 0 for i.
0, 1
Let z(t) be the second derivative of -13*t + 15/4*t**3 + 0 + 6*t**2 + 3/4*t**4 - 3/40*t**5. What is u in z(u) = 0?
-1, 8
Factor 14*w**2 - 16*w - 48*w - w**3 + 2*w**2 + 0*w**3.
-w*(w - 8)**2
Let h(w) be the first derivative of -8*w**3/3 + 41*w**2/2 - 5*w - 31. Factor h(m).
-(m - 5)*(8*m - 1)
Let a(t) be the second derivative of -t**7/63 + 4*t**6/9 - 29*t**5/30 - 73*t**4/9 + 124*t**3/3 - 72*t**2 - 18*t + 22. Solve a(z) = 0 for z.
-3, 1, 2, 18
Let l = -23 - -25. Solve 16*z**3 - z**l - 12*z**4 + z**3 - 5*z**2 + 3*z**5 - 2*z**3 = 0.
0, 1, 2
Let v = 109 + -105. Suppose -181*c**5 + 183*c**5 + 2*c**3 + 6*c**3 + 8*c**v = 0. Calculate c.
-2, 0
Let p(q) be the first derivative of -5*q**3/3 - 235*q**2/2 + 240*q + 220. Factor p(l).
-5*(l - 1)*(l + 48)
Let t(a) = a**2 + 6*a. Let r be t(-6). Suppose -s + r*s - 1 = 5*n, n + 17 = 4*s. Factor 6*b - 6*b**2 + 2*b**3 + 4 - 10 + s.
2*(b - 1)**3
Suppose -q = -3*x + 21, x = -x - 3*q + 3. What is y in 26*y + 20 + y**5 - x*y**5 - 25*y**4 + 14*y + 5*y**2 - 35*y**3 = 0?
-2, -1, 1
Let d(r) be the third derivative of -r**5/60 - 3*r**4/2 - 35*r**3/6 - 436*r**2. Solve d(i) = 0.
-35, -1
Let t = 4898/765 - 2/765. Solve 242/5*y**3 + 72*y - 1056/5*y**2 - t = 0.
2/11, 4
Let 4*g**5 - 18*g**2 - 342*g**4 - 4*g**3 + 346*g**4 + 14*g**2 = 0. Calculate g.
-1, 0, 1
Let c(n) = 450*n**4 - 105*n**3 - 52*n**2 - n. Let h(z) = 900*z**4 - 210*z**3 - 104*z**2 - 3*z. Let l(f) = 5*c(f) - 3*h(f). Factor l(b).
-b*(2*b - 1)*(15*b + 2)**2
Factor 320/7*g + 36/7*g**2 - 26/7*g**3 + 2/7*g**4 + 256/7.
2*(g - 8)**2*(g + 1)*(g + 2)/7
Let z(l) be the second derivative of 0 + 1/15*l**4 - 1/30*l**5 + 1/225*l**6 - 8/15*l**2 + 2*l + 4/45*l**3. Factor z(q).
2*(q - 2)**3*(q + 1)/15
Let v(k) = -k**3 - k**2 - 1. Let w(m) = 8*m**3 - 80*m**2 - 1056*m - 958. Let a(q) = 20*v(q) + 2*w(q). Factor a(g).
-4*(g + 1)*(g + 22)**2
Let s(q) = 2*q**3 - 1. Let u(k) = -9*k**3 + 87*k**2 + 1935*k + 1854. Let h(z) = 5*s(z) + u(z). Suppose h(v) = 0. Calculate v.
-43, -1
Let m(c) be the third derivative of -c**3 - 18*c**2 + 7/12*c**4 + 0 + 0*c - 1/6*c**5 + 1/60*c**6. Find r such that m(r) = 0.
1, 3
Let w = 268/1611 - -10/179. Let g(z) be the first derivative of w*z - 2/27*z**3 + 0*z**2 + 4. What is l in g(l) = 0?
-1, 1
Let r be (-3)/5 + (-39 - 10). Let z = 50 + r. Suppose 0 - 2/5*t**2 + z*t = 0. Calculate t.
0, 1
Let z(x) be the second derivative of -1/15*x**5 - 1/15*x**6 - 1/63*x**7 + 1/3*x**2 + 1/3*x**3 + 1/9*x**4 + 3*x - 5. Factor z(y).
-2*(y - 1)*(y + 1)**4/3
Suppose -4*g - 26*y + 11 = -29*y, 0 = 3*y + 3. What is p in 0*p**g + 8/5*p**3 + 0*p - 4/5*p**5 - 4/5*p**4 + 0 = 0?
-2, 0, 1
Let f(q) be the third derivative of -7/12*q**5 + 0*q + 0 - 9*q**2 + 25/24*q**4 + 1/8*q**6 - 5/6*q**3. Determine b, given that f(b) = 0.
1/3, 1
Suppose -2*a = -q - 0 + 5, 5*a - 2*q = -10. Suppose a = -6*y - 9*y + 45. Determine o so that -o - 13/2*o**y + 7/4*o**4 + 27/4*o**2 - 1 = 0.
-2/7, 1, 2
Suppose -u + 0*u = 5*c - 77, 5*c - 73 = u. Factor 3*q**5 + 17*q**3 - 37*q**3 + 2*q**5 + c*q**3.
5*q**3*(q - 1)*(q + 1)
Let r = 248 + -244. Let k(g) be the second derivative of -1/2*g**3 + 0 + 4*g + 1/4*g**r + 0*g**2. Factor k(z).
3*z*(z - 1)
Let v(n) be the first derivative of -1/22*n**4 + 4/11*n**2 + 8/11*n - 2/33*n**3 - 17. Find i, given that v(i) = 0.
-2, -1, 2
Factor 7 - 9 + 96 + 30*u + 23 - 3*u**2.
-3*(u - 13)*(u + 3)
Factor 1/4*f**2 + 100 + 10*f.
(f + 20)**2/4
Suppose y = -v - y + 12, 0 = 4*v + y - 13. Let r(m) be the third derivative of 0*m + 4*m**v - 1/120*m**5 + 1/12*m**3 - 1/240*m**6 + 1/48*m**4 + 0. Factor r(k).
-(k - 1)*(k + 1)**2/2
Determine p, given that -68/13 - 2/13*p**3 + 32/13*p**2 + 38/13*p = 0.
-2, 1, 17
Let h(p) be the third derivative of -3*p**6/80 + p**5/2 + 9*p**4/16 - 7*p**3/2 + 3*p**2 + 5*p. Factor h(x).
-3*(x - 7)*(x + 1)*(3*x - 2)/2
Suppose 21*k - 16*k = 10. Factor l**k + 4*l - 10 + 10.
l*(l + 4)
Let z(t) be the second derivative of 0*t**2 + 0*t**4 + 9/140*t**5 - 2/7*t**3 - 3 - 1/70*t**6 + 2*t. Factor z(l).
-3*l*(l - 2)**2*(l + 1)/7
Let t(d) = 82*d**3 + 161*d**2 - 6*d - 14. Let a(x) = -41*x**3 - 81*x**2 + 2*x + 6. Let i(g) = -14*a(g) - 6*t(g). Factor i(c).
2*c*(c + 2)*(41*c + 2)
Let m(w) be the third derivative of w**6/840 + 11*w**5/420 - 25*w**4/168 + 13*w**3/42 - 11*w**2 - 3. Factor m(s).
(s - 1)**2*(s + 13)/7
Let d(f) be the second derivative of -f**8/84 - 4*f**7/105 + 2*f**5/15 + f**4/6 + 4*f**2 - 25*f. Let q(r) be the first derivative of d(r). Factor q(p).
-4*p*(p - 1)*(p + 1)**3
Let p = -1159 - -193555/167. Let a = p + 324/835. Determine o so that 0 + a*o**3 + 0*o**4 - 2/5*o**5 + 0*o + 0*o**2 = 0.
-1, 0, 1
Let t(c) be the second derivative of 16/15*c**3 - 1/5*c**4 + 2/75*c**6 - 17*c + 0 - 2/25*c**5 - 8/5*c**2. Suppose t(v) = 0. What is v?
-2, 1, 2
Let t be 2/(-15)*117/26 - -1. Factor -4/5 + t*a + 2/5*a**2.
2*(a - 1)*(a + 2)/5
Let s = 8 - 8. Suppose -f - 5*t + s + 14 = 0, -3*f - t = -14. Solve -3*i + i**2 + f*i - 10*i**3 + i + 9*i**3 = 0.
-1, 0, 2
Let a(c) be the first derivative of -1/21*c**4 - 5*c - 3/70*c**5 + 0*c**3 + 0*c**2 - 5 - 1/105*c**6. Let j(n) be the first derivative of a(n). Factor j(w).
-2*w**2*(w + 1)*(w + 2)/7
Factor -48 - 1/3*s**2 - 8*s.
-(s + 12)**2/3
Let k(t) be the first derivative of -1/15*t**5 - 40 + 0*t**3 + 1/4*t**4 + 0*t - 2/3*t**2. What is i in k(i) = 0?
-1, 0, 2
Let a = 16/31 + -49/155. Factor -7/5*o**2 - o - 3/5*o**3 - a.
-(o + 1)**2*(3*o + 1)/5
Factor 3/8*b**3 - 3/8*b - 9/4 + 9/4*b**2.
3*(b - 1)*(b + 1)*(b + 6)/8
Find x, given that -8/5*x - 54/5*x**3 - 28/5*x**5 - 52/5*x**2 + 97/5*x**4 + 0 = 0.
-2/7, -1/4, 0, 2
Let d(v) be the first derivative of -v**6/120 + v**4/24 - v**2/2 + 12. Let f(p) be the second derivative of d(p). Factor f(o).
-o*(o - 1)*(o + 1)
Let r(k) be the first derivative of -k**5/20 + 5*k**4/36 - k**3/18 - k**2/6 - 8*k - 1. Let g(z) be the first derivative of r(z). Factor g(p).
-(p - 1)**2*(3*p + 1)/3
Let n(c) be the third derivative of -2*c**7/315 + 8*c**6/135 - 29*c**5/135 + 10*c**4/27 - 8*c**3/27 - 109*c**2. Solve n(b) = 0 for b.
1/3, 1, 2
Let b(p) be the third derivative of -p**8/12 - 44*p**7/315 + p**6/90 + 2*p**5/45 - p**2 + 14. Determine c so that b(c) = 0.
-1, -1/3, 0, 2/7
Let p be (-3 - (-3 - 1))*(6 - 5)/3. Solve d - 1/3 + p*d**3 - d**2 = 0 for d.
1
Let s(u) = -5*u**2 - 10*u - 15. Let l(p) = p - 8 + 4 + 3. Let r(g) = 5*l(g) - s(g). What is m in r(m) = 0?
-2, -1
Let v = 18044 - 162394/9. Solve -2/9*d**2 - v*d + 4/9 = 0.
-2, 1
Let i(m) be the third derivative of m**6/60 + 16*m**5/15 + 31*m**4/12 + 2*m**2 - 27*m. Factor i(t).
2*t*(t + 1)*(t + 31)
Let h be ((33/(-4))/(-11))/21. Let y(p) be the second derivative of -1/20*p**6 + 0*p**3 + 2*p + 0*p**2 - 3/40*p**5 + 1/8*p**4 + h*p**7 + 0. Factor y(l).
3*l**2*(l - 1)**2*(l + 1)/2
Let z be (-4)/(-10) - 18/(-5). Let k be (-64)/(-6) + 56/(-84). Determine g, given that 10*g + 6*g - z*g**2 + 10*g - k*g = 0.
0, 4
Let y = 38 + 86. Let u = -121 + y. Factor 9/5 + 1/5*w**3 + 7/5*w**2 + u*w.
(w + 1)*(w + 3)**2/5
Let m(c) = 16*c**2 + 26*c - 21. Let q(n) = 9*n**2 + 13*n - 10. Let t(a) = 4*m(a) - 7*q(a). Factor t(u).
(u - 1)*(u + 14)
Let m = 18 - 16. Solve 2 + 8*z**2 + 2 - 13*z**m + 7*z**2 + 6*z = 0 for z.
-2, -1
Suppose 85 + 85 = -5*f - 5*m, -4*m = -5*f - 152. Let x be f/10 + -1 + 5. Factor 2*h - 6/5*h**2 - x.
-2*(h - 1)*(3*h - 2)/5
Let d be -1 - (7 - -2) - -13. Factor 0*n**2 + 2/17*n**4 - 2/17 + 4/17*n**d - 4/17*n.
2*(n - 1)*(n + 1)**3/17
Let r(z) be the second derivative of -25*z - 1/195*z**6 - 2/39*z**3 + 0*z**5 + 0*z**2 + 1/26*z**4 + 0. Factor r(x).
-2*x*(x - 1)**2*(x + 2)/13
Let c = -3 + 7. Let n be (-10)/(-2) + -7 + c. Let -3*t**4 + 4*t**2 + 2*t + t**4 + 2*t**5 - t**3 - 3*t**3 - n = 0. Calculate t.
-1, 1
Let p(a) be the second derivative of -a**4/3 - 8*a**3 + 56*a**2 - 56*a - 1. Let p(z) = 0. What is z?
-14, 2
Let c(w) be the first derivative of 21/10*w**2 + 9/5*w**3 - 6/5*w - 5. Factor c(j).
3*(j + 1)*(9*j - 2)/5
Let p(x) = -x**2 - 6*x. Let u(s) = -2*s**2 - 13*s. Suppose -v = -0*v + 21. Let z = v + 12. Let h(r) = z*p(r) + 4*u(r). Suppose h(d) = 0. What is d?
-2, 0
Let b(c) = -4*c**2 - 7*c + 2. Let s(y) = 3*y**2 + 6*y - 1. Let q(j) = 4*b(j) + 6*s(j). Let m be q(-4). Let 0*g + 1/3*g**m + 0 = 0. What is g?
0
Let o(t) be the first derivative of 2*t**3 - 3/4*t**4 + 7 + 3/2*t**2 - 6*t