12. Let v be (x/(-9))/(1/(-3)). Suppose -2*r**2 + 0*r + 0*r + 0*r**v + 2*r = 0. Calculate r.
0, 1
Let i = 29 + -29. Let o(u) be the second derivative of 1/24*u**3 + 3/80*u**5 + i*u**2 + 0 + 1/120*u**6 - u + 1/16*u**4. Factor o(c).
c*(c + 1)**3/4
Let k(t) be the first derivative of -1444*t**5 - 7505*t**4/4 + 5*t**3 + 140*t**2 - 20*t - 9. What is y in k(y) = 0?
-1, -1/4, 2/19
Let y(x) be the first derivative of -x**4/4 + x**3/3 + x**2/2 - x - 26. Factor y(p).
-(p - 1)**2*(p + 1)
Let p(l) be the third derivative of 0*l + 1/30*l**5 + 0*l**3 + 0 + 1/180*l**6 + 1/18*l**4 - 2*l**2. Factor p(s).
2*s*(s + 1)*(s + 2)/3
Let h(j) be the second derivative of -6*j + 27/4*j**2 + 3/2*j**3 + 1/8*j**4 + 0. Factor h(n).
3*(n + 3)**2/2
Let t(d) be the second derivative of 3*d + 0 - 1/4*d**4 - 1/2*d**3 + 3/20*d**5 + 3/2*d**2. Find c such that t(c) = 0.
-1, 1
Let w(u) = u**2 + 22*u - 45. Let b be w(-24). Factor -1/4*n**4 + 0 + 1/4*n - 3/4*n**2 + 3/4*n**b.
-n*(n - 1)**3/4
Factor 242/5 + 156/5*x**2 - 891/5*x - 7/5*x**3.
-(x - 11)**2*(7*x - 2)/5
Let w(n) be the first derivative of -4*n**6 + 28*n**5/5 + 16*n**4 - 44*n**3 + 40*n**2 - 16*n + 4. Solve w(b) = 0 for b.
-2, 1/2, 2/3, 1
Let c(z) be the second derivative of z**8/3360 + z**7/1680 + z**3/2 - z. Let y(g) be the second derivative of c(g). Find a, given that y(a) = 0.
-1, 0
Suppose 0 = 3*o - 4*o - 1. Let d(z) = -17*z**4 + 14*z**3 + 8*z**2 - 5. Let t(x) = x**4 - x**3 - x**2 + 1. Let s(h) = o*d(h) - 5*t(h). Factor s(c).
3*c**2*(c - 1)*(4*c + 1)
Find b, given that 2*b**2 + 1/2*b**3 + 0 + 0*b = 0.
-4, 0
Let o(p) be the first derivative of -1/10*p**5 + 1/6*p**3 + 0*p**4 + 1/8*p**2 - 1/24*p**6 + 5 + 0*p. Factor o(g).
-g*(g - 1)*(g + 1)**3/4
Let q(s) be the third derivative of -s**6/480 - s**5/120 - s**4/96 + 3*s**2. Determine a, given that q(a) = 0.
-1, 0
Determine w so that -41 + 49*w - 17*w - 4*w**2 - 23 = 0.
4
Factor 29*g - 9*g + 10 + 28*g - 3*g + 20*g**2.
5*(g + 2)*(4*g + 1)
Let s(b) = -38*b**2 - 13*b + 3. Let g(k) = 113*k**2 + 38*k - 8. Let a(v) = -3*g(v) - 8*s(v). What is u in a(u) = 0?
-2/7, 0
Let a(f) = 0*f**4 + f - 2*f**4 + f**4. Let o(p) = 6*p**4 + 2*p**3 - 2*p**2 - 6*p. Let v = 51 - 50. Let b(l) = v*o(l) + 4*a(l). What is n in b(n) = 0?
-1, 0, 1
Let o(x) = -3*x**2 + 12*x + 9. Let b(p) = 4*p**2 - 11*p - 8. Let f(k) = -6*b(k) - 7*o(k). Factor f(t).
-3*(t + 1)*(t + 5)
Let x(q) be the first derivative of 2*q**5/55 - 3*q**4/22 + 4*q**2/11 + 8. Let x(h) = 0. What is h?
-1, 0, 2
Suppose -16 + 7 = 2*v - 3*f, 4*f = 4*v + 12. Factor 0 + 4/7*s**2 - 2/7*s**3 + v*s.
-2*s**2*(s - 2)/7
Let o(d) = 3*d. Let c be o(3). Let t be c/12 + 6/(-8). Factor 0*y**4 - 2/3*y**3 + 2/3*y**5 + t*y + 0 + 0*y**2.
2*y**3*(y - 1)*(y + 1)/3
Suppose 3*v - 14 = -c - 4, -4*v = -3*c + 4. Factor -2/5*j**3 + 0*j + 4/5*j**v + 0.
-2*j**2*(j - 2)/5
Let t = -159/2 + 80. Suppose 1/4*f**3 - 3/4*f + t + 0*f**2 = 0. What is f?
-2, 1
Let d(m) be the second derivative of m**6/10 - m**4/4 - 4*m. Factor d(p).
3*p**2*(p - 1)*(p + 1)
Determine c, given that 363/2*c**2 + 6 - 66*c = 0.
2/11
Suppose -3*b = -4*b - 1, -o = -b - 6. Find j, given that 2 + j**5 + 2*j**4 - 3*j**5 + j + 3*j**o - 4*j**2 - 2*j**3 + 0*j**4 = 0.
-2, -1, 1
Let g(i) be the third derivative of -i**6/1440 + i**4/96 + i**3/3 - 3*i**2. Let y(v) be the first derivative of g(v). Let y(h) = 0. Calculate h.
-1, 1
Factor 6*v**3 + 0 + 14/3*v**4 + 4/3*v**5 + 10/3*v**2 + 2/3*v.
2*v*(v + 1)**3*(2*v + 1)/3
Let x(l) be the first derivative of 0*l + l**2 + 0*l**5 + 0*l**3 + 0*l**4 - 3 - 1/420*l**6. Let u(z) be the second derivative of x(z). Factor u(h).
-2*h**3/7
Let g(w) = -10*w + 4. Let x be g(4). Let a be 8/x + (-20)/(-9). Find u, given that -14*u + 7*u**3 - 4 - 3*u**2 - u**2 - u**a - 2*u = 0.
-1, -2/7, 2
Let l be (-1)/2 - 1089/(-2160). Let z(a) be the third derivative of 0 - 1/48*a**4 + 0*a + l*a**5 + 1/480*a**6 + 0*a**3 + 3*a**2. Let z(r) = 0. What is r?
-2, 0, 1
Let n(t) be the first derivative of -2/5*t**5 - 1/9*t**6 - 1/2*t**4 - 1 + 0*t + 0*t**2 - 2/9*t**3. Suppose n(a) = 0. Calculate a.
-1, 0
Let x(w) = w**2 + 2*w - 2. Let r = 2 + -8. Let l be x(r). Solve -l*y - 10*y - 1 + 2 + 30*y**2 + 7 = 0 for y.
2/5, 2/3
Factor 1/6*o**2 - 2/3*o + 0 - 1/6*o**4 + 2/3*o**3.
-o*(o - 4)*(o - 1)*(o + 1)/6
Let p(r) be the third derivative of 0 + 0*r + 1/210*r**5 - 1/28*r**4 + 4*r**2 - 4/21*r**3. Suppose p(n) = 0. What is n?
-1, 4
Let d(t) be the second derivative of -t**5/30 - t**4/6 + 4*t**2/3 + 2*t. Let d(k) = 0. Calculate k.
-2, 1
Let p(j) = j. Suppose 3*g = -g. Let l be p(g). Solve -2/7*k**2 + l*k + 2/7 = 0 for k.
-1, 1
Let o(d) be the third derivative of d**5/15 - 2*d**3/3 + d**2. Determine l, given that o(l) = 0.
-1, 1
Let a(u) = -32*u + 291. Let g be a(9). Factor 2/3*c**2 - 2/15*c**g + 8/15 - 16/15*c.
-2*(c - 2)**2*(c - 1)/15
Suppose -1 = -g + 3. Factor 18*j**4 - j**3 + 3*j**2 - 21*j**g + 2*j**3 - 4*j**3 + 3*j.
-3*j*(j - 1)*(j + 1)**2
Let a be 30/35 + 4/(-7). Suppose 0*r**2 + 0 + 2/7*r**4 - a*r**3 + 0*r = 0. What is r?
0, 1
Let f be 2/(-30)*(25 - 35). Find a, given that -2/3*a + f - 2/3*a**2 + 2/3*a**3 = 0.
-1, 1
Let v(z) = 6*z**4 + 5*z**3 - 17*z**2 - 5*z + 6. Let j(t) = 7 + 26*t**2 + 3*t**4 - 4 + 3*t**3 - 35*t**2 - 3*t. Let b(h) = 5*j(h) - 3*v(h). Factor b(p).
-3*(p - 1)**2*(p + 1)**2
Let i(w) be the second derivative of -5*w**7/42 + w**6/3 - w**5/4 + 18*w. Factor i(z).
-5*z**3*(z - 1)**2
Factor 0 + 2/7*h**4 - 4/7*h**3 - 2/7*h**2 + 4/7*h.
2*h*(h - 2)*(h - 1)*(h + 1)/7
Let l(o) = o**3 - o**2 + 1. Let t be l(-1). Let a be (-4)/1*t/2. Factor 4*z**2 + 3*z**3 - 17*z**3 + 0*z**a.
-2*z**2*(7*z - 2)
Let n(r) = -r**2 + 2*r + 5. Let h(q) = q**2 - q - 4. Let i = -16 + 14. Let m(s) = i*n(s) - 3*h(s). Solve m(d) = 0 for d.
-2, 1
Let t(n) = -3*n**4 + n**3 + 3*n**2 + 3*n + 2. Let d(p) = -7*p**4 + 3*p**3 + 7*p**2 + 7*p + 5. Let y(g) = -2*d(g) + 5*t(g). Solve y(c) = 0 for c.
-1, 0, 1
Let c(v) be the first derivative of -v**3 - 3*v**2 + 2. Factor c(q).
-3*q*(q + 2)
Let k(a) = 31*a - 124. Let y be k(4). Determine r, given that 1/3*r + y + 1/3*r**2 = 0.
-1, 0
Let h(y) = -1. Let j(t) = -2*t**2 - 8*t - 2. Let q(u) = 6*h(u) + j(u). Factor q(k).
-2*(k + 2)**2
Let q(g) be the third derivative of 0 + 1/15*g**5 + 2*g**2 + 0*g + 0*g**4 - 2/3*g**3. Solve q(a) = 0 for a.
-1, 1
Let f be (-4 - -4)/(0 + -5 - -7). Suppose 0*i - 3/4*i**2 + f = 0. What is i?
0
Let v(n) = -n**2 - 6*n - 4. Let k(r) = r**2 + 6*r + 5. Let i(f) = 3*k(f) + 4*v(f). Let y be i(-5). What is h in -2*h - 4 + 0*h**3 + h**3 + y*h**2 + h**3 = 0?
-2, -1, 1
Let b = 29 - 25. Let j be 92/20*1 - b. Factor -3/5*o + j*o**3 + 0 + 0*o**2.
3*o*(o - 1)*(o + 1)/5
Let -3/2*m - 1/2*m**2 + 0 = 0. Calculate m.
-3, 0
Let a(w) be the third derivative of w**7/315 + w**6/90 - w**5/90 - w**4/18 - 14*w**2. What is m in a(m) = 0?
-2, -1, 0, 1
Let 3/2*k**2 - 9/4*k + 3/4*k**3 + 0 = 0. What is k?
-3, 0, 1
Let j be (-29)/(-9) - (-78)/(-351). Factor 1 + 3/2*r**j - 7/2*r + r**2.
(r - 1)*(r + 2)*(3*r - 1)/2
Let c(f) = -6*f**2 + 46*f + 18. Let n be c(8). Factor 1/2 + 7/4*z**n + 9/4*z.
(z + 1)*(7*z + 2)/4
Let f(y) be the third derivative of -y**7/70 - 3*y**6/20 - 13*y**5/20 - 3*y**4/2 - 2*y**3 + 2*y**2. Factor f(o).
-3*(o + 1)**2*(o + 2)**2
Let y(c) be the third derivative of -c**6/60 + c**5/15 - c**4/12 + 13*c**2. What is n in y(n) = 0?
0, 1
Let b(z) be the third derivative of -1/720*z**6 + 1/48*z**4 + 0*z**5 + z**2 + 1/6*z**3 + 0*z + 0. Let r(n) be the first derivative of b(n). Factor r(s).
-(s - 1)*(s + 1)/2
Let a(i) = -4*i**5 - 13*i**4 + 11*i**3 + 8*i**2 - 12*i - 5. Let y(n) = 2*n**5 + 6*n**4 - 6*n**3 - 4*n**2 + 6*n + 2. Let s(r) = 2*a(r) + 5*y(r). Factor s(c).
2*c*(c - 1)**2*(c + 1)*(c + 3)
Let m = -1201 - -1204. Determine f, given that -3/2*f**m + 5/2*f**4 + 3/2*f + 1 - 7/2*f**2 = 0.
-1, -2/5, 1
Factor 0*y**3 + 0*y - 3/7*y**5 + 3/7*y**4 + 0 + 0*y**2.
-3*y**4*(y - 1)/7
Suppose 6*n = 39 + 21. What is k in 3*k**5 - n*k**4 - 3*k**3 - 3*k**4 + 6*k**2 + 7*k**4 = 0?
-1, 0, 1, 2
Factor 3/8*w - 9/8*w**2 + 0 + 3/4*w**3.
3*w*(w - 1)*(2*w - 1)/8
Let u(g) be the third derivative of -g**5/20 - 11*g**4/4 - 121*g**3/2 + 20*g**2. Factor u(n).
-3*(n + 11)**2
Factor 14*z - 6*z - 3*z**2 - 2*z.
-3*z*(z - 2)
Let d be 4/2 - (2 + 5). Let x = d - -12. Determine h, given that x*h**3 + 2*h**3 - 9*h**2 + 5*h**4 + 3*h - 8*h**4 = 0.