(v).
-v**3/4
Let v(y) be the third derivative of -y**7/90 - y**6/20 + y**5/20 + 230*y**2. What is b in v(b) = 0?
-3, 0, 3/7
Let b = -3/92 - -91/1380. Let a(v) be the second derivative of -1/60*v**4 + 1/150*v**6 + 0*v**2 + 0 + 1/100*v**5 + 5*v - b*v**3. Suppose a(q) = 0. Calculate q.
-1, 0, 1
Let -26*q**3 + 0 - 4/5*q**4 - 68/5*q + 202/5*q**2 = 0. What is q?
-34, 0, 1/2, 1
Let t(r) be the first derivative of 28 + 28*r**2 - 2/3*r**3 - 392*r. Determine a, given that t(a) = 0.
14
Let m(u) be the third derivative of u**8/1008 - u**7/315 - u**6/60 + u**5/45 + 13*u**4/72 + u**3/3 - 4*u**2 + 10. Factor m(x).
(x - 3)*(x - 2)*(x + 1)**3/3
Let a(h) be the first derivative of 2*h**3/15 + 52*h**2/5 + 1352*h/5 + 95. Find f, given that a(f) = 0.
-26
Suppose -13*f + 16*f = 4*l + 200, -194 = -3*f + l. Let o(j) be the first derivative of -4/3*j**3 + 6 - f*j + 16*j**2. Factor o(k).
-4*(k - 4)**2
What is u in 1/5*u**3 - 33275 + 1815*u - 33*u**2 = 0?
55
Let c(u) = 8*u**2 - 232*u - 219. Let j(w) = 4*w**2 - 116*w - 108. Let n(b) = 4*c(b) - 7*j(b). Suppose n(l) = 0. What is l?
-1, 30
Let n(j) be the first derivative of 5*j**4/36 + 10*j**3/9 + 10*j**2/3 + 10*j + 2. Let x(b) be the first derivative of n(b). Factor x(w).
5*(w + 2)**2/3
Let v(b) be the second derivative of -24*b**6/5 - 161*b**5/5 - 70*b**4/3 - 16*b**3/3 + 72*b - 2. What is j in v(j) = 0?
-4, -1/4, -2/9, 0
Let w be (-14)/(-4) - (-19)/((-418)/33). Let s(h) be the first derivative of 6 + 0*h**w + 5*h - 5/3*h**3. Factor s(i).
-5*(i - 1)*(i + 1)
Let t(k) be the third derivative of k**6/300 - 3*k**5/50 + 2*k**4/15 - 15*k**2 - 3. Factor t(h).
2*h*(h - 8)*(h - 1)/5
Let a(u) be the first derivative of 0*u**2 - 5/3*u**3 + 31 + 0*u - 5/4*u**4. Find d such that a(d) = 0.
-1, 0
Suppose 0 = -4*a + 5*w + 250, 65 = a - w + 3. Let i = a + -55. Factor 2/3*o**i - 4/3*o**2 + 4/3*o**4 + 0 - 2/3*o + 0*o**3.
2*o*(o - 1)*(o + 1)**3/3
Let s(u) = 18*u + 1208. Let q be s(-67). Suppose -8/3 + 22/3*t**q + 16/3*t + 2*t**3 = 0. Calculate t.
-2, 1/3
Let h(v) = 5*v**3 - 4*v**2 + v + 1. Let u(l) be the first derivative of -l**4/4 - l**2/2 + l - 28. Let y(o) = h(o) + 3*u(o). Suppose y(m) = 0. What is m?
-1, 1, 2
Let w(v) be the second derivative of v**5/20 - 41*v**4/12 - 85*v**3/6 - 43*v**2/2 - v + 10. Suppose w(h) = 0. Calculate h.
-1, 43
Let q be 12/(-4) - -6 - -1*1. Factor -17*h**5 - 5*h**q + 13*h**5 + 0*h**4 + 4*h**2 + 4*h**3 + h**4.
-4*h**2*(h - 1)*(h + 1)**2
Let v(b) = b**3 - 12*b**2 + 2*b - 9. Let l be v(12). Let z be (-6)/18*(l*2)/(-3). Factor -4*j**3 - 2*j**2 - j**5 - z*j**4 - 1/3*j + 0.
-j*(j + 1)**3*(3*j + 1)/3
Suppose 15 + 60*c - 13 - 2 - 5*c**2 = 0. What is c?
0, 12
Let v(j) be the first derivative of -2*j**5/5 + 2*j**4 - 10*j**3/3 + 2*j**2 - 77. Solve v(p) = 0.
0, 1, 2
Let u(g) be the third derivative of -g**6/240 - g**5/120 + g**4/8 + 253*g**2. Factor u(v).
-v*(v - 2)*(v + 3)/2
Suppose 0 = -g - 2*g + 9. Let s be ((-1)/(g/(-6)))/(3/1). Solve -s*m + 2/3 + 2/3*m**3 - 2/3*m**2 = 0.
-1, 1
Let n(u) be the first derivative of -15 + 0*u - 2/11*u**2 + 2/33*u**3. Factor n(t).
2*t*(t - 2)/11
Let c = -484/7 - -2448/35. Let d(l) be the second derivative of -c*l**3 + 8*l + 6/5*l**4 + 1/5*l**2 + 0. Factor d(n).
2*(6*n - 1)**2/5
Let h(t) be the second derivative of 5*t**5/6 - 65*t**4/18 - 29*t**3/9 - t**2 - 38*t. Factor h(d).
2*(d - 3)*(5*d + 1)**2/3
Suppose -2*g + 0*g + 4 = 0. Factor 2*q**g - 12 - 5*q**2 - 3*q**3 - q**3 - 28*q - 17*q**2.
-4*(q + 1)**2*(q + 3)
Let d(l) be the first derivative of -l**6/24 + l**5/5 + 507. Factor d(i).
-i**4*(i - 4)/4
Let r(f) be the first derivative of -4*f**5/15 - 2*f**4/3 + 4*f**3/3 + 8*f**2/3 - 16*f/3 - 118. Suppose r(o) = 0. Calculate o.
-2, 1
Let r(l) = 10*l**2 + 12*l - 16. Let i(w) = w**2 + 3*w. Let g(c) = 18*i(c) - 2*r(c). Find h, given that g(h) = 0.
-1, 16
Let a(s) be the third derivative of s**9/1512 - s**8/420 + s**6/90 - s**5/60 + 13*s**3/3 + 2*s**2 + 21*s. Let n(k) be the first derivative of a(k). Factor n(r).
2*r*(r - 1)**3*(r + 1)
Let p = 314 - 25119/80. Let d(z) be the second derivative of 0*z**3 + 0 - z - 1/168*z**7 + 0*z**2 + 0*z**6 + 0*z**4 + p*z**5. Solve d(k) = 0.
-1, 0, 1
Let u = 282 - 859/3. Let c = 17/3 + u. Solve 1/3*l**3 + l**2 - c + 0*l = 0.
-2, 1
Let z be (16/(-6))/(1112/(-695)). Factor 0*q + 1/3*q**3 + 0 + z*q**2.
q**2*(q + 5)/3
Factor 9/5*n**3 + 1/5 + 7/5*n + 3*n**2.
(n + 1)*(3*n + 1)**2/5
Let v = 1236 + -1234. Solve 3/4*a**3 + 1/4*a + 0 - 3/4*a**v - 1/4*a**4 = 0.
0, 1
Suppose 4*v = 6*v. Suppose 5*i + 18 - 83 = v. Find c, given that -28*c**3 + 31*c**3 - 7*c + 31*c + 15*c**2 + i - 1 = 0.
-2, -1
Suppose 15*p = 97 - 67. Factor 3/2*f**p + 0 - 3/2*f.
3*f*(f - 1)/2
Let d be (5/(-10))/((168/(-5120))/7). Factor 0 - 80/3*l**2 - d*l - 5/3*l**3.
-5*l*(l + 8)**2/3
Let x(g) = 3*g**2 - 15*g - 40. Let n be x(-2). Let k(u) be the first derivative of 6*u**n - 18*u + 8 - 2/3*u**3. Factor k(y).
-2*(y - 3)**2
Let f(s) be the third derivative of -1/30*s**5 - 21*s**2 + 0 + 1/12*s**4 + 1/3*s**3 - 1/60*s**6 + 0*s. Determine l, given that f(l) = 0.
-1, 1
Let f(v) be the third derivative of 0*v**3 + 18*v**2 + 1/150*v**6 + 0*v**5 + 0*v + 0 - 1/30*v**4. Let f(u) = 0. Calculate u.
-1, 0, 1
Let o = 23 + -17. Let r(g) = 10*g**2 - 30*g + 6. Let s(t) = -2*t**2 + 6*t - 1. Let y(n) = o*r(n) + 28*s(n). Let y(w) = 0. Calculate w.
1, 2
Let s(g) be the third derivative of -121*g**5/150 - 33*g**4/10 - 27*g**3/5 + 222*g**2. Suppose s(p) = 0. Calculate p.
-9/11
Let i(m) be the third derivative of -2*m**7/21 + 13*m**6/24 + 8*m**5/3 + 25*m**4/8 + m**2 + 104. Determine p, given that i(p) = 0.
-1, -3/4, 0, 5
Let r(k) = 4*k**2 + k + 2. Let a(v) = 11*v**2 - 221*v - 212. Let b(u) = a(u) - 4*r(u). Suppose b(d) = 0. What is d?
-44, -1
Let x(o) be the first derivative of 4*o**5/5 - 54*o**4 + 972*o**3 + 139. Factor x(k).
4*k**2*(k - 27)**2
Suppose 16 = 2*y + 8. Factor 9*k**y - 1 + 2*k**3 - 5*k**5 - 125*k + 128*k - 10*k**2 + 2.
-(k - 1)**3*(k + 1)*(5*k + 1)
Let p(o) be the first derivative of -o**4/10 + 8*o**3/15 + 19*o**2/5 + 28*o/5 + 10. Factor p(s).
-2*(s - 7)*(s + 1)*(s + 2)/5
Let i(h) = 10*h**3 - 16*h**2 - 2*h + 20. Let t(q) = 22*q**3 - 32*q**2 - 4*q + 41. Let y(v) = -9*i(v) + 4*t(v). Factor y(n).
-2*(n - 8)*(n - 1)*(n + 1)
Let q(k) be the first derivative of 2/3*k**3 + 2/45*k**5 - 7/9*k**2 - 5/18*k**4 - 16 + 4/9*k. Suppose q(a) = 0. What is a?
1, 2
Let q(l) be the first derivative of -l**7/2240 - l**6/960 + l**5/320 + l**4/64 + 7*l**3/3 + 6. Let m(s) be the third derivative of q(s). Factor m(p).
-3*(p - 1)*(p + 1)**2/8
Let k = -17 + 19. Let l(x) = x**2 - 3*x + 5. Let o be l(k). Factor -3/7*a + 6/7*a**o + 0*a**4 + 0 - 3/7*a**5 + 0*a**2.
-3*a*(a - 1)**2*(a + 1)**2/7
Suppose -3*h = o + h + 10, -h - 7 = -2*o. Factor 215*q - 230*q - 17*q**o - 8*q**2 + 10.
-5*(q + 1)*(5*q - 2)
Let b(k) be the first derivative of k**5/10 - 3*k**4/8 + k**3/3 - 104. Factor b(d).
d**2*(d - 2)*(d - 1)/2
Let q(m) be the second derivative of -2/13*m**2 + 0 + 1/78*m**4 - 36*m + 1/39*m**3. Solve q(w) = 0.
-2, 1
Let p be (-2 - (-120)/65) + 86/52*1. Suppose -6 + 3/4*a**3 + p*a**2 - 3*a = 0. What is a?
-2, 2
Factor 112/17*y - 1568/17 - 2/17*y**2.
-2*(y - 28)**2/17
Let l be 0 - (-2 - -1)*1*3. Let o(w) be the first derivative of -2/33*w**3 - 2/11*w - l - 2/11*w**2. Factor o(a).
-2*(a + 1)**2/11
Let g(k) = -6*k**3 - 17*k**2 + 63*k + 88. Let o(t) = 5*t**3 + 17*t**2 - 63*t - 87. Let u(j) = -6*g(j) - 7*o(j). Factor u(m).
(m - 9)**2*(m + 1)
Suppose -2*t - 4 = 0, 0 = 5*x + 5*t - 1 - 4. Let l(q) be the second derivative of 0*q**x + 1/20*q**5 - 2*q + 0 - 1/6*q**4 + 0*q**2. Suppose l(g) = 0. What is g?
0, 2
Let z(u) be the second derivative of -u**4/12 + 4*u**3/3 - 7*u**2/2 + 5*u. Let a be z(6). Factor 2*r**3 + 5*r - a*r.
2*r**3
Let z = 55 + -54. Let x be 8/(-2) - (76/(-10))/z. Find k such that -4/5 - 2*k**2 + 14/5*k**4 + 18/5*k**3 - x*k = 0.
-1, -2/7, 1
Suppose 4/15*l**3 + 4/5*l**2 - 2/3*l + 2/5*l**5 - 14/15*l**4 + 2/15 = 0. Calculate l.
-1, 1/3, 1
Determine h so that 45/4*h**3 - 3*h**4 - 12*h**2 + 3/2 + 9/4*h = 0.
-1/4, 1, 2
Let o(x) be the third derivative of -x**5/24 + 5*x**3/3 + 4*x**2 - 2*x. Factor o(a).
-5*(a - 2)*(a + 2)/2
Let j(d) be the first derivative of 2*d**5/35 - 4*d**3/7 - 8*d**2/7 - 6*d/7 + 88. Factor j(l).
2*(l - 3)*(l + 1)**3/7
Let h(c) be the seco