*2/3
Suppose 750 = -5*z - 5*z. Let y = -75 - z. What is v in -4/5*v**2 + y + 0*v + 0*v**3 + 1/5*v**4 = 0?
-2, 0, 2
Let c(j) be the second derivative of 0*j**4 - 1/3*j**3 - 1/21*j**7 - j + 0*j**2 + 0 + 0*j**6 + 1/5*j**5. Factor c(q).
-2*q*(q - 1)**2*(q + 1)**2
What is t in 5*t**2 + 135*t - 233*t - 174*t + 9245 - 158*t = 0?
43
Let a(f) be the first derivative of f**8/630 - f**7/525 - f**6/900 + 3*f**2/2 + 7. Let x(m) be the second derivative of a(m). Find d, given that x(d) = 0.
-1/4, 0, 1
Let m be (0 + -4 - -5)*(0 + 3). Determine q, given that -48 + 8*q**2 + 28 - m*q**2 = 0.
-2, 2
Suppose -3*w + 5*r = -27, 7 = 11*w - 7*w + 3*r. Let t(d) be the third derivative of -6*d**2 + 0 + 1/90*d**5 + 0*d**3 + 1/36*d**w + 0*d. Factor t(q).
2*q*(q + 1)/3
Let l(t) be the third derivative of -t**6/240 + 7*t**5/360 + t**4/24 + 2*t**2 - 26. Factor l(g).
-g*(g - 3)*(3*g + 2)/6
Let q(m) be the third derivative of m**6/160 - 11*m**5/80 + 19*m**4/32 - 9*m**3/8 + m**2 + 40*m. Factor q(w).
3*(w - 9)*(w - 1)**2/4
Let u = -113 + 115. Factor -u*f**3 - 3*f - 19 + 10 + 13 - 4*f**2 + 5*f.
-2*(f - 1)*(f + 1)*(f + 2)
Solve 0 + 0*m + 4/9*m**2 + 2/9*m**3 - 2/9*m**4 = 0.
-1, 0, 2
Suppose 21*n + 2 = 22*n. Factor -3*k**2 - k**4 + 4*k**n + 0*k**2.
-k**2*(k - 1)*(k + 1)
Let x(q) = -q**4 - 2*q**3 - q**2 + q - 2. Let a(b) = -8*b**4 - 4*b**3 - 70*b**2 + 74*b - 42. Let m(z) = a(z) - 10*x(z). What is t in m(t) = 0?
-11, 1
Let j(w) be the third derivative of -w**8/1176 + 3*w**7/490 - w**6/70 + w**5/105 - 358*w**2. Suppose j(f) = 0. Calculate f.
0, 1/2, 2
Let q(g) = -g**3 + 2. Let y be q(0). Factor -89*m**5 - y*m**4 + 87*m**5 + 3*m**3 + m**3.
-2*m**3*(m - 1)*(m + 2)
Let z(h) be the first derivative of 1/3*h - 1/2*h**5 - 13/6*h**3 - 29 - 3/4*h**2 - 43/24*h**4. Factor z(i).
-(i + 1)**3*(15*i - 2)/6
Let -151/4*a**2 - 3/4*a**3 - 12*a + 25 = 0. What is a?
-50, -1, 2/3
Let q(x) = -x**2 - 11*x - 11. Let b(c) = 2*c**2 + 23*c + 22. Let z(l) = 2*b(l) + 5*q(l). Let v be z(-7). Solve -3/2 - 21/2*g - 33/2*g**2 - 15/2*g**v = 0.
-1, -1/5
Let s(p) be the first derivative of p**6/54 + 4*p**5/45 - p**4/18 - 8*p**3/27 + p**2/18 + 4*p/9 - 4. Solve s(w) = 0.
-4, -1, 1
Find i such that -i**5 + 448*i**3 - 7*i**4 - i**5 - 451*i**3 = 0.
-3, -1/2, 0
Find m, given that -16*m**3 - 4*m**5 - 270*m + 270*m + 16*m**4 = 0.
0, 2
Suppose 0 = -4*w + 3*f + 16, 3*w + f + f + 5 = 0. Let g be w*(-1 - 0) + 3. What is t in -t**4 - 7*t**2 + 2*t - 2*t**g + 4*t**2 + 4*t**3 = 0?
0, 1, 2
Let y(b) be the second derivative of b**5/300 + b**4/12 + 5*b**3/6 + 4*b**2 + 8*b. Let i(z) be the first derivative of y(z). Suppose i(x) = 0. What is x?
-5
Let v be 75/40*30/9*4. Find j such that -v*j**2 - 4*j + 4*j + 10*j = 0.
0, 2/5
Let s(y) = 44*y**2 - 432*y + 23322. Let r(p) = 51*p**2 - 432*p + 23321. Let z(u) = -6*r(u) + 7*s(u). Factor z(n).
2*(n - 108)**2
Let y = 38 - 33. What is o in y*o + 4*o**2 - 4*o**2 + 3*o**2 - 2*o**2 = 0?
-5, 0
Let j be (-18)/(-24) - (-5)/(-20). Let g(n) be the first derivative of 0*n**3 + 0*n + n**2 - 6 - j*n**4. Factor g(b).
-2*b*(b - 1)*(b + 1)
Let w(k) be the second derivative of -k**6/90 + k**5/12 - k**4/4 + 7*k**3/18 - k**2/3 - 33*k - 1. Factor w(c).
-(c - 2)*(c - 1)**3/3
Let d = 15688138/192549 + 1/9169. Let y = 253/3 - d. Determine a, given that -y*a**2 - 8/7 - 4*a = 0.
-1, -2/5
Let s(j) = 17*j + 34. Let h be s(-2). Let -1/4*r**3 + 0 - 1/2*r**2 + h*r = 0. Calculate r.
-2, 0
Let y(z) = 3*z**3 - 285*z**2 + 297. Let t(h) = 6*h**3 - 575*h**2 - h + 595. Let j(m) = -3*t(m) + 5*y(m). Suppose j(p) = 0. What is p?
-1, 1, 100
Let d(z) be the third derivative of z**8/20160 - z**6/180 - 7*z**5/60 - 2*z**2. Let s(x) be the third derivative of d(x). Suppose s(c) = 0. Calculate c.
-2, 2
Let b(g) = 80 + 16*g - 3*g - 9*g. Let d be b(-20). Let d + 4/7*k**2 - 4/7*k = 0. What is k?
0, 1
Let q = 6112/5 + -1222. Find b such that -2/5*b + q*b**2 - 2/5*b**4 + 0 + 2/5*b**3 = 0.
-1, 0, 1
Let t(w) be the first derivative of 2/3*w**3 + 8 + 32/3*w + 4*w**2 + 1/24*w**4. Factor t(a).
(a + 4)**3/6
Let r be 36/84 + (-23)/70. Let a(u) be the first derivative of 1/6*u**3 + 1/4*u**2 + 0*u + 3 - 1/8*u**4 - r*u**5. Determine y so that a(y) = 0.
-1, 0, 1
Let p be 5/((-6 - -11) + -4). Let g(f) be the third derivative of -1/105*f**7 + 0*f**3 + 0*f**6 + 0 + 0*f + 1/30*f**p + 4*f**2 + 0*f**4. Factor g(n).
-2*n**2*(n - 1)*(n + 1)
Let x(l) be the first derivative of l**6/2 - 24*l**5/5 - 9*l**4 + 22*l**3 + 129*l**2/2 + 54*l + 557. Suppose x(m) = 0. What is m?
-1, 2, 9
Determine i so that -2/13 + 4/13*i**2 + 8/13*i**5 - 16/13*i**3 - 2/13*i**4 + 8/13*i = 0.
-1, 1/4, 1
Let f(m) be the second derivative of 2*m**6/15 + m**5/5 - 4*m**4/3 - 8*m**3/3 + m + 15. Solve f(h) = 0 for h.
-2, -1, 0, 2
Let r(x) be the first derivative of 3/10*x**5 - 54 + 9/2*x**3 - 3*x**2 + 0*x - 9/4*x**4. Find w such that r(w) = 0.
0, 1, 4
Let c(r) be the first derivative of 5*r**6/9 - 7*r**5/5 + 5*r**4/12 + 11*r**3/9 - r**2/2 - 2*r/3 - 10. Let c(h) = 0. What is h?
-1/2, -2/5, 1
Let y(d) = -9*d**2 - d + 13. Let n(x) = x**2 - 4. Let j(g) = 12*n(g) + 4*y(g). Find z such that j(z) = 0.
-1/2, 1/3
Let v(k) = 2*k**4 - 10*k**3 - 16*k**2 + 29*k - 5. Let z(t) = -6*t**4 + 30*t**3 + 48*t**2 - 86*t + 14. Let j(o) = 14*v(o) + 5*z(o). Let j(d) = 0. What is d?
-2, 0, 1, 6
Let w(j) = -7*j - 61. Let p be w(-11). Factor -6*n**2 - 32/3 - 2/3*n**3 - p*n.
-2*(n + 1)*(n + 4)**2/3
Factor 6816*x - 340 + 6511*x + 70*x**2 - 5*x**3 - 13052*x.
-5*(x - 17)*(x - 1)*(x + 4)
Let b(q) be the first derivative of -4*q**3/3 - 6*q**2 - 8*q + 3. Suppose b(x) = 0. What is x?
-2, -1
Factor -11/4*a**2 + a + 15 + 1/4*a**3.
(a - 10)*(a - 3)*(a + 2)/4
Let b(n) be the third derivative of -n**8/1680 - n**7/175 + 7*n**6/120 - 4*n**5/25 + n**4/6 + 194*n**2. Find w such that b(w) = 0.
-10, 0, 1, 2
Let y(u) be the second derivative of 0 - 16*u - 10*u**2 - 1/4*u**5 + 5/4*u**4 + 0*u**3. Let y(q) = 0. What is q?
-1, 2
Let y(l) be the third derivative of 0*l + 3/80*l**5 + 30*l**2 + 0 + 5/32*l**4 + 1/4*l**3 - 1/280*l**7 - 1/160*l**6. Let y(t) = 0. What is t?
-1, 2
Let f(g) be the second derivative of -g**3/3 - 19*g**2 - 33*g. Let w be f(-19). Factor -1/4*n**3 + w*n + 0 + 0*n**2.
-n**3/4
Let h(u) be the first derivative of 2*u**4 - 16*u - 16/5*u**5 + 18 - 2*u**2 - 2/3*u**6 + 32/3*u**3. Find j, given that h(j) = 0.
-4, -1, 1
Let i(p) be the second derivative of -5*p**4/24 + 40*p**3 - 2880*p**2 + 3*p + 4. Solve i(r) = 0 for r.
48
Let i(s) be the second derivative of -s**9/45360 + s**8/6720 - s**7/3780 - 5*s**4/4 + 8*s. Let v(m) be the third derivative of i(m). Let v(j) = 0. What is j?
0, 1, 2
Let p(o) be the first derivative of o**7/315 - o**6/45 + 2*o**5/45 - 15*o**2/2 + 17. Let v(b) be the second derivative of p(b). Determine z so that v(z) = 0.
0, 2
Let v(d) = 3*d**5 - d**4 - 5*d**3 + d**2 + 2*d. Let w(s) = 4*s**5 - 2*s**4 - 6*s**3 + 2*s**2 + 2*s. Let g(z) = 5*v(z) - 4*w(z). Factor g(i).
-i*(i - 2)*(i - 1)**2*(i + 1)
Let b be (2 - 4/(-2))*4. Let h = 30 - b. Factor h*r**3 - 3*r + 3*r - 2*r + 5*r**2 - 16*r**3.
-r*(r - 2)*(2*r - 1)
Let z be 2/(-3) - 16/(-24). Suppose -6 = 2*s - 3*v, z*s - 5*s = -5*v + 10. Determine d, given that -2*d**4 + s*d + 24/11*d**3 + 0 - 8/11*d**2 + 6/11*d**5 = 0.
0, 2/3, 1, 2
Let n(j) be the first derivative of 0*j - 21 + 0*j**2 + 2/21*j**3 + 2/35*j**5 - 1/7*j**4. Suppose n(f) = 0. Calculate f.
0, 1
Factor 0 - 3/5*h**3 + 12/5*h + 9/5*h**2.
-3*h*(h - 4)*(h + 1)/5
Let i be (0/(-17))/((-3)/1). Let y(x) be the second derivative of 1/3*x**4 - 4*x**3 + 18*x**2 + i - 5*x. What is p in y(p) = 0?
3
Let o(s) be the second derivative of 1/5*s**3 + 0*s**2 + 1/20*s**4 - 3/100*s**5 - 2*s + 0. Solve o(n) = 0.
-1, 0, 2
Let m = 14 + -12. Let r(z) = -6*z**2 + 6*z**2 + 4*z**m + 34*z + 12 + 6*z**2. Let u(f) = 3*f**2 + 11*f + 4. Let s(g) = -3*r(g) + 8*u(g). What is b in s(b) = 0?
-2, -1/3
Let y(z) = z**2 + 17*z - 35. Let l be y(-19). Let w(j) be the first derivative of -l*j**2 + 0*j**3 + 1/2*j**4 + 4*j + 2. Factor w(p).
2*(p - 1)**2*(p + 2)
Let z(n) be the first derivative of n**7/4200 + n**6/450 + n**5/120 + n**4/60 + 5*n**3/3 - 5. Let m(r) be the third derivative of z(r). Factor m(g).
(g + 1)**2*(g + 2)/5
Let b(d) = -9*d - 18. Let s(i) = 5*i + 9. Let a(x) = 6*b(x) + 11*s(x). Let g be a(11). Determine k, given that 0*k - 2/5 + 2/5*k**g =