l. Let z(a) be the second derivative of t(a). Find j, given that z(j) = 0.
-1, 0, 2
Let u = 1836/7 + -262. Let n(p) be the first derivative of 2/21*p**3 + 0*p**2 - 7 + u*p**4 + 0*p. Factor n(r).
2*r**2*(4*r + 1)/7
Let o be (-2160)/14 - 20/(-70). Let a be (4 - o/(-35))*-1. Solve -a*n + 1/5*n**2 + 1/5 = 0 for n.
1
Let d(l) = -l**4 - l**2 - l. Let p(o) = 21*o**4 - 3*o**3 + 9*o**2 + 18*o. Let m(v) = 15*d(v) + p(v). Factor m(a).
3*a*(a - 1)*(a + 1)*(2*a - 1)
Let j(c) be the third derivative of c**5/30 - 17*c**4/12 - 6*c**3 + c**2 + 117. Solve j(t) = 0.
-1, 18
Let w(b) be the second derivative of -b**7/210 + b**6/60 + b**5/60 - b**4/12 + 19*b**2/2 - 6*b. Let k(s) be the first derivative of w(s). Factor k(o).
-o*(o - 2)*(o - 1)*(o + 1)
Let w be ((-32)/(-4))/((-1)/2). Let n be 1/4 - w/8 - 2. Determine u, given that 1/4*u**4 + 1/2 - n*u - 3/4*u**2 + 1/4*u**3 = 0.
-2, -1, 1
Let r(j) = j**3 - 13*j**2 - 6*j - 11. Let o be r(14). Let n = -98 + o. Factor 2/9*p - 4/9*p**4 + 0*p**n - 2/9*p**5 + 0 + 4/9*p**2.
-2*p*(p - 1)*(p + 1)**3/9
Suppose -41 + 1 = -8*m. Let d(f) be the third derivative of m*f**2 - 1/6*f**3 + 0*f + 1/120*f**5 + 0 + 1/48*f**4. Find q such that d(q) = 0.
-2, 1
Let a(d) be the first derivative of -d**5/20 + d**4/4 + 23*d**3/3 - 24*d**2 - 576*d + 83. Factor a(s).
-(s - 8)**2*(s + 6)**2/4
Let f be 0 + 78/8 + 1/4. Let x be (-3)/(-15) - (-18)/f. Factor 1/4*o**x - 1/4*o**3 + 0*o + 0.
-o**2*(o - 1)/4
Factor 52/3*w**2 - 2/3*w**3 - 338/3*w + 0.
-2*w*(w - 13)**2/3
Let d = -7 - 29. Let o = d + 39. Suppose -2/9*y**5 + 2/3*y + 4/9*y**2 + 2/9 - 4/9*y**o - 2/3*y**4 = 0. Calculate y.
-1, 1
Let d(q) = -q**3 + 4*q**2 + 14*q - 12. Let s be d(6). Let j(c) be the second derivative of 1/48*c**4 + s + 4*c - 1/4*c**2 + 1/24*c**3. What is k in j(k) = 0?
-2, 1
Let f(u) be the first derivative of 1/5*u**2 + 1/5*u + 0*u**3 - 1/10*u**4 + 11 - 1/25*u**5. Find w such that f(w) = 0.
-1, 1
Factor 0 + 0*l + 34/11*l**3 - 4/11*l**2.
2*l**2*(17*l - 2)/11
Suppose l - 5*f - 8 = 0, -4*f - 12 = 3*l - 4*l. Suppose -s + l = 6*s. Let -4/7*y**3 + 0 + 2/7*y**2 - 2/7*y**s + 4/7*y = 0. Calculate y.
-2, -1, 0, 1
Let b(s) = -545*s - 13622. Let o be b(-25). Factor 0 + 1/2*w**4 + 12*w**2 + 9/2*w**o + 8*w.
w*(w + 1)*(w + 4)**2/2
Let q(y) be the first derivative of -25*y**4/2 - 340*y**3/3 - 124*y**2 - 48*y - 36. Suppose q(d) = 0. What is d?
-6, -2/5
Suppose -2*p - 4*x + 6 = 26, 5*p - x - 27 = 0. Let 8/17*h**3 - 18/17 - 24/17*h - 2/17*h**p + 4/17*h**2 = 0. What is h?
-1, 3
Let b(y) be the first derivative of y**6/600 - y**4/40 + y**3/15 - 3*y**2/2 + 2. Let v(g) be the second derivative of b(g). Factor v(d).
(d - 1)**2*(d + 2)/5
Suppose -4*k + 15 = -5*y, -9 = -k - 2*k + 3*y. Let g be (2 - 14) + (-7392)/(-594). Solve 2/3*u**3 - 10/9*u**2 + k + g*u = 0 for u.
0, 2/3, 1
Let l(p) = -3*p**3 - 35*p - 22. Let b(n) = -n**3 + 2*n**2 - n. Let h(o) = -12*b(o) + 3*l(o). Factor h(w).
3*(w - 11)*(w + 1)*(w + 2)
Let l(s) be the first derivative of -s**8/2520 + s**7/525 - 35*s**2/2 - 13. Let k(y) be the second derivative of l(y). Suppose k(u) = 0. Calculate u.
0, 3
Let c(o) be the second derivative of -o**6/30 + 3*o**5/10 - 2*o**4/3 + 18*o + 2. Factor c(n).
-n**2*(n - 4)*(n - 2)
Suppose 4*i = g + 8, -i - g + 4 = i. Let -4*l**3 - i*l + 2*l - 3*l - 1 + 3*l**3 - 3*l**2 = 0. Calculate l.
-1
Let d(s) = s**2 + 3*s + 1. Let t be d(-3). Suppose t = 3*m - 11. Factor -6*a + a**2 + a**3 - a**m + a**3 + 0*a + 4*a.
-a*(a - 2)*(a - 1)*(a + 1)
Let z(d) = 3*d**2 - 3*d + 2. Let a(o) = -16*o**2 + 16*o - 11. Suppose -4*g - 5 = -21. Let w = g - 2. Let c(x) = w*a(x) + 11*z(x). What is l in c(l) = 0?
0, 1
Suppose 120*q + 45*q**2 - 10 + 105 + 5 + 5*q**3 = 0. What is q?
-5, -2
Let h(w) be the second derivative of 33*w**5/20 + 21*w**4/4 - w**3 - 6*w. Factor h(i).
3*i*(i + 2)*(11*i - 1)
Let g be (-5)/(-2)*(-8)/(-20). Let i(n) = n**3 + 2*n**2 - 2*n + 1. Let x be i(g). Let -8*c**3 + c**3 + 5*c**2 + x*c**3 = 0. Calculate c.
0, 1
Let a be ((-6)/3 - 22/(-6))*27/15. Let s = 3/2 + -1. What is x in 1/6*x**a + 1/6 + 1/2*x + s*x**2 = 0?
-1
Let m(x) be the first derivative of 0*x + 0*x**2 - 3*x**4 + 16/3*x**3 - 4/5*x**5 + 7. What is t in m(t) = 0?
-4, 0, 1
Let b(y) = 4*y + 1. Let j be b(1). Let s be (-1 + -5)*(-6 + j). Factor 4*w**5 - 6*w**4 + 0*w**5 - w**5 + s*w**2 - 3*w.
3*w*(w - 1)**3*(w + 1)
Let v(f) be the first derivative of f**3/6 - 7*f**2/2 + 12*f - 14. Factor v(u).
(u - 12)*(u - 2)/2
Suppose -5*m + 0*m + 12 = f, -4*m = -2*f - 18. Solve 4*v**3 - v**4 - 16*v**m + 4*v**3 - 3*v**4 = 0 for v.
-2, 0
Let w(m) be the third derivative of m**8/1512 - m**7/315 - m**6/90 + 13*m**5/135 - m**4/4 + m**3/3 - m**2 - 126*m. Determine p so that w(p) = 0.
-3, 1, 3
Let g(u) be the second derivative of -u**5/35 + 10*u**4/21 - 8*u**3/3 + 48*u**2/7 + 71*u. Determine l so that g(l) = 0.
2, 6
Suppose 22 = u - 4*n, -n - 15 = 49*u - 54*u. Factor -30*j**u + 24*j - 24/5.
-6*(5*j - 2)**2/5
Let m(c) = c**2 + 11*c + 13. Let l be m(-10). Factor 0*r**3 + 4*r**l + 2 - 1 + 4*r + 3*r**4 + 6*r**2 - 2*r**4.
(r + 1)**4
Let j(l) be the third derivative of -l**6/720 + 143*l**5/360 - 35*l**4 - 144*l**3 + 6*l**2 - 2. Let j(t) = 0. Calculate t.
-1, 72
Suppose 25*o - 27*o = -618. Factor -o + 2*j + 309 - 2*j**3.
-2*j*(j - 1)*(j + 1)
Let r be ((-6)/4)/(1/(-2)). Suppose -4*m - 5*w = -17, 3*w + 6 = r*m - 0. Determine l, given that -3*l**4 + l**4 + l**3 + l**4 - m*l**3 - l**2 = 0.
-1, 0
Let b(y) be the first derivative of 5*y**3 - 279*y**2/2 - 114*y + 13. Determine c, given that b(c) = 0.
-2/5, 19
Let m(q) = -q + 14. Let r be m(15). Let t be (-160)/85 + (-2)/r. Determine p, given that t*p**2 - 2/17 + 0*p = 0.
-1, 1
Find b such that -378463*b**2 + 26 + 378468*b**2 - 30*b - 1 = 0.
1, 5
Let r(u) be the third derivative of -10*u**2 - 1/30*u**6 + 0*u + 0*u**5 + 1/6*u**4 + 0 + 1/105*u**7 - 1/3*u**3. Let r(d) = 0. What is d?
-1, 1
Find k, given that 0*k + 13/7*k**4 + 2/7*k**3 + 0*k**2 + 0 = 0.
-2/13, 0
Let a(l) be the third derivative of -5*l**8/84 - 3*l**7/14 - 4*l**6/15 - 2*l**5/15 - 8*l**3/3 - 10*l**2. Let i(u) be the first derivative of a(u). Factor i(s).
-4*s*(s + 1)*(5*s + 2)**2
Suppose -2*v - 5*w + 21 = 0, 2*v + 11*w = 10*w + 9. Determine g, given that 0 - 1/2*g**v - g + 3/2*g**2 = 0.
0, 1, 2
Let i = 9751/5 - 10019/5. Let o = 54 + i. Suppose 0*n**4 + 0*n**2 - 2/5*n**5 + 0 - o*n + 4/5*n**3 = 0. What is n?
-1, 0, 1
Let p(j) be the third derivative of j**7/2940 + j**6/120 + 3*j**5/70 - 2*j**4 + 6*j**2. Let m(q) be the second derivative of p(q). Factor m(k).
6*(k + 1)*(k + 6)/7
Factor -30/7*q**2 - 261/7*q - 432/7 + 3/7*q**3.
3*(q - 16)*(q + 3)**2/7
Let y be (-38)/(-4) + (-93)/62. Suppose 3*d = 5*d - 36. Factor -y*k**3 - 6*k - 20*k**2 + 8 + 8*k**2 + d*k.
-4*(k - 1)*(k + 2)*(2*k + 1)
Let s(g) = 3*g**2 + 244*g - 2884. Let t(r) = -7*r**2 - 731*r + 8651. Let d(l) = 11*s(l) + 4*t(l). Factor d(a).
5*(a - 24)**2
What is d in 37/3*d**2 + 35/3 + 1/3*d**3 + 71/3*d = 0?
-35, -1
Let y(v) be the second derivative of -1/35*v**5 - 6/7*v**2 - 18*v - 5/21*v**4 - 2/3*v**3 + 0. Factor y(s).
-4*(s + 1)**2*(s + 3)/7
Let u = 65951 + -329754/5. Let s be (0 - 2/5)*-5. Suppose u*l**s - 1/5*l + 0 = 0. What is l?
0, 1
Let h be (-2 - -1) + 6/2. Find i, given that 8*i**2 - 5*i + 2*i**h - 4*i + 4*i - 15 = 0.
-1, 3/2
Let -37*z - 2189*z**2 + 20*z**3 + 5*z**5 + 10 + 2199*z**2 + 12*z - 20*z**4 = 0. Calculate z.
-1, 1, 2
Let p be (-137 - -149)/(33*1/2). Find a, given that p*a + 0 - 2/11*a**2 = 0.
0, 4
Let l(y) be the first derivative of -y**6/51 - 14*y**5/85 + 33*y**4/34 + 262*y**3/51 - 616*y**2/17 + 1176*y/17 - 137. What is c in l(c) = 0?
-7, 2, 3
Factor -i**2 - 62 + 19 + 3*i + 4*i**2 + 25.
3*(i - 2)*(i + 3)
Let v = 137/1590 - -5/106. Suppose 0*h**2 + v*h**3 - 8/15*h + 0 = 0. What is h?
-2, 0, 2
Suppose -3 = -3*j + 3*m - 4*m, 0 = 5*j - 3*m - 19. Let b(x) be the first derivative of 2/7*x**2 + j - 22/21*x**3 + 8/7*x**4 + 0*x - 2/5*x**5. Factor b(l).
-2*l*(l - 1)**2*(7*l - 2)/7
Let x(g) be the first derivative of 21/2*g**2 + 5 + 3*g**3 - 18*g. Factor x(z).
3*(z + 3)*(3*z - 2)
Suppose 2*q + 2 = -4*i, -4*q + 3 = -2*i + 7. Let u(h) be the second derivative of -6*h + 0 + i*h**3 + 0*h**2 + 1/16*h**4. Factor u(w).
3*w**2/4
Let j(q) be the first derivative of -11/8*q**4 + 1/4*q**6 + 3/2*q**3 - 1/10*q**5 - 4 - 2*q + q**2. Solve j(i) =