ive of -137*q**4/18 - 15*q**3 + 2*q**2/3 + 7*q - 12. Solve y(m) = 0 for m.
-1, 2/137
Let g(h) be the first derivative of -2/11*h + 9 - 2/33*h**3 + 2/11*h**2. Factor g(v).
-2*(v - 1)**2/11
Let 11*u**2 - 3*u**2 - 12*u + u**2 + 5*u**2 - 2*u**3 = 0. What is u?
0, 1, 6
Let y(v) = v**3 - 6*v**2 + 3*v + 12. Let l be y(5). Factor 20*i**3 - 8 - 6*i**4 + 28*i - 17*i**2 - 19*i**l + 2*i**4.
-4*(i - 2)*(i - 1)**3
Let p(l) be the first derivative of -2*l**3/9 + 158*l**2/3 - 12482*l/3 + 57. Solve p(x) = 0 for x.
79
Let s(z) = 13*z**3 + 54*z**2 + 137*z + 103. Let x(h) = -6*h**3 - 27*h**2 - 69*h - 51. Let p(r) = -3*s(r) - 7*x(r). Let p(k) = 0. What is k?
-4, -1
Let d(m) = m**2 - 13*m + 44. Let r be d(8). Find z, given that -11/2*z**3 - z**2 + 6*z - 3*z**r + 4 - 1/2*z**5 = 0.
-2, -1, 1
Let i(j) be the first derivative of -j**5 + 15*j**4/4 + 25*j**3/3 - 15*j**2/2 - 20*j - 113. Factor i(a).
-5*(a - 4)*(a - 1)*(a + 1)**2
Let a = -161 + 163. Factor -1/7*l**a + 1/7 + 0*l.
-(l - 1)*(l + 1)/7
Solve -8/9*t**2 - 4/9*t + 4/9*t**3 + 8/9 = 0 for t.
-1, 1, 2
Suppose -15 = r - 18. Factor 25 - 40 + 20*t - 2*t**2 - r*t**2.
-5*(t - 3)*(t - 1)
Suppose 17 = 5*b - 3*g, -13*b - 20 = -17*b - 4*g. Factor 0*n**b + 0 + 1/5*n**5 + 0*n - 3/5*n**3 - 2/5*n**2.
n**2*(n - 2)*(n + 1)**2/5
Let y(p) be the second derivative of 2248091*p**5/80 + 17161*p**4/8 + 131*p**3/2 + p**2 + 150*p. What is d in y(d) = 0?
-2/131
Let u(y) = -y**2 + 12*y - 4. Let h be u(7). Let z = -28 + h. Factor -4/9*n**2 + 0 - 2/9*n**z + 0*n.
-2*n**2*(n + 2)/9
Let m = -2 - -5. Factor 6*y**4 + 7*y**4 - 3*y**m - 10*y**4.
3*y**3*(y - 1)
Let y(a) be the second derivative of a**6/15 - a**5/5 - 4*a**4/3 + 6*a**3 - 9*a**2 - 32*a - 1. Factor y(v).
2*(v - 3)*(v - 1)**2*(v + 3)
Let x(t) be the second derivative of t**6/40 + 5*t**5/36 - t**4/12 - 6*t**2 - 29*t. Let r(d) be the first derivative of x(d). Find k such that r(k) = 0.
-3, 0, 2/9
Let q(u) be the first derivative of 6*u**4/5 + 134*u**3/15 - 32*u**2/5 - 24*u/5 - 13. Suppose q(d) = 0. What is d?
-6, -1/4, 2/3
Let j(f) be the first derivative of 1/14*f**2 + 0*f**4 - 43 + 0*f - 1/42*f**6 + 2/21*f**3 - 2/35*f**5. Factor j(s).
-s*(s - 1)*(s + 1)**3/7
Suppose 2*h = -11*h - 68 + 133. Let -12*j**3 - 40/3*j**2 - 2/3*j**h + 0 - 14/3*j**4 - 16/3*j = 0. Calculate j.
-2, -1, 0
Suppose 3*w + 3 = 0, 7 = 4*k - 2*w - 3. Factor f + 0 + f**k + 1/4*f**3.
f*(f + 2)**2/4
Factor -130*b**2 - 25*b**4 - 25 + 185/2*b + 85*b**3 + 5/2*b**5.
5*(b - 5)*(b - 2)*(b - 1)**3/2
Let w(i) = i**2 - 5*i - 63. Let a be w(-6). Let u(g) be the first derivative of 0*g**a + 0*g + 0*g**2 + 1/20*g**5 + 5 + 0*g**4. Factor u(o).
o**4/4
Factor -4/3 - 1/6*w**3 - 1/3*w + 5/6*w**2.
-(w - 4)*(w - 2)*(w + 1)/6
Let g(u) = 4*u**2 + 5*u. Let o be g(-2). Let c(f) be the second derivative of -1/4*f**4 + 0*f**2 + 1/2*f**3 + o*f + 0. Factor c(s).
-3*s*(s - 1)
Let i(z) be the second derivative of z**7/315 + z**6/180 - z**5/45 - 5*z**2 + 22*z. Let n(v) be the first derivative of i(v). Let n(t) = 0. What is t?
-2, 0, 1
Let q(o) = -o**3 + o**2 + 1. Let g(k) = -10*k**3 + 8*k**2 + 9. Let l be 5 - 5 - (3 + -5). Let n(d) = l*g(d) - 18*q(d). Suppose n(r) = 0. Calculate r.
-1, 0
Let d(t) be the second derivative of 1/10*t**6 + 0*t**2 + 0 + 27*t - 9/2*t**3 - 21/20*t**5 + 15/4*t**4. Solve d(x) = 0.
0, 1, 3
Let n(r) be the third derivative of 0 - 16*r**2 + 2/3*r**3 + 1/8*r**4 + 0*r - 1/60*r**5. Find l, given that n(l) = 0.
-1, 4
Let g = 14033/4914 + 1/702. Factor -g*o + 12/7*o**2 - 8/7.
4*(o - 2)*(3*o + 1)/7
Let d(q) be the first derivative of 8*q**3/3 - 30*q**2 + 88*q - 430. Let d(n) = 0. Calculate n.
2, 11/2
Let b = 627/17 + -9577/238. Let w = -20/7 - b. Solve 0*u**3 + w*u**4 + 1/2 - u**2 + 0*u = 0 for u.
-1, 1
Suppose 0 = -72*j + 70*j + 20. Suppose -3*c = 2*z - 6, -2*z + c - 6*c + j = 0. Factor -1/5*d**4 - 1/5 + z*d**3 + 2/5*d**2 + 0*d.
-(d - 1)**2*(d + 1)**2/5
Let z(j) = 9*j**3 - 1159*j**2 + 39179*j - 73717. Let w(a) = 3*a**3 - 386*a**2 + 13060*a - 24572. Let t(c) = -11*w(c) + 4*z(c). Factor t(f).
3*(f - 64)**2*(f - 2)
Let k(p) be the second derivative of p**6/210 + 17*p**5/140 + 85*p**4/84 + 53*p**3/14 + 45*p**2/7 - 24*p - 5. Find a such that k(a) = 0.
-10, -3, -1
Factor -5*l**2 - 4*l**2 - 2*l**2 + 6*l**2 + 250 - 72*l + 187*l.
-5*(l - 25)*(l + 2)
Let f(j) = 15*j - 69. Let u be f(5). Let r(i) = -5*i + 32. Let d be r(u). Suppose -d*t**3 - 6/7*t - 24/7*t**2 + 4/7 = 0. What is t?
-1, 2/7
Factor 0*f**2 + 2*f**2 - 2*f**2 - 2*f - 38*f**4 + 2*f**3 + 36*f**4 + 2*f**2.
-2*f*(f - 1)**2*(f + 1)
Let l = -2955/4 - -739. Let b(y) be the second derivative of 6*y - 2*y**3 - 6*y**2 - l*y**4 + 0. Factor b(r).
-3*(r + 2)**2
Let u(z) = 14*z**3 + 139*z**2 + 125*z - 289. Let r(k) = 3*k**3 + 28*k**2 + 25*k - 58. Let f(g) = -11*r(g) + 2*u(g). Factor f(i).
-5*(i - 1)*(i + 3)*(i + 4)
Let g(b) be the third derivative of -b**6/900 + 11*b**5/450 + 4*b**4/45 + 7*b**3/6 + 2*b**2. Let i(n) be the first derivative of g(n). What is u in i(u) = 0?
-2/3, 8
Let i = 79 - 77. Factor 2 - 44*o**3 + 15*o**2 - 8 + 32*o**3 - 36*o**4 - 9*o + 27*o**i + 21*o**5.
3*(o - 1)**3*(o + 1)*(7*o + 2)
Let u(l) be the second derivative of l**8/2240 - l**7/210 + l**6/240 + 3*l**5/20 - 5*l**4/12 + 23*l. Let q(s) be the third derivative of u(s). Factor q(b).
3*(b - 3)*(b - 2)*(b + 1)
Suppose 5*m - 23 = -4*h + 6*m, -2*h + 22 = -4*m. Factor -1/4*z**h - 3/4*z**3 + 0*z + 1/4*z**2 + 3/4*z**4 + 0.
-z**2*(z - 1)**3/4
Let r(x) be the third derivative of -x**10/75600 + x**8/3360 - x**7/1260 + x**5/30 - 7*x**2. Let b(k) be the third derivative of r(k). Factor b(i).
-2*i*(i - 1)**2*(i + 2)
Let o(u) be the first derivative of 7/19*u**2 - 3 - 3/19*u**4 + 2/19*u**5 - 6/19*u - 4/57*u**3 - 1/57*u**6. Suppose o(d) = 0. What is d?
-1, 1, 3
Let q(s) be the first derivative of s**6/72 + 3*s**5/10 + 121*s**4/48 + 10*s**3 + 50*s**2/3 - 74. Suppose q(k) = 0. What is k?
-5, -4, 0
Let y(a) be the third derivative of -a**6/360 - a**5/30 + 5*a**4/24 + 50*a**3/9 - 23*a**2 - 5*a. Find n such that y(n) = 0.
-5, 4
Let p be 4 + 0 + (-1134)/288. Let n(r) be the second derivative of 0*r**2 + 0 + 5*r - 3/80*r**5 - p*r**4 + 1/4*r**3. Factor n(b).
-3*b*(b - 1)*(b + 2)/4
Let u(m) = -m**3 - 3*m**2 - m + 2. Let i be u(0). Let k(g) = -g + 2. Let q be k(2). Let -2/3*p**4 + 4/3*p**i + q*p**3 + 0*p - 2/3 = 0. What is p?
-1, 1
Let k = -9449 + 66256/7. Let t = k + -16. Factor t*q**3 - 2/7*q**2 + 1/7*q + 0.
q*(q - 1)**2/7
Let t(g) be the first derivative of -1/21*g**2 + 2/7*g + 1/42*g**4 - 2/21*g**3 + 5. Factor t(s).
2*(s - 3)*(s - 1)*(s + 1)/21
Let b = -612 + 412. Let c = 203 + b. Determine s so that -8/3 - 80*s**2 + 28*s + 100/3*s**c = 0.
1/5, 2
Let j = -1109/70 + 187/10. Suppose -j*n - 8/7 - 8/7*n**2 = 0. What is n?
-2, -1/2
Let v(i) be the first derivative of -25 - 4/9*i**3 + 8/9*i**2 - 4/9*i. Factor v(m).
-4*(m - 1)*(3*m - 1)/9
Suppose -4*r = -26 + 10. Let -21*u - r*u**4 + 14*u**2 + 0*u**4 + 33*u**3 - 5*u**4 + 4 + 3*u**2 = 0. Calculate u.
-1, 1/3, 4
Let j(f) = -f**2 + 1. Let u(l) = 10*l**2 + 0*l**2 - 9*l + 72 - 14*l + 5*l. Let h(x) = 36*j(x) + 4*u(x). Factor h(t).
4*(t - 9)**2
Suppose 0*i = -5*i - m + 45, -30 = -2*i + 2*m. What is h in -i + 0*h**2 - 45*h + 43*h**3 + 35*h**4 - 25*h**2 + 2*h**3 = 0?
-1, -2/7, 1
Let v(o) be the first derivative of o**3/21 + 5*o**2/14 - 50*o/7 - 417. Let v(n) = 0. Calculate n.
-10, 5
Let g be (-4 + 2)*146/4 + -4. Let h = 387/5 + g. Factor -2/5*w**2 + 2/5*w**3 - 2/5*w + 0 + h*w**4.
2*w*(w - 1)*(w + 1)**2/5
Let z(b) be the second derivative of b**6/15 + 47*b**5/10 - 17*b**4 - 188*b**3/3 + 392*b**2 + 680*b. What is m in z(m) = 0?
-49, -2, 2
Let f(g) = -9 + 5 - 12*g + 4*g**2 + 12*g**2. Let b(k) = -17*k**2 + 13*k + 4. Let s(r) = 4*b(r) + 6*f(r). Factor s(o).
4*(o - 1)*(7*o + 2)
Let w(b) = -b**2 + b + 1. Let j(n) = n**3 + 17*n**2 + 6*n + 6. Let i(f) = j(f) - 6*w(f). Factor i(h).
h**2*(h + 23)
Let o(d) be the second derivative of -d**5/90 - 11*d**4/54 - 8*d**3/9 + 4*d**2 + 2*d + 52. Find n, given that o(n) = 0.
-6, 1
Let k(b) be the first derivative of -2*b**3/27 + 101*b**2/9 - 201. Factor k(t).
-2*t*(t - 101)/9
Let x(h) be the first derivative of h**4/12 - 5*h**3/6 + 2*h**2 + 27*h + 27. Let k(n) be the first derivative of x(n). Solve k(a) = 0.
1, 4
Let i(d) be the first derivative of -d**3/3 + 9*d**2/2 - 3*d + 5. Let 