a. Factor -y*u**2 - 2/7 + 6/7*u.
-2*(u - 1)*(2*u - 1)/7
Factor 0*v - 1/5*v**3 + 0 + 2/5*v**2.
-v**2*(v - 2)/5
Let k be (-5)/(-6)*24/60. Let t**3 + 1/3*t**4 + 0 + k*t + t**2 = 0. What is t?
-1, 0
Let o(p) be the second derivative of -3/20*p**5 + 0 + 0*p**2 + 9*p + 0*p**3 - 1/2*p**4. Factor o(y).
-3*y**2*(y + 2)
Let d = -52 + 160/3. Factor 0*f + 2/3*f**3 + 0*f**2 + d*f**4 + 2/3*f**5 + 0.
2*f**3*(f + 1)**2/3
Let m(v) be the first derivative of -v**5/2 + v**4 - v**3/6 - v**2/2 - 2. Solve m(d) = 0 for d.
-2/5, 0, 1
Let f(r) be the second derivative of -r**5/90 + r**4/54 + r**3/27 - r**2/9 + 3*r. Solve f(g) = 0 for g.
-1, 1
Let -1/4*o**4 + o - 1/2*o**3 + 3/4*o**2 - 1 = 0. What is o?
-2, 1
Let k(d) = d + 9. Suppose 0*l + 3*l = z - 3, 0 = l + 3. Let r be k(z). Solve r + 3*f**2 - 8*f + 5 - f**2 = 0.
2
Let -24*y**3 + 12*y**2 + 21/2*y + 3/2 = 0. What is y?
-1/4, 1
Let v be 16/(-12)*6/(-4). Let d be (-5)/(-2) + (-18 - -17). Solve -1/2*i - d*i**v + 1 = 0 for i.
-1, 2/3
Let j(k) = k**4 - 19*k**3 + 7*k**2 + 24*k - 13. Let x(d) = -d**4 + 10*d**3 - 4*d**2 - 12*d + 7. Let c(b) = -2*j(b) - 5*x(b). Let c(y) = 0. What is y?
-1, 1, 3
Let o(a) be the second derivative of -a**6/15 + 3*a**5/5 - 3*a**4/2 - 4*a**3/3 + 12*a**2 + 26*a - 2. Suppose o(p) = 0. What is p?
-1, 2, 3
Suppose 7*y**2 - 3 - 7*y**2 - 9*y**2 + 3*y**3 + 9*y = 0. What is y?
1
Let s(h) be the third derivative of h**5/420 - 2*h**3/21 - 14*h**2. Find p such that s(p) = 0.
-2, 2
Suppose 3*p - 16 = -p. What is a in a**2 + 0 + 2 - 3*a**2 - 4*a - p = 0?
-1
Let t(w) = -4 + w**2 - 1 + 3*w + w**2. Let b be t(-6). Determine d so that -18*d**2 + 17*d**2 + 4 + 27*d**2 - 28*d**3 - b*d**4 + 19*d**2 + 28*d = 0.
-1, -2/7, 1
Let c(d) = 2*d + 2 + 5*d - 3. Let r be c(1). Let -6*l**4 + r*l**5 - l**3 + 0*l - 15*l**5 + 0*l = 0. Calculate l.
-1/3, 0
Suppose -5*h = 2*m + 18, 6*m - m = h - 18. Let z(s) = s**3 + 3*s**2 + 2*s + 2. Let d be z(h). Find i such that -2*i + 4*i**2 + 0*i - 3*i**d = 0.
0, 2
Suppose 4*d + b = 117, 5*d - 35 - 110 = -b. Let w be 9/(-15) - d/(-30). Let -2/3*n**3 - w + 2/3*n + 1/3*n**4 + 0*n**2 = 0. What is n?
-1, 1
Let k(g) = -29 + 5 + 2*g - 9. Let o be k(19). Factor 0*b**4 - 1/2*b**o + 0 + 1/2*b**3 + 0*b + 0*b**2.
-b**3*(b - 1)*(b + 1)/2
Solve -8/11 + 0*d - 6/11*d**3 + 14/11*d**2 = 0.
-2/3, 1, 2
Let f(y) be the second derivative of -5*y**7/42 + y**6/6 + 3*y**5/4 - 25*y**4/12 + 5*y**3/3 - 20*y. Factor f(r).
-5*r*(r - 1)**3*(r + 2)
Let g = 124 + -122. Find d, given that 0 + 0*d + 3/4*d**3 + 0*d**g = 0.
0
Suppose -3*v + 4*w - 7 = 0, -v = w - 4 - 3. Let g(u) be the second derivative of 1/20*u**5 + 0*u**2 + 0 + 1/6*u**4 + u + 1/6*u**v. Factor g(x).
x*(x + 1)**2
Let h be -2 + 2 - (-4 - -2). Factor 0 - 2/3*q + 8/3*q**h.
2*q*(4*q - 1)/3
Suppose -38 = 3*c + 46. Let n be (-10)/(-24) - 7/c. What is w in -w**5 + 0*w + 1/3*w**4 + 0 + 0*w**2 + n*w**3 = 0?
-2/3, 0, 1
Let 3/2*a**2 + 3/2 - a**3 + 4*a = 0. Calculate a.
-1, -1/2, 3
Let t(h) be the second derivative of -5*h + 0 + 1/48*h**4 - 3/8*h**2 + 1/12*h**3. Factor t(y).
(y - 1)*(y + 3)/4
Let w(l) be the second derivative of -l**10/136080 + l**9/22680 - l**8/15120 - l**4/4 - 3*l. Let y(u) be the third derivative of w(u). Solve y(q) = 0 for q.
0, 1, 2
Let u(b) be the third derivative of -b**7/5040 + b**6/240 - 3*b**5/80 - b**4/12 + 4*b**2. Let j(f) be the second derivative of u(f). Solve j(k) = 0.
3
Let s be (-28 + 4)/(-4)*75/20. Determine t, given that 12*t + 25/2*t**3 + 2 + s*t**2 = 0.
-1, -2/5
Let u be -24*(2/(-4))/1. Let r be 6/u + (-3)/(-2). Solve -2/5*l + 0 - 4/5*l**3 + l**r + 1/5*l**4 = 0.
0, 1, 2
Let n(t) be the second derivative of -t**4/42 + t**3/21 + 15*t. Suppose n(l) = 0. Calculate l.
0, 1
Let d(h) = h**2 + 3*h + 5. Let i be d(-4). Let x be i/6 + 5/10. Solve -x - 1/2*z**2 + 2*z = 0 for z.
2
Let w = -10 - -14. Let o = w - 2. Let 2*g - 2*g**3 + 1 - 3 + 4*g**o - 1 - 1 = 0. Calculate g.
-1, 1, 2
Let b(c) be the third derivative of c**10/453600 - c**9/181440 - c**5/30 - 2*c**2. Let a(t) be the third derivative of b(t). Suppose a(w) = 0. What is w?
0, 1
Let q(z) be the second derivative of z**5/120 + z**4/24 + z**3/12 - 3*z**2/2 + z. Let m(o) be the first derivative of q(o). Let m(p) = 0. Calculate p.
-1
Let q(c) be the second derivative of c**4/4 + 6*c**3 + 54*c**2 - 23*c. Find x such that q(x) = 0.
-6
Suppose i = 2*x + 11, -2*i + 3*x = -6*i. Suppose 1 + i = o. Factor 2*r**o - r**5 - 2*r**2 - 3*r + 4*r + 2*r**3 - 2*r**3.
-r*(r - 1)**3*(r + 1)
Let g(n) be the first derivative of -n**4 + 4*n**3 - 4*n**2 - 63. Factor g(h).
-4*h*(h - 2)*(h - 1)
Let c be 12/(-27)*(3 + (-45)/12). Let w be (-7)/(-39) + (-8)/(-52). Find s, given that -c*s**2 + 0 + w*s**3 + 1/3*s**4 - 1/3*s = 0.
-1, 0, 1
Suppose 482*a - 15 = 477*a. Factor 0*v + 3*v**2 + 9/2*v**a + 3/2*v**4 + 0.
3*v**2*(v + 1)*(v + 2)/2
Let d(w) be the first derivative of 3*w**4/16 - 7*w**3/4 + 45*w**2/8 - 27*w/4 + 4. Solve d(r) = 0.
1, 3
Let m(z) be the third derivative of -z**7/84 + z**6/48 + z**5/8 - 5*z**4/48 - 5*z**3/6 - 17*z**2. Solve m(b) = 0 for b.
-1, 1, 2
Let w(i) be the second derivative of i**8/6720 - i**7/1260 - i**4/2 + 8*i. Let q(c) be the third derivative of w(c). Solve q(k) = 0 for k.
0, 2
Let b(m) = m**3 - 11*m**2 + 28*m + 14. Let j be b(6). Let 1/3*h**3 + 0 - 1/3*h + 1/3*h**j - 1/3*h**4 = 0. What is h?
-1, 0, 1
Suppose -2*g - 30 = 5*m, m + g + 24 = -3*g. Let p be (-10)/m*(-4)/(-7). Factor 18/7*u**3 + 0*u + p*u**5 + 0 - 24/7*u**4 - 4/7*u**2.
2*u**2*(u - 1)**2*(5*u - 2)/7
Suppose 3*b - m - 2*m = -6, -3*b + 2*m = 2. Factor -3/4*u**5 + 0 + b*u**4 + 1/2*u**2 + 0*u - 7/4*u**3.
-u**2*(u - 1)**2*(3*u - 2)/4
Let m(c) be the first derivative of -c**4/6 + 14*c**3/9 - 8*c**2/3 - 32*c/3 - 46. Determine a, given that m(a) = 0.
-1, 4
Let r be (-24)/(-36) - (-26)/6. Determine g so that 1/2*g**3 - 1/4 - 3/4*g - 1/2*g**2 + 1/4*g**r + 3/4*g**4 = 0.
-1, 1
Let z(w) be the second derivative of -w**5/50 + w**3/15 + 8*w. Determine y so that z(y) = 0.
-1, 0, 1
Let o(g) be the third derivative of 8*g**8/105 + 16*g**7/175 + g**6/25 + g**5/150 + 8*g**2. Factor o(l).
2*l**2*(4*l + 1)**3/5
Let r(p) be the third derivative of -p**8/112 - p**7/35 - p**6/40 + 12*p**2. Let r(c) = 0. What is c?
-1, 0
Let q(o) be the third derivative of -2*o**2 - 1/6*o**3 - 1/60*o**5 - 1/12*o**4 + 0*o + 0. Find d such that q(d) = 0.
-1
Let h = -54 - -56. Find p such that -1/4*p + 0 + 1/2*p**h - 1/4*p**3 = 0.
0, 1
Factor 2/9*b**3 - 2/9*b**5 + 0*b + 0*b**2 + 0 + 0*b**4.
-2*b**3*(b - 1)*(b + 1)/9
Let z(r) be the second derivative of 0 - 2*r**2 - 1/48*r**4 + 1/3*r**3 + 2*r. Factor z(h).
-(h - 4)**2/4
Let t(o) = -2*o - 14. Let k be t(-10). Let b = -3 + k. Factor 4/7*w**2 + 0 - 2/7*w**b - 2/7*w.
-2*w*(w - 1)**2/7
Let u(s) be the second derivative of -s**6/360 + s**5/60 - s**4/24 + s**3/6 - 4*s. Let v(f) be the second derivative of u(f). Factor v(j).
-(j - 1)**2
Let v(i) be the second derivative of -i**5/180 + i**4/24 - i**3/9 + 7*i**2/2 + 5*i. Let j(r) be the first derivative of v(r). Factor j(g).
-(g - 2)*(g - 1)/3
Let m(z) be the third derivative of z**8/5880 - z**6/1260 - z**3/3 - z**2. Let x(i) be the first derivative of m(i). Factor x(g).
2*g**2*(g - 1)*(g + 1)/7
Solve 32/3*g + 4/3*g**2 + 64/3 = 0 for g.
-4
Let i be -1 - 2/3*33/(-22). Let c(g) be the third derivative of 0*g**6 + 0*g**5 + 2*g**2 + i*g**3 + 1/70*g**7 + 0*g + 0*g**4 + 0. Factor c(p).
3*p**4
Let u = 14 - 11. Let i be (-9)/u*(-1)/9. Determine z, given that -i*z**2 + 4/3*z - 4/3 = 0.
2
Suppose 3*t + 6 = -0*t, -5*t - 16 = -3*q. Find x, given that -4/3 - 2/3*x**3 + 4/3*x**q + 2/3*x = 0.
-1, 1, 2
Suppose 3*u - 1 = -5*r, r = u - 4 + 1. Let t be r/3*2/(-1). Factor 4/3*s**2 + 2/3*s + 0 + t*s**3.
2*s*(s + 1)**2/3
Let f(s) be the first derivative of -s**7/105 - s**6/30 - 2*s**2 - 2. Let p(o) be the second derivative of f(o). Suppose p(m) = 0. Calculate m.
-2, 0
Let m(o) be the first derivative of o**5/60 - o**4/18 + o**3/18 + 8*o + 4. Let l(v) be the first derivative of m(v). Factor l(b).
b*(b - 1)**2/3
Let r(i) be the third derivative of i**6/24 - i**5/4 + 5*i**4/8 - 5*i**3/6 + 17*i**2. Factor r(n).
5*(n - 1)**3
Let n = 0 + 3. Suppose -3*h - 5*k + 6 = 0, 5*h = -n*k + 5*k + 10. Find f such that -1 - h*f**5 - 3 + 4*f**3 - 2*f**2 + f**4 + 5 - 2*f = 0.
-1, 1/2, 1
Let y(b) be the second derivative of -b*