second derivative of 5*y**7/21 + 3*y**6/4 + y**5/4 - 5*y**4/3 - 5*y**3/2 - 5*y**2/4 + y - 22. Let x(p) = 0. Calculate p.
-1, -1/4, 1
Let h(z) = 16*z**2 + 25*z + 6. Let v(n) = 3*n**2. Let m(u) = -h(u) + 4*v(u). Find l such that m(l) = 0.
-6, -1/4
Factor -40*n + 96*n**3 - 4*n**4 - 33*n + 101*n - 28*n.
-4*n**3*(n - 24)
Suppose 3*o - 49 - 9 = -2*l, -2*l + 62 = 4*o. Let b = 28 - l. Factor -4/3*d**4 + d**b + 2/3*d**2 + 0*d - 1/3*d**3 + 0.
d**2*(d - 1)**2*(3*d + 2)/3
Let s(a) be the second derivative of -a**5/40 + 7*a**4/24 - 7*a**3/6 + 2*a**2 - 3*a - 9. Factor s(y).
-(y - 4)*(y - 2)*(y - 1)/2
Let t(y) = y**3 - 21*y**2 - 51*y - 37. Let q(g) = g**3 - g**2 - g + 1. Let s(x) = 3*q(x) - t(x). Factor s(r).
2*(r + 2)**2*(r + 5)
Let i(n) be the second derivative of n**6/80 + n**5/10 + 3*n**4/16 - 10*n**2 + 14*n. Let w(d) be the first derivative of i(d). Factor w(s).
3*s*(s + 1)*(s + 3)/2
Let z = 34 - 30. Let f be ((-20)/(-16))/(z/32). Determine t, given that 15*t - 4*t**3 - t - f*t = 0.
-1, 0, 1
Let o = -69/2 + 223/6. Let s(z) be the third derivative of -9*z**2 + 1/60*z**6 + o*z**3 + 0*z + 0 + z**4 + 1/5*z**5. Factor s(a).
2*(a + 2)**3
Let c(z) be the third derivative of 0*z + 0 - 1/2*z**4 + 5/2*z**3 - 1/20*z**5 - 11*z**2. Factor c(q).
-3*(q - 1)*(q + 5)
Suppose 2*w = -u + 6*w + 20, 3*w = 4*u - 28. Factor 2*g**u + 2*g**2 - 6*g**2 + 4*g**3 + 2*g**2 - 4*g**4.
-2*g**2*(g - 1)**2
Solve -24*q**3 - 13*q**2 + 7030*q - 7042*q + 4*q**5 - 19*q**2 = 0.
-1, 0, 3
Let o(f) be the first derivative of -f**5/120 - 7*f**4/24 - 49*f**3/12 + 3*f**2/2 - 1. Let t(u) be the second derivative of o(u). Let t(k) = 0. What is k?
-7
Let l(d) = d**2 + 4*d - 4. Let y be l(2). Let j(m) = m**3 - 6*m**2 - 16*m. Let n be j(y). Solve 0 + 1/3*h**2 + n*h + 1/2*h**3 = 0 for h.
-2/3, 0
Let t(f) be the third derivative of -1/150*f**5 + 0*f**4 + 0*f - 5*f**2 + 1/15*f**3 + 0. Solve t(o) = 0.
-1, 1
Factor -8066/3*z + 7772/3*z**2 - 142/3*z**4 + 2738/3 - 2/3*z**5 - 2300/3*z**3.
-2*(z - 1)**3*(z + 37)**2/3
Let l(t) = -t**5 + t**2 + t + 2. Let n(c) = 47*c**5 + 50*c**4 - 8*c**3 - 5*c**2 + 3*c + 6. Let o(d) = -3*l(d) + n(d). Suppose o(g) = 0. Calculate g.
-1, -2/5, 0, 2/5
Let p(f) = -5*f**4 - 42*f**3 - 73*f**2 + 123*f. Let b(v) = 15*v**4 + 127*v**3 + 218*v**2 - 368*v. Let z(q) = -3*b(q) - 8*p(q). Let z(d) = 0. What is d?
-6, -4, 0, 1
Let s(h) = -h**3 - 3*h**2 - h + 2. Let l be s(-2). Suppose -2*f - 10 = 0, l = 3*k + f - 8 - 8. Factor -3*x**2 - k*x**5 + 5*x**3 - 2*x**3 + 4*x**5 + 3*x**4.
-3*x**2*(x - 1)**2*(x + 1)
Let i(z) be the second derivative of z**4/4 + 9*z**3/2 - 33*z**2 - 57*z. Factor i(h).
3*(h - 2)*(h + 11)
Suppose i + 2 = -5*p - 3, -15 = -3*i. Let y be (-11 - -12)*p/(-10). Factor 1/5*s**2 - y*s**3 + 1/5*s - 1/5.
-(s - 1)**2*(s + 1)/5
Let i(l) be the second derivative of l**5/8 - 23*l**4/24 + 5*l**3/6 + 2*l**2 + 3*l + 1. Factor i(u).
(u - 4)*(u - 1)*(5*u + 2)/2
Let w(q) be the second derivative of q**4/78 + 2*q**3/13 + 24*q. Let w(t) = 0. What is t?
-6, 0
Suppose 0 = 5*h + 3*i - 7, 23*i = 28*i + 5. Let a(j) be the first derivative of 1/15*j**5 + 0*j**2 + 1/12*j**4 + 0*j - 1/9*j**3 - h - 1/18*j**6. Factor a(v).
-v**2*(v - 1)**2*(v + 1)/3
Let n be 11/6 - -1 - ((-2425)/(-150) - 16). Suppose 11 = 5*b - 2*j, 3*b - 4*j = -2 + 3. Suppose n*q**2 - 2*q**b + 2/3*q - 4/3 = 0. Calculate q.
-2/3, 1
Let p be -5 - ((-990)/(-12))/(-11) - 2. Factor -1/2*v**2 + 0*v - p*v**3 + 0.
-v**2*(v + 1)/2
Let a(b) be the second derivative of -1/3*b**3 + 1/2*b**4 + 0 - 3/10*b**5 + 1/15*b**6 - 41*b + 0*b**2. Factor a(y).
2*y*(y - 1)**3
Let f = 996958891/3395216 + -1/308656. Let u = f + -290. Factor -u*p + 8/11 + 50/11*p**2.
2*(5*p - 2)**2/11
Suppose 6*t = -3*q + 7*t + 15, -q + 13 = -3*t. Let r be q*(-6 + 5) + 13/3. Factor -4/3*f**2 - r*f**3 + 0 - 4/3*f.
-f*(f + 2)**2/3
Let k(n) be the third derivative of -n**8/1344 + n**7/42 - n**6/3 + 8*n**5/3 + 17*n**4/24 - 10*n**2. Let r(v) be the second derivative of k(v). Factor r(d).
-5*(d - 4)**3
Let s(z) be the third derivative of z**8/2240 + z**7/105 + 7*z**6/240 + 23*z**4/24 + 3*z**2. Let f(h) be the second derivative of s(h). Factor f(c).
3*c*(c + 1)*(c + 7)
Let z(k) = 15*k - 3*k**2 + 5 + 2*k**2 + 11*k**2. Let r(v) be the first derivative of 5*v**3/3 + 7*v**2/2 + 3*v - 18. Let n(s) = 5*r(s) - 3*z(s). Factor n(h).
-5*h*(h + 2)
Let v be (-12)/102 + (-2349)/(-459). Factor -2/3*n**v - 8/3 - 16/3*n**4 - 34/3*n - 56/3*n**2 - 44/3*n**3.
-2*(n + 1)**4*(n + 4)/3
Let u(v) be the third derivative of v**6/72 + 61*v**5/18 + 800*v**4/3 + 2000*v**3 + 29*v**2. Factor u(l).
5*(l + 2)*(l + 60)**2/3
Let m be 24/84 + 11440/(-7). Let a = m - -11458/7. Factor -10/7*v - 2/7 - 10/7*v**4 - a*v**2 - 20/7*v**3 - 2/7*v**5.
-2*(v + 1)**5/7
Let v = 56881/180 - 316. Let x(b) be the third derivative of -1/12*b**4 + 3*b**2 - v*b**5 - 1/2*b**3 + 0*b + 0. Factor x(n).
-(n + 3)**2/3
Let p(h) = 3*h**2 - 5*h + 7. Let r be p(3). Suppose -r = -3*w + 3*a + 2, 3*w = 4*a + 26. Factor 2/9*i**w + 4/9*i + 2/9.
2*(i + 1)**2/9
Let m(f) = f**3 - 20*f**2 - 63*f - 134. Let c be m(23). Let -7/3*t**c - 5/3*t**3 + 2/3*t**2 + 0*t + 0 = 0. Calculate t.
-1, 0, 2/7
Let j = 12187 - 511829/42. Let p = -2/21 + j. Suppose 0*c + 0 - p*c**2 + 1/4*c**3 = 0. Calculate c.
0, 2
Let z be 2 + 0*4/(-8). Let 18*q**3 - 4 - 12*q**4 + 34*q**4 + 8*q**3 - 18*q**z - 26*q = 0. What is q?
-1, -2/11, 1
Let t be (-306)/45 + 8 + (4 - 0). Determine w, given that 0 - 2/5*w**2 - 4/5*w + 18/5*w**3 + t*w**4 + 2*w**5 = 0.
-1, 0, 2/5
Solve 40*a - 4*a**2 - 103*a**4 - 430*a**3 - 97*a**4 + a**2 + 195*a**4 + 105*a**5 + 23*a**2 = 0 for a.
-2, -2/7, 0, 1/3, 2
Let i(t) = t**3 - 14*t**2 + 24*t - 9. Let o be i(12). Let f be (o/(-21))/(0 + (-18)/(-12)). Factor -f*j**2 - 18/7 - 12/7*j.
-2*(j + 3)**2/7
Let a = 158 + -158. Determine z, given that -1356 - z**2 + a*z**2 + 1360 = 0.
-2, 2
Let j be (-1012)/(-77) - 1 - 11. Find c such that j*c**2 - 10/7*c - 2/7*c**3 + 4/7 = 0.
1, 2
Let n(h) be the second derivative of -h**5/20 + 2*h**3/3 + 468*h. Find d, given that n(d) = 0.
-2, 0, 2
Suppose 7*q = -q + 8. Let n be (-1)/(3 + -4)*q/3. Determine i, given that 0 - n*i**2 + 1/3*i = 0.
0, 1
Let j(h) = -9*h**2 - 9*h + 30. Let c(x) = 19*x**2 + 20*x - 62. Let r(v) = -6*c(v) - 13*j(v). Solve r(u) = 0 for u.
-2, 3
Let b(t) = 2*t**3 + 4*t**2 - 11*t + 2. Let m(h) = -12*h**3 - 18*h**2 + 54*h - 10. Let z(f) = 14*b(f) + 3*m(f). Factor z(j).
-2*(j - 1)*(j + 1)*(4*j - 1)
Let b be (-658)/(-102) + 8/476*-7. Let d = b - 203/33. Let 48/11*r + d*r**2 + 2/11*r**4 - 12/11*r**3 + 32/11 = 0. Calculate r.
-1, 4
Suppose 1326*m = 1325*m + 6. Let x(v) be the third derivative of 0*v**3 + 0 + 0*v**4 + 1/30*v**m + 1/35*v**7 - 1/30*v**5 + 0*v + 5*v**2. Factor x(k).
2*k**2*(k + 1)*(3*k - 1)
Let z be (-60)/(-8)*72/15. Let -6*d**3 + z*d**2 + 24 - 10*d**4 - 8*d**3 + 12*d**4 - 8 - 40*d = 0. Calculate d.
1, 2
Let h = 64 + 20. Let d be h/90 - -4*(-1)/12. Suppose 0 + 0*v - 9/5*v**3 + d*v**5 - 6/5*v**2 + 0*v**4 = 0. Calculate v.
-1, 0, 2
Factor 0 - 4/5*w**3 - 2/5*w + w**2 + 1/5*w**4.
w*(w - 2)*(w - 1)**2/5
Let s(j) be the second derivative of -j**4/114 + 2*j**3/19 - 9*j**2/19 - 2*j - 4. What is z in s(z) = 0?
3
Let g(l) = -l**3 - 38*l**2 + 80*l + 2. Let n be g(-40). Factor -d**3 + 0*d**n - 1/2*d**4 + 0 + 0*d.
-d**3*(d + 2)/2
Let p(r) be the second derivative of 1/2*r**3 + 0 + 0*r**4 + 0*r**2 - 1/1800*r**6 - 1/300*r**5 - 8*r. Let o(d) be the second derivative of p(d). Factor o(m).
-m*(m + 2)/5
Let w be (18/45*5)/3. Let m = -20/13 - -86/39. Suppose -2/3 + m*v**2 + w*v**3 - 2/3*v = 0. Calculate v.
-1, 1
Let z(y) = y + 5. Suppose -4*a - 2 = -3*a. Let h be z(a). Suppose 0 - 2/5*k**h + 0*k + 0*k**2 + 2/5*k**4 = 0. What is k?
0, 1
Let d(r) be the first derivative of 18*r**2 - 20/3*r**3 - 9*r**4 + 28/5*r**5 - 8*r - 13. Let d(f) = 0. What is f?
-1, 2/7, 1
Let l be (-108)/(-210) + 2/7. Let g = -393/38 - -2117/190. Factor -g*u**3 - 4/5*u**4 + 4/5*u**2 + l*u + 0.
-4*u*(u - 1)*(u + 1)**2/5
Let g(s) be the second derivative of s**6/135 + s**5/45 + s**4/54 + 10*s + 4. Find i, given that g(i) = 0.
-1, 0
Let h = -34 + 38. Suppose h*w = -l + 18, 3*l = l + 5*w - 16. Suppose 6*r**2 - 5*r**l + 2*r + 25 - 12*r = 0. What is r?
5
Suppose 0 = 4*x - 2*k - 86, -961*x + 964*x + 3*k = 51. Factor x*s - 24/5 + 24*s**3 - 32*s**2 - 8*s**4 + 4/5*s**5.
4*(s - 6