the second derivative of -3/5*r**5 - 2/3*r**3 + 0 + 0*r**2 + 2/15*r**6 - 9*r + r**4. Find a, given that u(a) = 0.
0, 1
Suppose 0 = 15*m + 119 - 119. Let i(k) be the second derivative of -3*k**2 + m - 8*k**4 - 57/10*k**5 - 5/14*k**7 - 11/5*k**6 + 14*k - 13/2*k**3. Solve i(w) = 0.
-1, -2/5
Let v(u) be the first derivative of -u**3/33 + 27*u**2/22 + 28*u/11 - 19. Factor v(h).
-(h - 28)*(h + 1)/11
Let m = 132 - 115. Suppose 5 = -4*n + m. Suppose -4/3 - 5/3*d**2 + 8/3*d + 1/3*d**n = 0. Calculate d.
1, 2
Suppose -5*n - 6 = -16, -3*n - 4 = -5*v. Suppose 2*y + 3*p + 2 = 3*y, -2*y = -4*p - 4. Factor 5*q**2 + v*q**2 + 4*q - 6*q**y + q**2.
2*q*(q + 2)
Let w be -58*4/104 + (-20 - (-44 + 21)). Factor 8/13*n**2 - 2/13*n**3 - w*n + 4/13.
-2*(n - 2)*(n - 1)**2/13
Let b be ((-299)/(-91) + -3)/(1/4 + 0). Let b*k**2 + 4/7*k**3 + 0*k + 0 = 0. Calculate k.
-2, 0
Let o = -346 + 346. Let w(c) be the first derivative of o*c - 4 - 1/3*c**3 - 1/2*c**2. Let w(u) = 0. What is u?
-1, 0
Let r(x) = 2*x**2 - 11*x - 6. Let q(b) = -2*b**2 + b + 1. Let v(f) = 4*q(f) + 2*r(f). Factor v(c).
-2*(c + 4)*(2*c + 1)
Let g(v) be the first derivative of -7*v**6/30 + 2*v**5 - 6*v**4 + 16*v**3/3 + 8*v**2 + 2*v + 15. Let a(w) be the first derivative of g(w). Factor a(s).
-(s - 2)**3*(7*s + 2)
Suppose 2*w = -0*w + 12. Suppose -4*h + 6 + w = 0. Factor -6*q**2 + 4 - 4*q**h - 6*q**2 - 8 - 12*q.
-4*(q + 1)**3
Let f(z) be the third derivative of 1/60*z**6 - 1/630*z**7 + 6*z**2 - 1/15*z**5 + 1/9*z**4 + 0*z + 0 + 0*z**3. What is y in f(y) = 0?
0, 2
Let i be ((-20)/6)/((-12)/9 - -1). Suppose 2*o = 2*j - 8, -5*o + 3*o = -3*j + i. Factor -17/6*t**j + 10/3*t + 2/3*t**3 - 2/3.
(t - 2)**2*(4*t - 1)/6
Suppose -16 = -294*t + 568*t - 282*t. Let 2/15*d**t - 8/5 - 2/15*d = 0. Calculate d.
-3, 4
Suppose -3*o - 4*b = 24, -3*o - 5*b + 11 - 41 = 0. Let p = -3 + 5. Factor -x**3 + 0*x + 1/3*x**p + o.
-x**2*(3*x - 1)/3
Let y(a) = -a**3 + 10*a**2 - 14*a - 9. Let p be y(8). Let b be (-86)/(-84) + p/(-42). Factor -b*g**2 - 2/7 + 18/7*g**3 - 10/7*g.
2*(g - 1)*(3*g + 1)**2/7
Let z(u) be the third derivative of u**11/66528 - u**9/6048 + u**7/1008 + u**5/10 + u**2. Let g(y) be the third derivative of z(y). Find v, given that g(v) = 0.
-1, 0, 1
Let p(m) be the third derivative of m**6/72 + m**5/24 - m**3 - 13*m**2. Let b(w) be the first derivative of p(w). Factor b(t).
5*t*(t + 1)
Suppose 15*n = 13*n + 4. Let -6*w**3 + 7*w**3 + 16*w**n - 10*w**3 + 4*w**4 - 7*w**3 = 0. What is w?
0, 2
Suppose -3*a**4 - 2531*a + 15*a**4 - 120*a**3 + 20*a**3 + 116*a**2 + 2503*a = 0. What is a?
0, 1/3, 1, 7
Factor -64/7*r - 4/7*r**4 - 32/7*r**3 - 72/7*r**2 - 20/7.
-4*(r + 1)**3*(r + 5)/7
Factor 0 + 4/7*x**4 + 6/7*x**3 - 8/7*x - 2/7*x**5 - 8/7*x**2.
-2*x*(x - 2)**2*(x + 1)**2/7
Let r(x) be the third derivative of -x**5/20 - 11*x**4/2 - 242*x**3 - x**2. Solve r(u) = 0.
-22
Let a(b) = -b**2 + 7*b. Let d(c) = 16*c**2 - 212*c - 84. Let f(o) = 36*a(o) + 2*d(o). Determine r, given that f(r) = 0.
-42, -1
Let t(s) be the third derivative of -s**6/72 + 2*s**5/45 - s**4/72 - s**3/9 + 7*s**2. Factor t(b).
-(b - 1)**2*(5*b + 2)/3
Let n(m) = 5*m**2 - 7*m. Let f(z) be the second derivative of -27*z**4/4 + 37*z**3/2 - 3*z. Let u(i) = 2*f(i) + 33*n(i). Factor u(r).
3*r*(r - 3)
Let k be (-6 - -3) + 2 + 182/70. Factor 8/5*d - k + 2/5*d**4 + 6/5*d**2 - 8/5*d**3.
2*(d - 2)**2*(d - 1)*(d + 1)/5
Let b(z) be the first derivative of -z**4/32 + 11*z**3/24 - 21. Solve b(w) = 0 for w.
0, 11
Suppose 0 = 4*f, -3*f = -2*p - 5*f. Factor 0*d + p + 0*d**2 - 1/3*d**3.
-d**3/3
Let w = 1209/1555 + 7/311. Factor 2/5*j + 2/5*j**2 - w.
2*(j - 1)*(j + 2)/5
Let k = -98 + 690/7. Let g = -80 + 562/7. Solve -2/7 - g*y**4 + 2/7*y + 4/7*y**2 + 2/7*y**5 - k*y**3 = 0 for y.
-1, 1
Let l(i) be the third derivative of -1/75*i**3 + 1/1500*i**6 + 0*i + 0 - 1/250*i**5 - 3*i**2 + 1/100*i**4. Factor l(c).
2*(c - 1)**3/25
Let m(g) be the first derivative of 2*g**5/5 - 11*g**4/2 + 52*g**3/3 - 16*g**2 - 208. Factor m(r).
2*r*(r - 8)*(r - 2)*(r - 1)
Let z(u) = u**2 - 3*u + 2. Let d be z(3). Suppose 0 = -4*h + 3*m + m + 20, 0 = -h + d*m + 4. Solve 2*f + 4 - f**2 - h*f + 0*f + 2*f**2 = 0.
2
Let j(s) be the second derivative of s**9/1512 - s**7/210 + s**5/60 - 7*s**3/3 - 13*s. Let x(w) be the second derivative of j(w). Let x(d) = 0. Calculate d.
-1, 0, 1
Let f(m) be the first derivative of -2*m**5/5 - 22*m**4 - 968*m**3/3 + 170. Factor f(s).
-2*s**2*(s + 22)**2
Let m(t) be the first derivative of 8/3*t**3 - 30*t**2 + 28*t - 16. Factor m(c).
4*(c - 7)*(2*c - 1)
Let g be (-4)/20 - ((-1)/5 + -3). What is y in -3*y**3 - 2*y**2 + 11*y - 6*y + 2 - 2*y**g = 0?
-1, -2/5, 1
Let a = 62 + -64. Let r(v) = -5*v**4 - 16*v**3 - 13*v**2 - 5*v. Let y(n) = n**4 + n**2 - n. Let k(q) = a*r(q) + 2*y(q). Factor k(p).
4*p*(p + 1)**2*(3*p + 2)
Let t(h) be the second derivative of -h**7/420 - 13*h**6/540 - 4*h**5/45 - h**4/9 - h**3 + 3*h. Let y(c) be the second derivative of t(c). Factor y(x).
-2*(x + 2)**2*(3*x + 1)/3
What is c in -21*c + 8*c**3 - 52*c**2 + 19*c + 12*c**3 + 26*c = 0?
0, 3/5, 2
Let r(l) be the second derivative of -l**7/84 - l**6/12 - 9*l**5/40 - 7*l**4/24 - l**3/6 - 129*l. Factor r(b).
-b*(b + 1)**3*(b + 2)/2
Let m be (-476)/(-221) - (-4)/(-26). Solve 7*q - 49/2 - 1/2*q**m = 0.
7
Let x(m) = 3*m**3 - 4*m + 5*m + 4 - 4*m**3. Let r be x(0). Let s**3 - 6*s**2 + 6*s**3 - 16*s**2 + 21*s**3 + r*s = 0. What is s?
0, 2/7, 1/2
Let m(j) be the second derivative of 1/35*j**5 + 0 + 16/21*j**3 - 1/3*j**4 - 17*j + 32/7*j**2. Let m(k) = 0. Calculate k.
-1, 4
Suppose 0 + o**3 - 1/2*o**2 + 1/2*o**4 - o = 0. What is o?
-2, -1, 0, 1
Let v(j) be the first derivative of -j**5/2 - 7*j**4/6 + 8*j**3/3 + 4*j**2 - 16*j - 12. Let r(m) be the first derivative of v(m). Determine o so that r(o) = 0.
-2, -2/5, 1
Let f = 48 + -33. Let k be ((-36)/f + 2)*-5. Factor -13*y**2 + 17*y**k - 14*y**2 - 5*y - 10*y**3 - 5*y**4 - y**5 - 1.
-(y + 1)**5
Let i be (-4)/(-5)*((-21)/18 - -2). Let -2/3*f**2 + 4/3 + i*f = 0. Calculate f.
-1, 2
Let s(a) be the second derivative of -a**4/90 - a**3/9 + 2*a**2/5 - 11*a + 2. Factor s(i).
-2*(i - 1)*(i + 6)/15
Let d = -1468/5 + 294. Determine t so that 8/5 - 8/5*t**2 - 2/5*t**3 + d*t = 0.
-4, -1, 1
Suppose 3*j - 14 = -254. Let v = -77 - j. Determine d so that 2/15*d**v - 2/15*d**2 - 8/15*d + 8/15 = 0.
-2, 1, 2
Let o(i) = i**2 - 6*i + 14*i**3 - 25*i**3 + 13*i**3. Let m(z) = 3*z**3 - 7*z. Let s(f) = -3*m(f) + 4*o(f). Factor s(l).
-l*(l - 3)*(l - 1)
Let g be ((-21)/(-245))/((-9)/(-63)). Factor 3/5 + 6/5*v + g*v**2.
3*(v + 1)**2/5
Suppose 4*m = y + 21, 5*m = -3*y + 5 - 0. Suppose -w - 12 = -m*w. Factor -4*o**4 + o**2 + 4*o**w - o**4.
-o**2*(o - 1)*(o + 1)
Let q(y) be the second derivative of -y**6/6 + 3*y**5/2 - 5*y**4 + 20*y**3/3 + 2*y + 24. Factor q(w).
-5*w*(w - 2)**3
Let g(n) be the first derivative of 0*n + 0*n**3 - 1/6*n**2 + 11 + 1/12*n**4. Factor g(f).
f*(f - 1)*(f + 1)/3
Let f(v) be the third derivative of v**5/12 - 265*v**4/24 + 130*v**3/3 + 5*v**2 - 74. Solve f(a) = 0 for a.
1, 52
Factor -145*v + 3*v**3 - 107*v + 24*v**2 - 3*v**4 + 216*v.
-3*v*(v - 2)**2*(v + 3)
Let i(w) be the second derivative of -1/2*w**2 + 0 - 1/6*w**3 + 1/20*w**5 + 1/12*w**4 + 4*w. Factor i(c).
(c - 1)*(c + 1)**2
Let x(s) = 4*s**4 - 12*s**3 + 15*s**2 + 11*s - 5. Let b(g) = -5*g**4 + 13*g**3 - 16*g**2 - 10*g + 6. Let k(f) = 5*b(f) + 6*x(f). What is q in k(q) = 0?
-8, -1, 0, 2
Suppose 3*q + 1 = -2*c - 41, -3*c + 3 = -q. Let y be -6 + 4 - (-4)/(q/(-15)). Factor -3/5*l**4 + 0 + 6/5*l + 12/5*l**y - 3*l**2.
-3*l*(l - 2)*(l - 1)**2/5
Let u(i) be the first derivative of 0*i**2 - 14/15*i**3 + 0*i - 1/10*i**4 - 44. Factor u(t).
-2*t**2*(t + 7)/5
Determine d so that 24/7*d**4 - 18/7*d**3 - 24/7*d**2 + 3*d - 3/7*d**5 + 0 = 0.
-1, 0, 1, 7
Factor -2*s**4 - 60 + 41*s**2 - 52*s + 0*s**4 + 74*s**3 - 16*s**3 + 21*s**2 - 6*s.
-2*(s - 30)*(s - 1)*(s + 1)**2
Let q(k) be the second derivative of -49*k**7/12 - 539*k**6/60 - 7*k**5/4 + 53*k**4/12 - 19*k**3/12 + k**2/4 - 10*k + 9. Factor q(m).
-(m + 1)**2*(7*m - 1)**3/2
Let c be (-30)/15 - (-8 + 0). Let k be -8*c/(-72)*(-9)/(-2). Suppose u**k + 0*u - u**2 - 1/4*u**4 + 0 = 0. What is u?
0, 2
Suppose v - 8 = -5. Let c(m) be the first derivative of 1/4*m**2 - 1/6*m**3 + 0*m + 1/10*m**5 + v - 1/8*m**4. Factor c(r)