*x = 0.
1
Let t = 1069/72 - 117/8. Let -2/9*m**2 + 0 + t*m = 0. What is m?
0, 1
Let p(k) be the second derivative of -k**6/40 + 3*k**5/40 + 5*k**4/16 - 3*k**3/4 - 37*k. Factor p(n).
-3*n*(n - 3)*(n - 1)*(n + 2)/4
Let v be 1/(-2) + (-9)/(-18). Let p be (-1)/(-15) - 2/(-6). Factor 0 - p*b**5 + 0*b + 0*b**2 + v*b**3 - 2/5*b**4.
-2*b**4*(b + 1)/5
Let a(t) be the second derivative of t**4/32 - 3*t**2/16 - t + 21. Factor a(o).
3*(o - 1)*(o + 1)/8
Let w(l) be the second derivative of l**7/3360 - l**6/480 + l**5/160 - l**4/96 + l**3/3 - l. Let t(n) be the second derivative of w(n). Factor t(r).
(r - 1)**3/4
Let x = -1318 + 9248/7. What is z in -4/7 - x*z - 18/7*z**2 = 0?
-1, -2/9
Let y(k) = 36*k**3 + 21*k**2 - 36*k - 36. Let o(i) = 5*i**3 + 3*i**2 - 5*i - 5. Let u(f) = 15*o(f) - 2*y(f). Let u(s) = 0. Calculate s.
-1, 1
Let c(y) be the second derivative of -y**4/36 + 2*y**3/9 - 5*y. Solve c(g) = 0.
0, 4
Suppose 0*q + 25 = 5*q. Let x(b) be the third derivative of -7/27*b**4 + 0*b - 1/60*b**6 + 0 - 8/27*b**3 - 1/9*b**q + 2*b**2. Factor x(u).
-2*(u + 2)*(3*u + 2)**2/9
Let x be (-2 + 2 + 0)/2. Suppose -a - 3*a + 16 = x. Let 2*o**3 + o**4 + 3*o**a - 2*o**4 = 0. What is o?
-1, 0
Let x = -12 + -1. Let h = x - -13. Solve h + 2/3*f**3 - 4/3*f - 2/3*f**2 = 0.
-1, 0, 2
Let n(i) = 3*i**5 - 9*i**3. Let z(m) = -3*m**5 + 10*m**3 + m. Let d(g) = -4*n(g) - 3*z(g). Factor d(v).
-3*v*(v - 1)**2*(v + 1)**2
Let n(s) be the first derivative of -s**6/720 - s**5/60 - s**4/12 + 2*s**3 + 2. Let b(k) be the third derivative of n(k). What is d in b(d) = 0?
-2
Factor 135/7*m**2 + 6/7 - 81/7*m**4 - 51/7*m - 81/7*m**3.
-3*(m + 2)*(3*m - 1)**3/7
Let i = -112/25 - -12101/2700. Let l(d) be the third derivative of -1/108*d**4 - 1/27*d**3 + 0*d + 2*d**2 + 1/270*d**5 + i*d**6 + 0. Factor l(a).
2*(a - 1)*(a + 1)**2/9
Factor -16/3*a**4 + 0*a**2 + 0 - 4/3*a**5 + 0*a**3 + 0*a.
-4*a**4*(a + 4)/3
Let v be 2 + -5 + 3 - 3/(-1). Let z(k) be the second derivative of 1/3*k**v + 1/10*k**6 - 7/20*k**5 + 0*k**2 + 5/42*k**7 + k - 1/4*k**4 + 0. Factor z(y).
y*(y - 1)*(y + 1)**2*(5*y - 2)
Let n(c) = -3*c**2 - 19*c - 12. Let v(p) = -3*p**2 - 18*p - 12. Let q(m) = 6*n(m) - 7*v(m). Factor q(o).
3*(o + 2)**2
Let c(h) be the first derivative of -1 - 1/12*h**3 + 0*h - 1/4*h**2. Factor c(y).
-y*(y + 2)/4
Let h(k) be the first derivative of -1 + 0*k**2 + 1/12*k**4 + k - 1/6*k**3. Let q(r) be the first derivative of h(r). Find i, given that q(i) = 0.
0, 1
Suppose -4*v = 4*c - 24, -4*c + 12 = -4. Let n be (-4)/3 + 78/135*3. Suppose -n*i + 0 + 2/5*i**v = 0. What is i?
0, 1
Let n = -101 - -304/3. What is g in -1/3*g + 1/3*g**3 + 0 - 1/3*g**4 + n*g**2 = 0?
-1, 0, 1
Let s(p) be the first derivative of p**2/2 + 7*p + 13. Let v be s(-5). Factor 6/5*j**v - 6/5*j + 2/5 - 2/5*j**3.
-2*(j - 1)**3/5
Factor -1 + 5/4*p - 1/4*p**2.
-(p - 4)*(p - 1)/4
Let w(y) be the second derivative of -3*y**5/140 + y**4/14 - y**3/14 + 5*y. Factor w(d).
-3*d*(d - 1)**2/7
Let i(u) be the first derivative of -4*u**5/5 - 3*u**4 + 8*u**2 - 12. What is r in i(r) = 0?
-2, 0, 1
Let h be (-1 - 2) + 3 + 0. Suppose 12 = 4*f - h*f. Factor 2/5*w + 2/5*w**2 - 2/5 - 2/5*w**f.
-2*(w - 1)**2*(w + 1)/5
Let j(c) = -c**5 + c**4 + c**3 - c**2 + c - 1. Let u be (6 - 7)/((-1)/3). Let d(r) = -r**4 + 2*r**3 - r**2 + 3*r - 3. Let f(o) = u*j(o) - d(o). Factor f(m).
-m**2*(m - 1)**2*(3*m + 2)
Suppose 5*o = 2 + 18. Factor 2*t**2 + t**o + 2 - 2*t**4 - 3.
-(t - 1)**2*(t + 1)**2
Let v(g) be the third derivative of g**7/105 - g**6/10 + 3*g**5/10 - 15*g**2. Determine k, given that v(k) = 0.
0, 3
Factor -2/19*l**3 + 0 + 0*l + 6/19*l**2.
-2*l**2*(l - 3)/19
Let x(r) = -9*r**3 - 14*r**2 + 5*r + 14. Let a(z) = 19*z**3 + 29*z**2 - 10*z - 29. Let c(m) = -4*a(m) - 9*x(m). Suppose c(i) = 0. What is i?
-2, -1, 1
Let w be (-83)/84 + (2 - -2) + -3. Let s(p) be the third derivative of 1/105*p**7 + w*p**6 + 0 + 0*p**4 - 1/105*p**5 - 2*p**2 + 0*p**3 + 0*p. Solve s(v) = 0.
-1, 0, 2/7
Find k such that -k + 1/2 - 1/2*k**4 + 0*k**2 + k**3 = 0.
-1, 1
Let l(g) = g**2 + 2*g + 2. Let j(p) = -p**2 - 3*p - 3. Let s = -3 - -1. Let r(q) = s*j(q) - 3*l(q). Suppose r(i) = 0. Calculate i.
0
Let r be (-171)/(-105) + (-27)/63. Factor 4/5 + r*t + 2/5*t**2.
2*(t + 1)*(t + 2)/5
Factor -2*i**4 + 0*i**5 + 10*i**3 - i**5 - 9*i**3 + 2*i**2 + 0*i**4.
-i**2*(i - 1)*(i + 1)*(i + 2)
Suppose -h + 1/3*h**3 + 2/3 + 0*h**2 = 0. What is h?
-2, 1
Suppose 8 = 4*g - 0*g. Let l(y) be the first derivative of 0*y**g + 2/25*y**5 + 0*y + 2/15*y**3 + 3 - 1/5*y**4. Find f such that l(f) = 0.
0, 1
Solve 4/5*s**4 + 4/5 + 0*s**3 - 8/5*s**2 + 0*s = 0 for s.
-1, 1
Let d(p) be the first derivative of 4*p**5/5 - p**4 + 2. Solve d(r) = 0.
0, 1
Let l(p) be the third derivative of 2*p**2 + 1/480*p**6 + 0 + 1/24*p**3 + 0*p - 1/96*p**4 - 1/240*p**5. What is i in l(i) = 0?
-1, 1
Let t(j) = 5*j**2 - 3*j. Let o(p) = p**2 - p. Let s(d) = 4*o(d) - 2*t(d). Factor s(q).
-2*q*(3*q - 1)
Let x = -89 - -91. Factor -1/7*t**x + 3/7*t - 2/7.
-(t - 2)*(t - 1)/7
Let q(b) = -b**2 + b. Let u(o) = 4*o**3 - 6*o**3 - 3*o**2 + o**3. Let d(t) = 4*q(t) - 4*u(t). Factor d(a).
4*a*(a + 1)**2
Let i(c) be the second derivative of -c**7/42 - c**6/6 - 7*c**5/20 - c**4/4 - 17*c. Factor i(t).
-t**2*(t + 1)**2*(t + 3)
Suppose 5*h - 41 = -4*n, 2*h + h + 6 = n. Let u be ((-5)/15)/(n/(-12)). Factor -2/9*s**2 + 0 - u*s**5 + 0*s + 0*s**3 + 2/3*s**4.
-2*s**2*(s - 1)**2*(2*s + 1)/9
Let q be (1/3)/(24/18). Let g(k) be the first derivative of -4 - 1/6*k**3 - q*k**2 + 0*k. Suppose g(p) = 0. What is p?
-1, 0
Solve h**3 - h + h**3 - h - 7*h**4 + 6*h**4 + h**2 = 0 for h.
-1, 0, 1, 2
Let w be 10/(-12)*4 - 16/(-4). Factor -1/2*o**3 - 1/3 + 1/6*o + w*o**2.
-(o - 1)**2*(3*o + 2)/6
Let y be ((-294)/(-49))/(13/2 + -2). Factor -y*k**2 - 16/3*k**3 + 4/3 + 16/3*k.
-4*(k - 1)*(k + 1)*(4*k + 1)/3
Let k(l) be the third derivative of l**6/180 + l**5/60 - l**4/6 + l**3/2 - 6*l**2. Let d(a) be the first derivative of k(a). Factor d(n).
2*(n - 1)*(n + 2)
Factor -2/9*w**2 + 2/9*w**5 + 2/3*w**3 - 2/3*w**4 + 0 + 0*w.
2*w**2*(w - 1)**3/9
Solve -408*h**4 - 72*h**2 + 156*h**4 + 318*h**3 + 8*h - 100*h**3 + 98*h**5 = 0 for h.
0, 2/7, 1
Let u(t) = t**2 - t + 1. Let w(z) = -3*z**2 + 3*z - 5. Let m(v) = 3*v**2 - 3*v + 5. Let n(g) = -6*m(g) - 7*w(g). Let j(y) = -n(y) + 5*u(y). Factor j(p).
2*p*(p - 1)
Find z such that 2/15*z**2 + 2/15*z - 4/5 = 0.
-3, 2
Let o(d) be the second derivative of -d**7/168 + d**6/60 - d**5/80 + d. What is a in o(a) = 0?
0, 1
Let l(z) be the third derivative of z**5/75 - 4*z**4/15 + 32*z**3/15 + 9*z**2. Solve l(a) = 0 for a.
4
Let t = 809/2 + -404. Factor 1/4 + 1/4*n**2 + t*n.
(n + 1)**2/4
Let d(r) be the second derivative of -r**5/5 + r**4 - 2*r**3 + 2*r**2 - 6*r. Determine h, given that d(h) = 0.
1
Let b(w) be the third derivative of w**9/241920 + w**8/40320 - w**7/20160 - w**6/1440 + w**5/30 - 6*w**2. Let t(o) be the third derivative of b(o). Factor t(r).
(r - 1)*(r + 1)*(r + 2)/4
Suppose 2*x + 0 - 8 = 0. Let 0*d + 1/4*d**x - 1/4*d**2 + 0*d**3 + 0 = 0. Calculate d.
-1, 0, 1
Let o be 0/(-2) + -1 - -27. Suppose -5*m + o = 1. Factor -3*h**3 + 3*h**m - 2*h**5 + 2*h**3.
h**3*(h - 1)*(h + 1)
Let l(b) be the first derivative of b**4/2 + 8*b**3/3 - 5*b**2 - 12. Solve l(n) = 0.
-5, 0, 1
Let m be (-6)/((-3)/(-6) - 2). Suppose g - 4*l - 6 = -l, 0 = -m*g + 4*l + 8. What is y in -3*y**2 + g*y - 4*y - 2 + y**2 = 0?
-1
Let n(t) be the second derivative of -t**4/6 + t**3 - 2*t**2 - 27*t. Factor n(r).
-2*(r - 2)*(r - 1)
Let x(f) be the second derivative of f**7/5 + 8*f**6/75 - 11*f**5/50 + f**4/15 + f. Determine g, given that x(g) = 0.
-1, 0, 2/7, 1/3
Let h be (-91)/(-196) + 5/(70/4). Solve -3/4 + 3/2*j - h*j**2 = 0.
1
Suppose 4*w - 5 - 3 = 0. Suppose 10*b**w + 0*b**3 + 0 - 1 + 4*b**3 + 2*b - 3 = 0. What is b?
-2, -1, 1/2
Let g be 24/9*(-9)/(-6). Find l, given that -9*l - 2*l**5 + 6*l**2 + 9*l**3 - 3*l**3 + 4 + 5*l**5 - 1 - 9*l**g = 0.
-1, 1
Let h(j) = 7*j + 19. Let a be h(-2). Solve 0 + 1/2*s + s**4 - 1/2*s**a - s**2 + 0*s**3 = 0 for s.
-1, 0, 1
Let t be (5 - 4)/(2/8). Factor 2*f**t + 55*f + 2*f**3 - 55*f.
2*f**3*(f + 1)
Let n(h) be the first derivative of -4*h**5/5 + h**4 + 8*h**3/3 - 7. Solve n(g) = 0.
-1, 0, 2
Let h(j) = -8*j**5 + 44*j**4 + 8*j**3 - 8*j**2 - 12*j + 12. Let f(t) = t**5 + t**4 + t**