econd derivative of 0 - 1/189*g**7 + 7/27*g**3 - 2/135*g**6 - 7*g + 1/45*g**5 + 4/27*g**4 + 2/9*g**2. Let l(a) = 0. What is a?
-1, 2
Solve 38/11*p**2 - 10/11*p**4 + 12/11*p + 16/11*p**3 + 0 = 0.
-1, -2/5, 0, 3
Let p be (-39)/(-5) + (-28)/35. Suppose 2*c**5 - c**5 - 11*c**3 + 16*c**2 + 22*c**3 - p*c**4 - 3*c**3 = 0. Calculate c.
-1, 0, 4
Factor 0 + 90*v**3 + 25*v**4 - 5/2*v**5 + 4320*v - 1620*v**2.
-5*v*(v - 6)**3*(v + 8)/2
Suppose 25/4*x**3 + 105/2*x**2 + 255/4*x + 35/2 = 0. Calculate x.
-7, -1, -2/5
Factor -6*w**3 - 144/7*w**2 - 150/7*w + 3/7*w**4 - 51/7.
3*(w - 17)*(w + 1)**3/7
Suppose 82 = -5*i + 72, -4*t - 5*i = -2. Determine r, given that 26/7*r**t - 24/7*r**2 + 8/7*r + 0 + 2/7*r**5 - 12/7*r**4 = 0.
0, 1, 2
Let m = -1040 + 1043. Determine w so that 16/11*w**4 - 2/11*w**m + 0*w + 0 - 10/11*w**5 - 4/11*w**2 = 0.
-2/5, 0, 1
Let s be (-135)/(-18)*(-6)/(-5). Let f be (9/10)/(s/15). Solve -f*i**2 + 0 - i**3 + i = 0.
-2, 0, 1/2
Let a(g) be the first derivative of g**4/4 + 4*g**3/3 + 3*g**2/2 - 93. Solve a(w) = 0.
-3, -1, 0
Let c(t) be the first derivative of t**6/36 + t**5/15 - 11*t**4/24 - 20*t**3/9 - 11*t**2/3 - 8*t/3 - 113. Suppose c(h) = 0. What is h?
-2, -1, 4
Let q(b) = 4*b**4 - 11*b**3 + 10*b**2 - 3*b + 3. Let g(y) = y**4 - 2*y**3 + 2*y**2 - y + 1. Let a(x) = 15*g(x) - 5*q(x). What is h in a(h) = 0?
0, 1, 4
Let u = 4 + 1. Let r be 0 - -1 - (7 + -4 + -7). Factor -6*n**4 - 2*n**3 - 30*n**5 + 7*n**r - 3*n**4 + 16*n**u.
-n**3*(n + 1)*(7*n + 2)
Let -114*k - 72/5*k**2 + 1444/5 - 2/5*k**3 = 0. What is k?
-19, 2
Let a(u) be the first derivative of -5*u + 5/2*u**2 - 2*u**3 + 3 + u**4. Let z(r) = 5*r**3 - 7*r**2 + 6*r - 6. Let q(k) = -6*a(k) + 5*z(k). Factor q(b).
b**2*(b + 1)
Let o(k) be the first derivative of -k**4/10 + 8*k**3/15 + 11*k**2/5 + 12*k/5 + 136. Suppose o(i) = 0. Calculate i.
-1, 6
Factor 103*l**3 + 3*l - 198*l**3 + 8*l**2 + 99*l**3 - l**2.
l*(l + 1)*(4*l + 3)
Let g(n) be the first derivative of -12*n - 3 - 9*n**2 - 9/4*n**3 - 3/16*n**4. Determine h so that g(h) = 0.
-4, -1
Solve 45/2*k**2 - 195/4*k + 25 + 5/4*k**3 = 0 for k.
-20, 1
Let d(z) be the second derivative of -3/2*z**3 + 5*z + 1/4*z**4 + 3*z**2 + 0. Factor d(r).
3*(r - 2)*(r - 1)
Let j be (4 + -3)/(3/27). Factor v**3 + 10*v - j*v**2 + v**3 - 2*v + v**2.
2*v*(v - 2)**2
Let y(f) = f**2 + 2*f + 2. Let b(d) = -d**2 - d - 1. Let j(p) = -4*b(p) - 3*y(p). Let h(n) = n. Let q(k) = -4*h(k) - 4*j(k). Determine c, given that q(c) = 0.
-1, 2
Find j, given that 4/9*j**3 + 116/9*j**2 + 784/9 + 896/9*j = 0.
-14, -1
Let a = 12 + -21. Let y = -6 - a. Factor 6*o**3 - 18*o**y + 6*o**3 + 3*o**5 + 3*o.
3*o*(o - 1)**2*(o + 1)**2
Let t(i) = 3*i**2 - 39*i - 2. Let a(c) = -5*c**2 + 80*c + 5. Let b(q) = 2*a(q) + 5*t(q). Find x, given that b(x) = 0.
0, 7
Factor 0*j**3 - 15*j**2 + 23*j + 3*j**3 - 2*j - 9.
3*(j - 3)*(j - 1)**2
Let u be (-9)/(-3)*(-6)/((-36)/10). Let k be (-3)/(u/(-6)*72/16). Let -2/5*s**2 - k - 6/5*s = 0. What is s?
-2, -1
Let s(o) be the third derivative of 0*o**3 + 1/570*o**5 + 6*o**2 - 1/1995*o**7 + 0*o**4 + 0*o + 0 + 0*o**6. Determine r so that s(r) = 0.
-1, 0, 1
Factor 2*w + 1/4 + 4*w**2.
(4*w + 1)**2/4
Let l = -167 - -169. Suppose -2*b - 9 + 13 = -l*f, 12 = 4*b - 2*f. Factor -1/2*y**5 + 0*y**b + 0*y**2 + y**3 - 1/2*y + 0.
-y*(y - 1)**2*(y + 1)**2/2
Let p be 0 - 2/((-4)/4). Let -4*h**4 + 2*h - 19*h**3 - p + 4*h**2 + 6*h**5 + 2 + 11*h**3 = 0. What is h?
-1, -1/3, 0, 1
Let -2*u**4 - 4*u**4 - u**4 + 5*u**4 + 2*u**2 = 0. What is u?
-1, 0, 1
Let a(h) = -7*h**3 - 175*h**2 + 1621*h - 1451. Let j(o) = -100*o**3 - 2450*o**2 + 22695*o - 20315. Let b(y) = -85*a(y) + 6*j(y). Suppose b(n) = 0. Calculate n.
1, 17
Let h(l) = -2*l**2 - 51*l - 40. Let t be h(-25). Let b = t + 17. Factor 2/9*j**b + 8/9 + 8/9*j.
2*(j + 2)**2/9
Let t(y) be the third derivative of y**5/20 - 27*y**4/2 + 1458*y**3 + 210*y**2. Factor t(l).
3*(l - 54)**2
Let w(v) be the first derivative of 2*v**4/21 - v**3/21 + v + 12. Let j(t) be the first derivative of w(t). Factor j(r).
2*r*(4*r - 1)/7
Solve 392/11 - 2/11*m**3 - 336/11*m - 54/11*m**2 = 0.
-14, 1
Let v(y) be the second derivative of y**4/42 - 101*y**3/21 + 100*y**2/7 - 7*y - 7. Factor v(a).
2*(a - 100)*(a - 1)/7
Let a = 29941/17 + -1761. Let s(m) be the first derivative of -8 + a*m - 4/51*m**3 + 1/17*m**2 - 1/34*m**4. Find o such that s(o) = 0.
-2, -1, 1
Factor 13*a**2 + 18*a**2 + a**2 + 24 + 3*a**3 + 36*a - 14*a**2.
3*(a + 2)**3
Let f = -13 + 13. Solve -66 - p**3 - 5*p + 68 + 4*p**2 + f*p**3 = 0 for p.
1, 2
Let v(w) be the third derivative of 8*w**2 + 0*w + 1/270*w**6 + 1/315*w**7 + 0 + 1/1512*w**8 - 1/36*w**4 - 1/27*w**3 - 1/135*w**5. Factor v(z).
2*(z - 1)*(z + 1)**4/9
Suppose 6*c + 25 = c, 4*c + 11 = -3*n. Factor 6*u**2 - 27*u**n - 13*u**4 + 17*u**4 - 15*u**5 + 32*u**4.
-3*u**2*(u - 1)**2*(5*u - 2)
Let d(n) = n**4 + 2*n**3 + 2*n + 1. Let t(m) = 10*m**4 + 39*m**3 - 123*m**2 + 197*m - 69. Let s(x) = 36*d(x) - 4*t(x). Determine q, given that s(q) = 0.
-26, 1, 3
Suppose 5*w - 6*w - 3*m = 18, 0 = w - 6*m - 36. Factor w + 2/7*p**2 - 6/7*p.
2*p*(p - 3)/7
Let w = -34247/4 - -8562. Factor -1/4*j**2 + 0*j + 0*j**3 + w*j**4 + 0.
j**2*(j - 1)*(j + 1)/4
Let y(l) be the third derivative of -l**5/20 - 5*l**4/8 - 2*l**3 - 345*l**2. Solve y(q) = 0 for q.
-4, -1
Let f(z) = -2*z**2 + 41*z - 11. Let y be f(19). Let q = y - 46. Determine c so that q + 9/2*c**2 + 9/2*c**3 + 3/2*c + 3/2*c**4 = 0.
-1, 0
Let w(v) = -7*v**4 - 23*v**3 - 8*v**2. Let y(q) = -362*q**2 - 22*q**3 - 3 + 3 + 354*q**2 - 6*q**4. Let s(k) = 6*w(k) - 5*y(k). Find m such that s(m) = 0.
-2, -1/3, 0
Let o be ((-6)/(-26))/(2034/113). Let v(t) be the second derivative of 0 - 4/39*t**3 - 4/13*t**2 - 7*t - o*t**4. Find f, given that v(f) = 0.
-2
Let d = -34/155 - -2332/3565. Let 34/23*v**2 + 8/23 - 32/23*v - d*v**3 = 0. Calculate v.
2/5, 1, 2
Let t(v) be the first derivative of v**3 - 38 + v + 1/4*v**4 + 3/2*v**2. Factor t(k).
(k + 1)**3
Let q = -71 + 67. Let h be (126/(-72))/(5/q). Find l, given that -12/5*l + 6/5*l**2 - 8/5 - 3/5*l**4 + h*l**3 = 0.
-1, -2/3, 2
Let h(m) be the first derivative of 20*m**3 - 90*m**2 - 5/4*m**4 + 0*m - 30. Factor h(o).
-5*o*(o - 6)**2
Let s(z) = z**2 + 4*z + 1. Let b(o) = 14*o**2 + 320*o + 9260. Let d(p) = -b(p) + 12*s(p). Determine u so that d(u) = 0.
-68
Let z(o) be the second derivative of 1/14*o**5 - 4/105*o**6 + 36*o + 0*o**3 - 1/21*o**4 + 0*o**2 + 1/147*o**7 + 0. Factor z(w).
2*w**2*(w - 2)*(w - 1)**2/7
Let a(l) be the third derivative of -l**5/80 + 11*l**4/32 + 13*l**3/4 + l**2 + 74*l. Suppose a(n) = 0. Calculate n.
-2, 13
Factor -13/3*q**2 - 1/3*q**3 - 5 + 29/3*q.
-(q - 1)**2*(q + 15)/3
Let l(v) be the second derivative of v**7/1008 - 11*v**6/288 + 5*v**5/24 + 11*v**4/4 + 20*v. Let i(w) be the third derivative of l(w). Solve i(p) = 0.
1, 10
Let q(c) be the third derivative of c**6/160 - 3*c**5/40 + 9*c**4/32 - 211*c**2. Solve q(g) = 0.
0, 3
Solve 28/9*y + 32/3 + 2/9*y**2 = 0.
-8, -6
Determine h so that -5*h**2 + 1 + 9 + 1569*h - 1564*h = 0.
-1, 2
Factor 2/7*f**2 + 18/7 - 12/7*f.
2*(f - 3)**2/7
Let q(p) be the second derivative of p**7/840 + p**6/80 + p**5/20 + 7*p**4/4 + 9*p. Let v(z) be the third derivative of q(z). Suppose v(h) = 0. What is h?
-2, -1
Let m(t) = 6*t**2 - 34*t - 24. Let d(h) = -h**2 + 7*h + 5. Let n = 36 - 52. Let f(a) = n*d(a) - 3*m(a). Factor f(b).
-2*(b + 1)*(b + 4)
Let l(s) be the first derivative of 2*s**5/45 + 56*s**4/9 - 76*s**3/3 + 344*s**2/9 - 230*s/9 + 632. Factor l(p).
2*(p - 1)**3*(p + 115)/9
Let d(m) = -13*m - 414. Let s be d(-32). Determine h, given that -1/4*h**3 + 1/2*h + 0 + 1/4*h**s = 0.
-1, 0, 2
Let z be 5*1/(-1)*-1. Determine l, given that 5*l**4 - z*l**2 + 5*l**5 + 6*l**3 + 10*l**3 - 21*l**3 = 0.
-1, 0, 1
Let g(r) be the first derivative of -36/5*r - 102/5*r**2 - 42 - 49/5*r**4 - 364/15*r**3. Factor g(f).
-4*(f + 1)*(7*f + 3)**2/5
Let q(p) = -4*p + 10. Let o be q(2). Suppose -5*f + o*f = -5*f. Suppose 0*s - 1/3*s**4 + 4/3*s**3 + f - 4/3*s**2 = 0. Calculate s.
0, 2
Factor 0 - 2/11*a**5 + 48/11*a + 12/11*a**3 - 56/11*a**2 + 6/11*a**4.
-2*a*(a - 2)**3*(a + 3)/11
Let j(k) be the third derivative of 0 + 0*k**4 - 1/252*k**8 - 1/90*k**6 + 0*k**5 + 0*k**3 - 4/315*k**7 + 15*k**2 + 0*k. Factor j(d).
-4*d**3*(d + 1)**2/3
Suppose -3*q + 26 = 20. Suppose -6*