What is g in -14*g**3 + g**j + g**5 + g**2 + 11*g**3 = 0?
-2, 0, 1
Let f(l) = -l**2 + 5*l - 4. Let k be f(3). What is r in 2*r**2 - r - k*r + 7*r + 2 = 0?
-1
Let d(k) be the second derivative of -3/4*k**5 - 3/4*k**4 + 4*k + 3/10*k**6 + 0*k**2 + 0 + 1/2*k**3 + 2/7*k**7. Find n, given that d(n) = 0.
-1, 0, 1/4, 1
Let s(t) be the first derivative of 9*t + 3/5*t**5 - 15*t**2 - 9/2*t**4 + 6 + 12*t**3. Let s(x) = 0. What is x?
1, 3
Let t(b) be the second derivative of -b**7/441 + b**6/35 - 23*b**5/210 + b**4/18 + 8*b**3/21 - 16*b**2/21 - 15*b. Solve t(y) = 0 for y.
-1, 1, 4
Let x = -57/2 + 115/4. Factor -x*w**5 + 0*w**3 + 0*w + 1/4*w**4 + 0*w**2 + 0.
-w**4*(w - 1)/4
Let z(x) = -x**3 + x. Let y(c) = -19*c**3 + 36*c**2 - 23*c + 6. Let u(g) = y(g) - 4*z(g). Find h such that u(h) = 0.
2/5, 1
Let h = 530 + -7948/15. Let 8/15*w + h*w**2 + 8/15 = 0. Calculate w.
-2
Factor -5/4 - n + 1/4*n**2.
(n - 5)*(n + 1)/4
Find l, given that -l**2 - 6*l**5 + l**5 + 11*l**2 + 5*l**4 + 15*l**4 - 25*l**3 = 0.
0, 1, 2
Let v(u) = -u + 11. Let c be v(9). Suppose 0 = -4*g - 0*g. Let c + g + 0*n - 3*n + n**2 = 0. What is n?
1, 2
Determine a so that 12*a**3 - 3*a + 5*a**4 + 0*a - 9*a**5 - 11*a**4 + 0*a + 6*a**2 = 0.
-1, 0, 1/3, 1
Solve 1/4*a**3 - 1/2*a**2 + 1/4*a + 0 = 0.
0, 1
Let b = 16 - 79/5. Solve b*x**2 + 1/5*x + 0 = 0.
-1, 0
Suppose -7*c**3 - 2*c**4 - 6*c**4 + 8*c**2 + 4*c**5 + 3*c**3 = 0. Calculate c.
-1, 0, 1, 2
Factor 3/4*i + 1/4*i**2 + 1/2.
(i + 1)*(i + 2)/4
Factor -33*c - 12 - 51*c**3 + 8*c**2 - 9*c**2 - 26*c**2 + 48*c**3 + 3*c**4.
3*(c - 4)*(c + 1)**3
Let x(d) be the third derivative of -d**8/1680 - d**7/1050 - 5*d**2. Factor x(h).
-h**4*(h + 1)/5
Let z = 7 + -4. Suppose 157*g**2 + 3*g - z*g**3 - 157*g**2 = 0. Calculate g.
-1, 0, 1
Let c = 8/39 + 22/273. Factor 0 + 2/7*u**2 - c*u.
2*u*(u - 1)/7
Let h = 47 + -71. Let q be 28/45 + h/60. Factor -4/9 + q*a**2 - 2/9*a.
2*(a - 2)*(a + 1)/9
Let b(w) be the second derivative of w**4/8 + w**3 + 3*w**2 - 31*w. Solve b(d) = 0 for d.
-2
Let z(f) be the third derivative of f**6/30 - 7*f**5/30 + 25*f**4/96 - f**3/8 + 5*f**2. What is v in z(v) = 0?
1/4, 3
Let b(f) = -23*f**4 + 26*f**3 + 20*f**2 - 10*f - 5. Let o(a) = -15*a**4 + 17*a**3 + 13*a**2 - 7*a - 3. Let d(w) = -5*b(w) + 8*o(w). Factor d(c).
-(c - 1)**2*(c + 1)*(5*c - 1)
Let h(x) be the third derivative of 1/16*x**6 - 7/40*x**5 - 6*x**2 - 1/140*x**7 + 0*x**3 + 3/16*x**4 + 0 + 0*x. Find i such that h(i) = 0.
0, 1, 3
Suppose 0 = 4*x - 9*x + 30. Let g(z) be the third derivative of 0*z + 0 + 1/108*z**4 - 2*z**2 + 1/540*z**x + 0*z**3 + 1/135*z**5. Factor g(n).
2*n*(n + 1)**2/9
Suppose -3*b + 4*c = -3, 0*c = -5*c. Let o(l) = -2*l**3 - 3*l**2 - l. Let v be o(-2). Solve 1 - v*j**2 + 8*j - 2 - b = 0.
1/3, 1
Let l = 64 - 521/8. Let x = l - -53/40. Suppose -x*n + 1/5*n**2 - 1/5 + 1/5*n**3 = 0. What is n?
-1, 1
Let w(y) = -12*y**2 - 17*y + 6. Let b(i) = i**2. Let s(v) = 36*b(v) + 4*w(v). Let s(z) = 0. What is z?
-6, 1/3
Factor 0 - 2/5*s**2 + 4/5*s.
-2*s*(s - 2)/5
Let s(n) be the first derivative of 11*n**4 - 8*n**3/3 - 22*n**2 + 8*n - 20. Factor s(f).
4*(f - 1)*(f + 1)*(11*f - 2)
Suppose -3*l = l - 12. Suppose -20*z**2 + z**l + 2*z**3 + 17*z**2 = 0. Calculate z.
0, 1
Let t(j) be the third derivative of j**8/112 - 3*j**7/140 - j**6/40 + 3*j**5/40 - 12*j**2. Solve t(r) = 0.
-1, 0, 1, 3/2
Let u(x) be the third derivative of x**8/672 - x**6/240 + 18*x**2. Solve u(z) = 0 for z.
-1, 0, 1
Let m(q) be the second derivative of -q**5/120 - q**4/18 - q**3/9 - 6*q. Factor m(g).
-g*(g + 2)**2/6
Let z(w) be the third derivative of -w**7/14 + 11*w**6/12 - 5*w**5/12 - 35*w**4/12 + 7*w**2. Factor z(h).
-5*h*(h - 7)*(h - 1)*(3*h + 2)
Let g(n) = n**3 + 8*n**2 + n + 11. Let p be g(-8). Let k = -6 + 8. Factor 2 + p - 2*w**2 + 2 - 3 + k*w.
-2*(w - 2)*(w + 1)
Factor 1/4*m**2 + 0 - 1/4*m**3 + 0*m - 1/2*m**4.
-m**2*(m + 1)*(2*m - 1)/4
Let p be 3/(-2) - 9/(-6). Let t(a) be the first derivative of -1/2*a**2 + p*a + 2 + 1/3*a**3. Factor t(d).
d*(d - 1)
Let z be (-5)/(-15) - 46/(-6). Suppose z*x - 5*x = 9. What is v in 8*v**5 + 6*v**2 - 7*v**x - 3*v**3 + 0*v**3 - 6*v**4 + 2*v = 0?
-1, -1/4, 0, 1
Let o = 871/3 + -288. Let -o*w - 5/3*w**2 - 1/3*w**3 - 1 = 0. Calculate w.
-3, -1
Let n be ((-2 - -13) + -10)/(3/6). Factor 3/5*t + 0 - 3/5*t**n.
-3*t*(t - 1)/5
What is f in -17/4*f**3 + 5*f + 7/2*f**4 - 3/4*f**5 - 2 - 3/2*f**2 = 0?
-1, 2/3, 1, 2
Let k be (1/2)/(5/20). Suppose 0 = -4*b - 3*n - 5 + 15, 3*b - 14 = n. Factor -b*z**2 - 4*z**k + 10*z**2.
2*z**2
Factor -2*s**2 - 16*s + 0*s**2 + 0*s**2 - 2*s**2 - 16.
-4*(s + 2)**2
Let x(g) be the first derivative of -g**5/240 + g**3/24 - 3*g**2/2 + 3. Let w(p) be the second derivative of x(p). Determine u so that w(u) = 0.
-1, 1
Factor -3/2*l**2 + 0*l + 2 - 1/2*l**3.
-(l - 1)*(l + 2)**2/2
Let r(b) be the third derivative of -b**9/1008 + b**7/280 + b**3/2 + 5*b**2. Let x(a) be the first derivative of r(a). Factor x(t).
-3*t**3*(t - 1)*(t + 1)
Let i = 511/3 + -170. Factor -1/3 + 2/3*c**3 - 1/3*c - 1/3*c**4 - i*c**5 + 2/3*c**2.
-(c - 1)**2*(c + 1)**3/3
Let m(x) = -2*x**3 + 2*x**2 + 4*x + 2. Let p(q) = 10*q**3 - 10*q**2 - 20*q - 11. Let u(s) = 22*m(s) + 4*p(s). Suppose u(k) = 0. What is k?
-1, 0, 2
Let l be 10/8 - (-1)/(-4). Let w = l - 1. Let 1/3*s**4 - 2/3*s**3 + w*s**2 + 2/3*s - 1/3 = 0. Calculate s.
-1, 1
Factor 14*f**3 + 0*f**4 - 2*f**5 - 2*f + 2 - 10*f**3 + 2*f**4 - 4*f**2 + 0*f**4.
-2*(f - 1)**3*(f + 1)**2
Suppose -m + 10*d + 6 = 13*d, 0 = -4*m - 3*d + 15. Solve 0*h**2 - 1/4*h + 0 + 1/4*h**m = 0.
-1, 0, 1
Let m(s) be the second derivative of -3*s**5/10 + 7*s**4/3 - 7*s**3/3 - 4*s**2 + 9*s. Factor m(q).
-2*(q - 4)*(q - 1)*(3*q + 1)
Let x(b) = -b + 8. Let c(s) = -s + 8. Let g(k) = 6*c(k) - 5*x(k). Let p be g(8). Factor 1/4*z**2 + p + 1/2*z.
z*(z + 2)/4
What is a in -2/5*a**5 + 2*a**3 + 0*a**2 + 0*a**4 - 8/5*a + 0 = 0?
-2, -1, 0, 1, 2
Let m = 6671/27 + -247. Let p(z) be the third derivative of m*z**4 - 4*z**2 + 1/540*z**6 + 0*z + 0 + 1/54*z**5 + 4/27*z**3. What is w in p(w) = 0?
-2, -1
Let c(t) = t**2 + 3*t + 2. Let z be c(-2). Find l such that 2*l**2 - l + z*l + l**3 + 2*l = 0.
-1, 0
Determine g, given that -112/3*g + 280/3*g**2 - 304/3*g**3 + 145/3*g**4 - 25/3*g**5 + 16/3 = 0.
2/5, 1, 2
Let r(x) be the second derivative of x**4/78 - x**2/13 + 3*x. Factor r(s).
2*(s - 1)*(s + 1)/13
Let i(g) = g**2 + 10*g - 169. Let h be i(-19). Factor -3/5*n**4 - 12/5*n - 12/5 + 6/5*n**3 + 9/5*n**h.
-3*(n - 2)**2*(n + 1)**2/5
What is x in -11*x**3 - 4*x**4 - 96*x + 4*x**2 + 104*x + 3*x**3 = 0?
-2, -1, 0, 1
Let x(j) be the third derivative of j**6/24 - j**5/6 + 5*j**4/24 - 10*j**2. Factor x(o).
5*o*(o - 1)**2
Let g = 37/42 - 3/14. Solve 0 - g*c - 2/3*c**2 = 0 for c.
-1, 0
Let h be 6/(-4) - (-6)/(-4). Let s be 54/10 + h - 2. Factor 1/5*g**5 - 1/5*g + 0 + s*g**4 - 2/5*g**2 + 0*g**3.
g*(g - 1)*(g + 1)**3/5
Suppose -3*v - 2*y = -19, -8*y = -v - 9*y + 8. Factor 1/4*u**2 - 1/4*u**4 + 0 + 1/4*u**v - 1/4*u.
-u*(u - 1)**2*(u + 1)/4
Let y(n) be the third derivative of n**6/600 - n**5/300 - n**4/60 + 17*n**2. Factor y(b).
b*(b - 2)*(b + 1)/5
Let a(p) = 8*p**2 - 2*p. Let q(x) = 11*x - 19*x + 10*x - 4*x**2 - 3*x**2. Let c(n) = -5*a(n) - 6*q(n). Let c(w) = 0. Calculate w.
0, 1
Let q(n) be the second derivative of -57/20*n**5 + 0*n**2 - 3/14*n**7 - n**3 + 11/4*n**4 + 13/10*n**6 + 0 - 5*n. Find i such that q(i) = 0.
0, 1/3, 1, 2
Let 2/9*w - 2/9*w**2 + 0 = 0. Calculate w.
0, 1
Let d(f) be the third derivative of -169*f**5/330 + 26*f**4/33 - 16*f**3/33 + 10*f**2. Factor d(i).
-2*(13*i - 4)**2/11
Let q be 1 - 1 - (-6)/4. Let g = 70 + -70. Suppose 3/2*t**4 + 3/2*t**5 + g*t + 0 - 3/2*t**3 - q*t**2 = 0. What is t?
-1, 0, 1
Let l(p) = -2*p**2 + 6*p + 2. Let f(z) = z**3 - 8*z**2 + 25*z + 9. Let q(k) = 4*f(k) - 18*l(k). Solve q(h) = 0 for h.
-2, 0, 1
Let f = -26 - -57. Suppose -3*x - f = -4*x. Determine a, given that -20*a**5 + 5*a**3 + 18*a - 33*a**4 - 3*a + x*a**2 + 2 + 0 = 0.
-1, -2/5, -1/4, 1
Let u(h) be the first derivative of -2*h**4/19 - 6*h**3/19 - 6*h**2/19 - 2*h/19 + 19. Solve u(f) = 0.
-1, -1/4
Determine v, given that 6*v**4 - 597*v**5 + 3*v**4 + 600*v**5 + 9*v**3 + 3*v**2 = 0.
-1, 0
Let z be 14*(-11)/((-462)/4). Factor -1 - 1/3*p**2 - z*p.
-(p + 1)*(p + 3)/3
Let n(q) = 7*q**2 - 3*q + 8. Let p(f) = -6*f**2