*k**5 + c*k**2 + 0 + 0*k + 1/144*k**4. Factor u(n).
-n*(n + 1)*(4*n - 1)/6
Suppose 7*i + 3 = 10. Let o(m) be the first derivative of -4/21*m**3 - i + 0*m**2 + 0*m + 9/14*m**4 - 2/5*m**5. Factor o(j).
-2*j**2*(j - 1)*(7*j - 2)/7
Let d(z) be the first derivative of -z**7/315 + z**5/90 + 5*z**2/2 - 5. L