((-6)/16)/((-3)/2). Suppose g - 4*l + 9*l = 27, 0 = 4*g - l - 3. Factor -t - j**g + 5/4*j.
-(j - 1)*(4*j - 1)/4
Let n(t) be the second derivative of -t**7/294 - t**6/105 + 3*t**5/140 + t**4/21 - 2*t**3/21 + 7*t. Let n(i) = 0. What is i?
-2, 0, 1
Let g(s) be the third derivative of -s**6/720 + 13*s**5/360 - s**4/3 + s**3 + 2*s**2. Determine m, given that g(m) = 0.
1, 6
Let l be 2/(-8) + (-95)/20. Let i be (-22)/(-5) - (-2)/l. Factor -v**5 + 5*v**4 + 2*v**4 - 8*v**i.
-v**4*(v + 1)
Let q(g) be the third derivative of -g**8/26880 + g**7/10080 - g**4/8 + g**2. Let s(c) be the second derivative of q(c). Factor s(d).
-d**2*(d - 1)/4
Let a(d) be the first derivative of -2*d**5/65 + 2*d**4/13 - 10*d**3/39 + 2*d**2/13 + 17. Suppose a(h) = 0. What is h?
0, 1, 2
Let r be 3/((-1 - -4)/3). Solve -k**3 - r*k**4 + 9*k**5 - 10*k**5 + 5*k**4 = 0 for k.
0, 1
Let h(u) be the first derivative of u**6/27 - 4*u**5/45 + 4*u**3/27 - u**2/9 + 21. Suppose h(t) = 0. Calculate t.
-1, 0, 1
Let d(l) be the third derivative of l**6/320 + l**5/80 - 3*l**4/64 - l**2. Factor d(j).
3*j*(j - 1)*(j + 3)/8
Let t(k) be the third derivative of k**5/30 - k**4/4 - 5*k**2. Suppose t(a) = 0. Calculate a.
0, 3
Let g(z) = -z**3 + 3*z**2 - 1. Let o be g(3). Let b be 4/((o - -2)/1). Determine a so that b*a - 4*a + 2*a**2 - a**2 + a = 0.
-1, 0
Let v be (-63)/(-28) - (-3)/4. Find l such that -v*l - 3/4*l**2 - 3 = 0.
-2
Let a = 496/235 + -24/47. Factor a*h + 4/5 + 4/5*h**2.
4*(h + 1)**2/5
Let o be 1 + ((-6)/(-3) - 0). Factor -4*m**2 + 2*m + 6*m**2 - 3*m - m**o.
-m*(m - 1)**2
Let x = 4 + -4. Suppose 2*y - 4 = -x*y. Factor -h**2 - h**y - h**4 + 3*h**4.
2*h**2*(h - 1)*(h + 1)
Factor 24 + 12*b**2 + 0*b**4 + 21*b**3 - 36*b - 3*b**2 + 9*b**4 - 27*b**2.
3*(b - 1)*(b + 2)**2*(3*b - 2)
Suppose -3/7*f**3 - 3/7*f + 0 + 6/7*f**2 = 0. Calculate f.
0, 1
Suppose 0*i - 10 = -2*i. Let o(w) = -7*w**3 - 10*w**2 - 11*w - 8. Let c(p) = 6*p**3 + 9*p**2 + 10*p + 7. Let s(x) = i*o(x) + 6*c(x). Factor s(j).
(j + 1)**2*(j + 2)
Let m(i) = -i - 2. Let r be m(-2). Find f, given that r - 3*f - 4 + f**3 + 2 = 0.
-1, 2
Let w = 13 + -16. Let v = 0 - w. Let -2/7*x**4 - 2/7 - 8/7*x**v - 8/7*x - 12/7*x**2 = 0. What is x?
-1
Suppose -q = 4*f - 21, 5*f = q + 24 - 0. Let y be 4/(-22) + 48/22. Suppose 4*b**5 - 6*b**3 + 2*b**2 + 4*b**f - y*b**5 - 2*b**4 = 0. Calculate b.
-1, 0, 1/3, 1
Let g = 6 + -2. Let i(h) be the first derivative of 2 - 4/3*h**3 + 5/2*h**g - 5*h**2 + 4*h. Solve i(f) = 0.
-1, 2/5, 1
Let w = -509/6 + 85. Let g(v) be the second derivative of 0 + 2/3*v**3 + 0*v**2 + w*v**4 + 3*v. Solve g(n) = 0 for n.
-2, 0
What is i in -3*i**4 - 10*i**5 + i**5 - 12*i**4 - 6*i**3 = 0?
-1, -2/3, 0
Let l(q) be the third derivative of -q**6/210 + q**5/105 + 10*q**2. Solve l(r) = 0 for r.
0, 1
Suppose 2*p + 0*p - 2 = -2*h, 2*h + 10 = 4*p. Let g be h + 2 - (1 - 2). Factor 3*x - 3*x**3 + 0*x - g*x - x**4 + x**2 + 2*x**5.
x*(x - 1)**2*(x + 1)*(2*x + 1)
Factor 4/3*k + 0 + 1/6*k**3 - k**2.
k*(k - 4)*(k - 2)/6
Solve -5 - 33*r**3 + 72*r**3 + 0 - 65*r**2 - 20*r**4 + 30*r + 21*r**3 = 0.
1/2, 1
Let c(j) = -j**5 - j**4 + j**2 - j. Let n(g) = 6*g**5 - 2*g**4 - 4*g**3 + 8*g**2 + 6*g - 6. Let i(h) = 4*c(h) + n(h). Determine o, given that i(o) = 0.
-1, 1, 3
Let z = 108 - 108. What is t in 0*t + z - 3/2*t**3 + 3/2*t**2 = 0?
0, 1
Let y(b) = -b**3 - 4*b**2 - b. Let k be y(-5). Factor -h**2 + 6*h**3 + 2*h**4 - k*h**3 + 19*h**2 - 4*h + 8*h**4.
2*h*(h - 1)**2*(5*h - 2)
Let k(y) be the second derivative of -y + 0*y**4 - 1/56*y**7 + 0*y**2 + 0*y**3 + 0 + 1/120*y**6 + 1/40*y**5. Factor k(s).
-s**3*(s - 1)*(3*s + 2)/4
Let z = 2022/5 - 402. Find j, given that -z*j + 18/5 + 2/5*j**2 = 0.
3
Let w(c) be the first derivative of -3*c**4/2 - 8*c**3/3 - 7*c**2/2 + c - 1. Let r(n) = -1 + 0 - n**3 + 2. Let x(o) = -3*r(o) + w(o). What is s in x(s) = 0?
-1, -2/3
Suppose 4*q = 5*q + 2*u + 7, -3*u - 21 = -2*q. Factor 0 - 8/9*g**q - 4/9*g - 2*g**2.
-2*g*(g + 2)*(4*g + 1)/9
Let m be 12/(-9)*(-3)/2. Determine p, given that 3*p + 2*p + 0*p**2 + p**m - 4*p = 0.
-1, 0
Let s = 730993 + -373537249/511. Let z = s + -4/73. Let z*a**2 + 0*a - 2/7 = 0. Calculate a.
-1, 1
Let g = -322 + 324. Factor 1/2 - 3/2*m - 2*m**g.
-(m + 1)*(4*m - 1)/2
Suppose -2*w = 5*c - 2, -4*w = -4*c - 4 - 0. Let -4/13*z**2 + c*z**3 + 4/13*z**4 - 2/13*z**5 + 0 + 2/13*z = 0. Calculate z.
-1, 0, 1
Let -j**2 + 0 - 1/2*j**3 + 0*j = 0. What is j?
-2, 0
Determine s, given that 0*s**2 - 2/13*s**4 - 2/13*s**3 + 0 + 0*s = 0.
-1, 0
Let k be (-1)/(-3) - (-3)/18. Solve 0*b + 0*b**3 + 0 + k*b**2 - 3/2*b**4 - b**5 = 0 for b.
-1, 0, 1/2
Determine q so that -6*q**3 + 8*q**4 - 11*q**5 + q**4 + 8*q**5 = 0.
0, 1, 2
Let s(z) be the first derivative of z**6/120 - 3*z**2/2 + 1. Let q(v) be the second derivative of s(v). Factor q(i).
i**3
Let u be 9 + (45/25 - 10). Find r, given that 4/5*r**2 + 4/5*r**3 - 4/5 - u*r = 0.
-1, 1
Let w = -247 - -247. Factor 2/3 + w*i - 2/3*i**2.
-2*(i - 1)*(i + 1)/3
Let r(z) = -2*z + 1. Let g be r(-7). Let a = g + -15. Factor 2/5*t**2 + a + 0*t.
2*t**2/5
Let t(g) = -g**3 + 2*g**2 - 2*g + 1. Let o be ((5 + 3)*1)/2. Let u(f) = -f**3 + 2*f**2 - f. Let s(z) = o*t(z) - 6*u(z). Factor s(j).
2*(j - 2)*(j - 1)*(j + 1)
Let f(y) be the second derivative of y**7/1120 + y**3/6 + y. Let a(s) be the second derivative of f(s). Factor a(z).
3*z**3/4
Let q(t) be the third derivative of -t**5/135 + 7*t**4/27 - 98*t**3/27 - 16*t**2. What is g in q(g) = 0?
7
Let u = 71/195 - 2/65. Factor u - y + 2/3*y**2.
(y - 1)*(2*y - 1)/3
Factor 12 + 5*w**3 - 3*w**3 - 58*w + 0 + 60*w**2 - 16*w**3.
-2*(w - 3)*(w - 1)*(7*w - 2)
Let -2/5*s**5 - 4/5 + 2*s - 4/5*s**2 - 8/5*s**3 + 8/5*s**4 = 0. What is s?
-1, 1, 2
Let k(r) be the second derivative of -r**6/180 - r**5/30 - r**4/12 - r**3/9 - r**2 - 4*r. Let j(n) be the first derivative of k(n). Factor j(c).
-2*(c + 1)**3/3
Solve 3/4*y**2 - 3/4*y**3 - 3/4 + 3/4*y = 0.
-1, 1
Let n(l) = 5*l**2 - 3*l - 2. Let y(s) be the second derivative of 3*s**4 - 7*s**3/2 - 15*s**2/2 + 7*s. Let r(o) = -15*n(o) + 2*y(o). Solve r(k) = 0 for k.
0, 1
Let q(a) be the second derivative of -1/30*a**6 + 4*a + 0*a**5 + 1/6*a**4 - 1/2*a**2 + 0 + 0*a**3. Determine g so that q(g) = 0.
-1, 1
Let j be 6/8 + (-2645)/1804. Let l = -7/41 - j. What is n in l*n**2 + 0 + 2/11*n + 6/11*n**3 + 2/11*n**4 = 0?
-1, 0
Let q be (-4 + (-46)/(-12))*(-1 + -1). Let j(r) be the second derivative of 1/15*r**6 + 0*r**3 + 0 + 0*r**2 - q*r**4 - r + 1/10*r**5. Factor j(f).
2*f**2*(f - 1)*(f + 2)
Let g(o) be the third derivative of -o**7/1120 + o**6/480 - 2*o**3/3 + 3*o**2. Let t(l) be the first derivative of g(l). Factor t(b).
-3*b**2*(b - 1)/4
Suppose -96 = -72*w + 24*w. Factor 4/7*m**w + 2/7*m**3 + 2/7*m + 0.
2*m*(m + 1)**2/7
Factor 2*k**2 + 2*k - 4*k**2 + k**2 + 0*k**2.
-k*(k - 2)
Let o(y) be the third derivative of 0*y**4 + 0 - 2*y**2 + 0*y**3 + 0*y**5 + 0*y - 1/720*y**6. Factor o(q).
-q**3/6
Let q(n) be the second derivative of -n**4/12 - 7*n. Find u such that q(u) = 0.
0
Let j = 4291/4 + -1072. Solve 9/4*o**3 - 3/4*o**4 - 9/4*o**2 + j*o + 0 = 0 for o.
0, 1
Let z(p) = -5*p**5 - 10*p**4 - 5*p**3 - 5*p**2 - 5*p. Let x(w) = w**4 - w**3 - w**2 - w. Let f(o) = -5*x(o) + z(o). Solve f(c) = 0.
-3, 0
Suppose 7*y + 10 = 12*y, -5*q + 18 = 4*y. Let n(u) be the first derivative of 1 + 0*u - 1/10*u**4 + 2/5*u**q - 2/15*u**3. Let n(d) = 0. What is d?
-2, 0, 1
Let q(i) be the third derivative of i**7/1365 + i**6/390 - i**5/390 - i**4/78 - 3*i**2. Suppose q(h) = 0. Calculate h.
-2, -1, 0, 1
Let r be 0/(-2) - 2 - -4. Let y be (r/2)/(1/4). Factor -2/7*l**5 + 0*l**y + 0*l + 0 + 0*l**2 + 0*l**3.
-2*l**5/7
Let -1/8*j**3 + 0*j**2 + 1/2*j + 0 = 0. Calculate j.
-2, 0, 2
Let f(y) be the third derivative of y**5/100 + 7*y**4/60 - y**3/6 + 27*y**2. Let f(b) = 0. What is b?
-5, 1/3
Suppose -3*o = -2 - 4. Let l**2 + 3*l**2 + o*l**3 + 0*l**2 = 0. What is l?
-2, 0
Let x = -1/129 + 89/387. What is h in -x*h**4 - 4/9*h**3 + 0 + 2/9*h**2 + 4/9*h = 0?
-2, -1, 0, 1
Solve p + 1/6*p**2 + 0 = 0 for p.
-6, 0
Suppose 3*x + 12*x = 30. Let z(f) be the second derivative of 0 + 3*f - 1/120*f**5 + 1/36*f**3 + 1/12*f**x - 1/72*f**4. Solve z(c) = 0.
-1, 1
Let z(m) be the first derivative of -5*m**4/4 + 5*m**3/3 + 5*m**2/2 - 5*m + 3. Factor z(j).
-5*(j - 1)**2*(j + 1)
Suppose -5 = x + 5*v,