- -40/2163. Let u(n) be the second derivative of -2/105*n**6 - x*n**3 + 1/21*n**4 + 0 + 0*n**2 + 0*n**5 + 1/147*n**7 + n. Factor u(m).
2*m*(m - 1)**3*(m + 1)/7
Let i(z) be the third derivative of 8*z**7/525 + z**6/12 - z**5/30 - 5*z**4/12 - z**3/5 - 114*z**2 + 3*z. Find m such that i(m) = 0.
-3, -1, -1/8, 1
Let m(n) be the first derivative of 4*n**3/21 + 26*n**2/7 + 88*n/7 - 464. Factor m(l).
4*(l + 2)*(l + 11)/7
Let g be (-10)/4 - (-175)/70. Let j(q) be the first derivative of -2 + 0*q**3 + g*q - 1/8*q**4 + 0*q**2 - 1/10*q**5. Suppose j(s) = 0. What is s?
-1, 0
Let b = 3309 - 6429/2. Let w = 96 - b. Suppose -w*m + 3/2*m**3 - 3 + 3*m**2 = 0. What is m?
-2, -1, 1
Factor 12*n - 9 - 21/4*n**2 + 3/4*n**3.
3*(n - 3)*(n - 2)**2/4
Let c(s) = s**5 - 10*s**4 - 5*s**3 + 6*s**2 + 4*s. Let g(i) = -5*i**5 + 40*i**4 + 20*i**3 - 25*i**2 - 15*i. Let n(y) = -15*c(y) - 4*g(y). Solve n(f) = 0.
-1, 0, 1, 2
Let k(z) be the third derivative of 2/525*z**7 + 0*z + 0*z**4 + 0*z**6 + 1/1680*z**8 + 9*z**2 + 0*z**3 + 0*z**5 + 0. Suppose k(s) = 0. Calculate s.
-4, 0
Suppose 4*l = -4*x, 4*x - 16 = 2*l + 14. Suppose t + 16 = x*t. Suppose 5*y**3 + t - 7*y**2 + 4*y**4 - 6*y**2 - 2*y + 5*y**2 - y**3 - 2*y**5 = 0. What is y?
-1, 1, 2
Let x be ((-2002)/(-2145))/((63/10)/9). Determine h so that -4/3 + 8/3*h**3 + 8/3*h**4 - 10/3*h - x*h**2 + 2/3*h**5 = 0.
-2, -1, 1
Let g(f) be the second derivative of 2*f + f**2 + 0 + 11/6*f**3 - 1/4*f**4. Let n(o) = -6*o**2 + 23*o + 5. Let l(m) = -5*g(m) + 2*n(m). Factor l(z).
3*z*(z - 3)
Let r(x) = -10*x**2 - 18*x + 6. Let y(v) = -2*v**2 + v + 1. Let l(k) = r(k) - 6*y(k). What is p in l(p) = 0?
0, 12
Let f(s) be the second derivative of -5*s**4/12 + 5*s**3/2 - s - 1. Suppose f(w) = 0. Calculate w.
0, 3
Let a(l) be the third derivative of -2/525*l**7 + 0 + 0*l + 0*l**4 - 2/75*l**6 - 4/75*l**5 + 0*l**3 - 12*l**2. Suppose a(w) = 0. What is w?
-2, 0
Let f(x) be the second derivative of 1/70*x**5 - 2/7*x**2 + 0 - 10*x + 0*x**4 - 1/7*x**3. Find l, given that f(l) = 0.
-1, 2
Let r = -17737/7 - -2534. Let 0 - 3/7*o - 4/7*o**2 - r*o**3 = 0. What is o?
-3, -1, 0
Let f(i) be the second derivative of -25*i + 0*i**2 + 1/7*i**4 + 0 + 0*i**3 - 1/35*i**5. Factor f(t).
-4*t**2*(t - 3)/7
Let x(b) = 11*b**4 - 18*b**3 - 5*b**2 + 12*b - 3. Let i(a) = 2*a**4 - a**3 - a - 1. Let h(p) = -3*i(p) + x(p). Let h(r) = 0. What is r?
-1, 0, 1, 3
Let u(m) be the second derivative of -m**6/288 + 17*m**5/480 - m**4/16 - 3*m**3 - 9*m. Let f(o) be the second derivative of u(o). Factor f(v).
-(v - 3)*(5*v - 2)/4
Let k = -336 - -340. Let j(c) be the first derivative of 0*c**2 + 0*c - 4/3*c**3 + 1/6*c**6 + 0*c**4 - k + 3/5*c**5. Factor j(q).
q**2*(q - 1)*(q + 2)**2
Let p(l) = 18*l**5 - 6*l**4 - 6*l**3 + 2*l**2 - 6*l. Let b(a) = 18*a**5 - 6*a**4 - 4*a**3 + 4*a**2 - 9*a. Let o(z) = -2*b(z) + 3*p(z). Let o(u) = 0. What is u?
-1/3, 0, 1
Suppose -i + 47 = 15. Let v be 6/(-24) + 36/i. Factor 1/4*z - 5/8*z**2 + 0 - v*z**3.
-z*(z + 1)*(7*z - 2)/8
Factor 220*l**2 + 4*l**4 + 2730*l - 100*l**3 - 16*l**3 - 2838*l.
4*l*(l - 27)*(l - 1)**2
Let t(n) be the first derivative of -1/80*n**5 + 1/8*n**2 - 3*n + 1/16*n**4 - 3 - 1/8*n**3. Let f(a) be the first derivative of t(a). Factor f(g).
-(g - 1)**3/4
Let n be (26/(-12) - (-5)/30)/(22/(-33)). Suppose 8/7*c**5 + 0*c**2 + 2/7*c**n + 0*c + 0 - 10/7*c**4 = 0. Calculate c.
0, 1/4, 1
Suppose 0 + 2/3*v + 1/3*v**2 = 0. Calculate v.
-2, 0
Let o(h) be the third derivative of h**5/15 - 4*h**4/3 + 8*h**3 - 51*h**2 - 1. Solve o(g) = 0 for g.
2, 6
Let m(u) be the first derivative of -5*u**6/24 - 11*u**5/4 - 10*u**4/3 + 10*u**3 + 3*u**2 - 2*u - 45. Let s(z) be the second derivative of m(z). Factor s(q).
-5*(q + 1)*(q + 6)*(5*q - 2)
Let z(u) be the first derivative of 3*u**4 + 6*u + 2/5*u**5 + 3 + 8*u**3 + 10*u**2. What is m in z(m) = 0?
-3, -1
Let q be 6/(-39) - 112/(-52). Factor 1 - 6*g - 10*g**3 - 19*g**4 - 5*g**2 + 22*g**4 + 17*g**q.
(g - 1)**3*(3*g - 1)
Let z(m) be the second derivative of m**7/84 - m**6/60 - m**5/10 + m**4/6 + 4*m + 7. Find o such that z(o) = 0.
-2, 0, 1, 2
Factor -8/3*v**3 - 4*v**2 + 0*v + 4/3.
-4*(v + 1)**2*(2*v - 1)/3
Let r(m) be the first derivative of -43/18*m**4 - 56/9*m**2 - 146/27*m**3 - 22/45*m**5 - 32/9*m + 16 - 1/27*m**6. Find x, given that r(x) = 0.
-4, -1
Let k be (-2)/12*-349 + 20/40. Let l = -58 + k. Suppose 0*g + l*g**3 - 1/3*g**2 + 0 = 0. What is g?
0, 1/2
Let f(v) be the second derivative of 4*v**4/21 + 82*v**3/21 + 20*v**2/7 + 145*v. Find i, given that f(i) = 0.
-10, -1/4
Let x = 7960 + -1042754/131. Let j = 828/917 - x. Factor 3/7*o**2 - j - 3/7*o.
3*(o - 2)*(o + 1)/7
Let s(x) = -x**2 + 9*x - 6. Let i be s(6). Let 3*a**4 + 89*a**2 - i*a - 89*a**2 + 9*a**3 = 0. Calculate a.
-2, 0, 1
Let z = 50 + -48. Factor -36 - 120*l - 13*l**2 - 19*l**z - 31*l**2 - 37*l**2.
-4*(5*l + 3)**2
Suppose -5*k + 3*l = -4*k - 17, 30 = 5*k - 4*l. Find o such that -19*o**2 + 15*o**k - 6*o + 49*o**2 = 0.
0, 2/15
Find s, given that -7*s + 15*s - 8 - 162*s**2 - 2*s**3 + 164*s**2 = 0.
-2, 1, 2
Let s(n) = 3*n**2 + 85*n. Let z(t) = -25*t**2 - 595*t. Let d(a) = -15*s(a) - 2*z(a). Let d(b) = 0. What is b?
0, 17
Let n(s) = -72*s - 428. Let m be n(-6). Let i(h) be the second derivative of -5*h + 6*h**2 + 5/4*h**4 + m*h**3 + 3/20*h**5 + 0. Solve i(w) = 0 for w.
-2, -1
Let w(q) be the first derivative of 3*q**4/8 - 5*q**3/2 - 69*q**2/2 - 60*q - 674. Factor w(y).
3*(y - 10)*(y + 1)*(y + 4)/2
Let o = -2993/2 - -1501. Factor -3/2*b**3 - 3 + 0*b**2 + o*b.
-3*(b - 1)**2*(b + 2)/2
Find p such that -2/19*p**2 + 4/19*p + 0 - 4/19*p**3 + 2/19*p**4 = 0.
-1, 0, 1, 2
Let c(a) be the third derivative of -a**10/50400 + a**8/3360 - a**6/240 + a**5/5 + 13*a**2. Let i(l) be the third derivative of c(l). Factor i(u).
-3*(u - 1)**2*(u + 1)**2
Factor 85750/13 + 210/13*h**2 + 2/13*h**3 + 7350/13*h.
2*(h + 35)**3/13
Let h = -35 - -24. Let l = h + 13. Determine k, given that 7 - 3*k**2 + 12*k - 2*k**2 - 19 + 2*k**l = 0.
2
Let r(a) = 4*a**2 + 33*a - 42. Let o(i) = 6*i**2 + 49*i - 66. Let g(z) = 5*o(z) - 7*r(z). Factor g(f).
2*(f - 2)*(f + 9)
Let s(g) = -1. Let z(q) be the third derivative of q**5/60 - q**4/12 - q**3/3 + 16*q**2. Let w(r) = 3*s(r) - z(r). Solve w(i) = 0.
1
Let z be (-27267)/(-4172) + (-1)/4. Let 4/7*q**3 + z*q - 36/7*q**2 + 4/7*q**4 - 16/7 = 0. Calculate q.
-4, 1
Let y(o) be the third derivative of -o**7/840 - o**6/90 - o**5/40 + 11*o**3/6 - 4*o**2. Let w(p) be the first derivative of y(p). Let w(v) = 0. What is v?
-3, -1, 0
Suppose -f + o = -o - 5, 0 = -2*f + 2*o + 8. Suppose -26 + 16 = -5*z. Let -2*l**2 + 0*l**z - l + f - 3*l - 5 = 0. Calculate l.
-1
Let x(y) = -y**3 - 10*y**2 - 20*y - 28. Let s be x(-8). Factor 44/5*g**3 + 2/5*g + 0 + 48/5*g**s + 18/5*g**5 + 16/5*g**2.
2*g*(g + 1)**2*(3*g + 1)**2/5
What is b in -21*b**3 + 4*b**4 + 13*b + 1449*b**2 - 1453*b**2 - b + 9*b**3 = 0?
-1, 0, 1, 3
Let x be 4/(-14) + 10378/(-35). Let q = x + 298. Solve 6/5 + 3/5*n**3 - 3/5*n - q*n**2 = 0.
-1, 1, 2
Suppose 7*q + 12 = 3*m, -4*q + 0 - 16 = -4*m. Let s(t) be the second derivative of 0 - 6*t + q*t**4 + 0*t**5 + 0*t**2 - 1/150*t**6 + 0*t**3. Factor s(y).
-y**4/5
Let r = 11341 - 22681/2. Factor r*z**2 + 1 - 3/2*z.
(z - 2)*(z - 1)/2
Factor -2/9*p + 4/9*p**4 + 0 + 8/9*p**2 - 10/9*p**3.
2*p*(p - 1)**2*(2*p - 1)/9
Factor -3/7*v**3 + 162/7*v**2 + 17496/7 - 2916/7*v.
-3*(v - 18)**3/7
Suppose -6 - 79 = -17*u. Suppose -s = -u*s + 16. What is o in -26/7*o**2 + 12/7*o**3 - 8/7 - 2/7*o**s + 24/7*o = 0?
1, 2
Let p = 146950/7 - 20992. Let p*b**5 + 10/7*b**4 - 4/7*b - 2/7*b**3 + 0 - 10/7*b**2 = 0. Calculate b.
-1, -2/3, 0, 1
Let v(t) be the third derivative of -3/4*t**5 - 4*t**2 - 40/3*t**3 + 1/24*t**6 + 0 + 0*t + 5*t**4. What is h in v(h) = 0?
1, 4
Let g(c) = -15*c**4 - 60*c**3 - 85*c**2 - 35*c + 5. Let q(r) = -7*r**4 - 30*r**3 - 43*r**2 - 18*r + 2. Let y(f) = 2*g(f) - 5*q(f). Factor y(x).
5*x*(x + 1)**2*(x + 4)
Let a be -11 - ((-63)/3 + 7). Let x(i) be the first derivative of 7 - 1/8*i**4 + 1/4*i**2 + i - 1/3*i**a. Factor x(z).
-(z - 1)*(z + 1)*(z + 2)/2
Let g(t) = -3343*t + 10033. Let l be g(3). Solve -l*r**2 + 16/3 + 16/3*r + 4/3*r**4 - 8/3*r**3 = 0 for r.
-1, 2
What is s in 28*s**2 + 4*s**4 - 6*s**3 - 12*s + 68 - 14*s**3 - 68 = 0?
0, 1, 3
Suppose -2*s - i = 2, -s = 4*s + 4*i + 8. Determin