ird derivative of -11*k**2 + 0*k + 2/9*k**4 + 1/45*k**5 + 0 + 0*k**3 - 1/180*k**6. Suppose m(d) = 0. What is d?
-2, 0, 4
Let o(f) be the first derivative of f**6/70 - 9*f**5/70 + 9*f**4/28 - 2*f**3/7 - 17*f - 38. Let w(u) be the first derivative of o(u). Factor w(j).
3*j*(j - 4)*(j - 1)**2/7
Let a = 43/102 + -3/34. Let v(x) be the first derivative of 0*x**2 - a*x**3 + 0*x + 4. Let v(g) = 0. What is g?
0
Let z = -2686539/11 + 244450. Let k = z - 219. Determine q, given that -4/11*q**3 + 2/11*q**5 + 0 + 0*q - k*q**4 + 0*q**2 = 0.
-1, 0, 2
Suppose 3*y - r - 7 - 4 = 0, 0 = 3*y - 3*r - 21. Factor -y*k**3 + 0 + 0*k - 6/5*k**4 - 4/5*k**2.
-2*k**2*(k + 1)*(3*k + 2)/5
Suppose 164*s - 12*s**4 - 92*s**2 - 164*s**3 + 90 - 56 + 70 = 0. Calculate s.
-13, -1, -2/3, 1
Factor -5*j**2 + 34*j - 315 + 134*j - 130*j + 82*j.
-5*(j - 21)*(j - 3)
Suppose -o = z - 5*o - 20, -4*z - 3*o = 15. Factor 0*h + z + 16/9*h**3 + 32/9*h**2 + 2/9*h**4.
2*h**2*(h + 4)**2/9
Let a(z) = -28*z**4 - 208*z**3 - 784*z**2 + 16. Let b(d) = -3679*d**2 + 3940*d**2 - 3*d**4 + 12*d**4 - 5 + 69*d**3. Let f(y) = 5*a(y) + 16*b(y). Factor f(l).
4*l**2*(l + 8)**2
Let x(p) be the first derivative of 6*p - 1/8*p**4 - 6 - 9/4*p**2 - p**3. Let z(b) be the first derivative of x(b). Find r such that z(r) = 0.
-3, -1
Let q = 54 + 5. Let s = 119/2 - q. Solve 0 + s*j - 1/2*j**2 = 0 for j.
0, 1
Let b be (3825/50)/17*(-2)/(-12). Determine t, given that 3/2*t**2 + 0*t**3 + 0*t - 3/4*t**4 - b = 0.
-1, 1
Let f(l) = 3*l - 5. Let q(p) = -p + 2. Let d(h) = -4*f(h) - 11*q(h). Let b be d(-6). Find i, given that 3*i**2 - b + 4 - 6*i = 0.
0, 2
Suppose 0 = 9*w + 10 - 1. Let u be (-5)/w - (-558)/(-126). Factor 2*o**3 + 0 + u*o - 18/7*o**2.
2*o*(o - 1)*(7*o - 2)/7
Factor 10*r**2 + 4*r**3 - 23/4*r + 3/4.
(r + 3)*(4*r - 1)**2/4
Let d = 4/2573 - -82316/12865. Solve 24/5*p - d - 4/5*p**2 = 0.
2, 4
Let t(w) = w**2 + 9*w - 9. Let r be t(-10). Let d be (-5 + (-2)/r)*(-10)/245. Suppose -2/7*p**4 - 2/7*p**3 + 0 + 2/7*p**2 + d*p = 0. What is p?
-1, 0, 1
Let v(t) be the third derivative of t**9/7560 + t**8/1120 + t**7/420 + t**6/360 + 5*t**4/8 + 41*t**2. Let n(f) be the second derivative of v(f). Factor n(u).
2*u*(u + 1)**3
Let h be (1/(-3))/(12/(-72)). Factor r**h - r - r**4 - r + 30*r**3 - 28*r**3.
-r*(r - 2)*(r - 1)*(r + 1)
What is i in 122/9*i + 40/3 + 2/9*i**2 = 0?
-60, -1
Suppose -3*t + 2*i = 7*i - 23, 2*i = -2*t + 14. Let m(j) be the first derivative of 0*j**4 + 0*j - 4 + 1/12*j**t - 1/3*j**3 - 1/4*j**2 + 1/5*j**5. Factor m(u).
u*(u - 1)*(u + 1)**3/2
Let v(g) = -17. Let r(s) = s - 16. Let i(c) = 3*r(c) - 4*v(c). Let y be i(-6). Let -8*b + b**3 - 2*b**3 + 2*b + 9*b + y = 0. What is b?
-1, 2
Let x be 7/6*1280/140. Factor 16/3*f + x + 2/3*f**2.
2*(f + 4)**2/3
Factor 32*c + 5*c**2 + 2*c**3 - 105*c + 15*c + 30 + 21*c**2.
2*(c - 1)**2*(c + 15)
Let z = 1174 + -1171. Let u(f) be the second derivative of 0*f**2 + 2/21*f**3 + z*f + 0 + 1/42*f**4. Factor u(c).
2*c*(c + 2)/7
Let i(f) be the second derivative of f**7/840 - f**5/40 + f**4/12 + f**3/3 - 17*f. Let k(y) be the second derivative of i(y). Let k(z) = 0. Calculate z.
-2, 1
Let y(p) be the first derivative of p**6/9 - 2*p**5/3 + 4*p**4/3 - 8*p**3/9 + 9. Suppose y(j) = 0. What is j?
0, 1, 2
Let t be (6*2/4)/((-11610)/(-1548)). Factor 1/5*k**5 - 2/5*k**2 + 0 - 1/5*k + 0*k**3 + t*k**4.
k*(k - 1)*(k + 1)**3/5
Let y(j) be the third derivative of 12*j**2 + 4/45*j**3 + 0 + 0*j - 2/45*j**4 - 1/900*j**6 + 1/90*j**5. Factor y(f).
-2*(f - 2)**2*(f - 1)/15
Let x(z) be the second derivative of 1/10*z**6 - 1/6*z**4 - 1/42*z**7 + 1/2*z**3 + 13*z - 1/2*z**2 + 0 - 1/10*z**5. Factor x(l).
-(l - 1)**4*(l + 1)
Let m(n) = -3*n**2 + 2*n - 1. Let j(o) = -6*o**2 - 3. Let c(r) = -j(r) + 3*m(r). Factor c(s).
-3*s*(s - 2)
Let r(p) be the first derivative of p**5/80 - p**4/32 - 9*p**2/2 - 6. Let x(o) be the second derivative of r(o). Determine t, given that x(t) = 0.
0, 1
Let z(d) be the first derivative of 1 + 0*d**2 + 4/7*d - 1/7*d**3 - 1/28*d**4. Suppose z(a) = 0. Calculate a.
-2, 1
Suppose -396/5*a**2 + 0 - 57/5*a - 48/5*a**5 - 87*a**3 + 936/5*a**4 = 0. Calculate a.
-1/4, 0, 1, 19
Let j be ((-161)/(-184)*(-4)/(-14))/(12/256). Find b, given that -40/3*b + 25/3 + j*b**2 = 0.
5/4
Let d(g) be the second derivative of g**6/120 - g**4/24 + g**2/8 - 2*g + 7. What is s in d(s) = 0?
-1, 1
Let r(d) be the first derivative of -2*d**3/3 + 27*d**2 - 219. Find x, given that r(x) = 0.
0, 27
Let d(c) = 10*c**3 + 25*c**2 - 195*c - 210. Let q(t) = -5*t**3 - 13*t**2 + 98*t + 106. Let j(x) = 3*d(x) + 5*q(x). Factor j(i).
5*(i - 4)*(i + 1)*(i + 5)
Let z(n) be the third derivative of -n**8/40320 - n**7/336 - 5*n**6/32 - n**5/5 - 9*n**2 - 3*n. Let w(p) be the third derivative of z(p). Solve w(m) = 0.
-15
Suppose -1/5*j**4 - 4/5*j + 4/5*j**2 + 1/5*j**3 + 0 = 0. What is j?
-2, 0, 1, 2
Factor 4 + 7/4*h**5 - 26*h**2 + 28*h**3 - 47/4*h**4 + 4*h.
(h - 2)**3*(h - 1)*(7*h + 2)/4
Let p = -23379 - -23384. Find y such that 1/3*y**4 + 6 + y**3 - 7/3*y**2 - p*y = 0.
-3, 1, 2
Let l(s) be the first derivative of 10 + 3/8*s**2 - 1/4*s**3 + 9/2*s. Factor l(b).
-3*(b - 3)*(b + 2)/4
Let c(q) = -q + 21. Let u be c(5). Determine z, given that -14*z**2 - 18*z**3 - 2*z - 10*z + u*z = 0.
-1, 0, 2/9
Let h(k) = 12*k**3 - 4*k**2 + 38*k + 23. Let n(r) = r**3 - r**2 + 2*r + 1. Let j(p) = 2*h(p) - 22*n(p). Determine i so that j(i) = 0.
-3, -2
Let s(b) be the second derivative of b**6/120 - b**5/8 - b**4/16 + 7*b**3/6 + 5*b**2/2 + 114*b + 1. Factor s(t).
(t - 10)*(t - 2)*(t + 1)**2/4
Suppose -2*c = s + 2*s, -3*c = -3*s. Let p(m) be the first derivative of 8 + 2/3*m**2 - 2/3*m**3 + c*m + 1/6*m**4. Let p(t) = 0. Calculate t.
0, 1, 2
Find a, given that -250*a**4 - 10*a**2 + 120*a**4 + 25*a**3 + 120*a**4 = 0.
0, 1/2, 2
Factor 8/5 + 1/5*o**2 + 9/5*o.
(o + 1)*(o + 8)/5
Suppose -20*g = -17*g - 15. Suppose -33/5*s**4 + 3/5 + 2*s**3 + 6*s**2 - 19/5*s + 9/5*s**g = 0. What is s?
-1, 1/3, 1, 3
Let s be (-8)/(-14) + 424/42 + -8. Let d(o) = 2*o + 1. Let c be d(1). Factor 1/3*y**4 + 8*y**2 + 32/3*y + s*y**c + 16/3.
(y + 2)**4/3
Factor -176/5*m + 128/5 + 52/5*m**2 - 4/5*m**3.
-4*(m - 8)*(m - 4)*(m - 1)/5
Suppose 1000051*d**2 + d**4 - 1000051*d**2 = 0. What is d?
0
Suppose b - 1 = -t, -11*b + 3 = -12*b. Factor 0*n - 8/3*n**2 + 0 - 4/3*n**4 - t*n**3.
-4*n**2*(n + 1)*(n + 2)/3
Let t(j) = 2*j**2 + 2*j - 1. Let z(b) = 35*b**2 + 540*b - 20. Let q(p) = 20*t(p) - z(p). Factor q(h).
5*h*(h - 100)
Let o(u) be the third derivative of 0 - 4/27*u**3 - 1/315*u**7 + 7/270*u**5 + 0*u - 1/540*u**6 - 14*u**2 + 0*u**4 + 1/1512*u**8. Solve o(a) = 0 for a.
-1, 1, 2
Let f(n) be the first derivative of -2*n**3/51 - 2*n**2/17 + 80. Factor f(z).
-2*z*(z + 2)/17
Let p(s) be the second derivative of -s**4/96 - 11*s**3/48 + 3*s**2/4 - 9*s. Factor p(d).
-(d - 1)*(d + 12)/8
Let x = 1109/6 - 60923/330. Let a = x + -1/55. Factor 2/5 + 1/5*h**4 - 1/5*h**3 + a*h - 3/5*h**2.
(h - 2)*(h - 1)*(h + 1)**2/5
Let n(m) = 11*m**3 - 156*m**2 + 1024*m + 5. Let a(l) = 27*l**3 - 390*l**2 + 2559*l + 12. Let i(t) = -5*a(t) + 12*n(t). Factor i(p).
-3*p*(p - 13)**2
Let o(x) = -x**2 + 42*x - 39. Let c be o(30). Let q = c + -959/3. Find l, given that 2/3*l**2 - 4/3*l - 2/3 + q*l**3 = 0.
-1, -1/2, 1
Let z(u) be the second derivative of -u**7/105 + 11*u**6/75 - u + 18. Determine l, given that z(l) = 0.
0, 11
Let a(y) = 3*y**4 + y**3 + 4*y**2 - 6*y + 2. Let l(z) = 2*z**4 - z**3 + 2*z**2 - z + 1. Let o(d) = -a(d) + 2*l(d). Factor o(t).
t*(t - 2)**2*(t + 1)
Let v = 31954/7 - 4558. Suppose -v - 3*y**4 - 3/7*y**5 + 24/7*y + 69/7*y**2 - 3*y**3 = 0. What is y?
-4, -1, 1
Suppose 3*b - 6 = -2*u, 3*u - 118*b = -113*b - 10. Determine q so that 4/3*q - 4/3*q**3 - 2*q**2 + 2*q**4 + u = 0.
-1, 0, 2/3, 1
Let t(f) = 3*f**5 + 2*f**4 - 7*f**3 + f**2 - f + 1. Let w(z) = z**4 + z**3 - z**2 + z - 1. Let m(h) = t(h) + w(h). Determine u, given that m(u) = 0.
-2, 0, 1
Let v(n) = -6*n - 48. Let d be v(-11). Solve -12*k**2 - 30 - 30 + d - 92*k - 14 = 0 for k.
-7, -2/3
Let k = 2054 + -12299/6. Determine u so that 1/6*u**2 + k - 5/3*u = 0.
5
Let z(g) be the third derivative of g**6/180 - g**5/30 - g**4/4 + 5*g**3/6 - 16*g**2. Let a(w) be the first derivative of z(w). Factor a(q).
2*(q - 3)*(q + 1)
Let l be -5 - -3 - 21/(-3). Suppose 2*r - l = -4*o +