t + 1)**3
Factor -7*u**3 - 5*u**3 + 90*u**2 - 4*u - 51*u**2 - 51*u**2 - 4*u**4.
-4*u*(u + 1)**3
Let r be (12/(-18))/(2/(-12)). Suppose -k - 18 = -5*z, -k - 2 = -r. Find m such that -2*m**3 - 4*m + 3*m**2 - 2*m**2 + z*m = 0.
0, 1/2
Let c(s) = 1. Let t be 10 + 2 + -1*2. Suppose -3*g + t = -4*u + 44, 5*g + 34 = u. Let l(a) = a**3 + a**2 - a + 5. Let r(j) = g*c(j) + l(j). Factor r(f).
(f - 1)*(f + 1)**2
Let s(k) = -k**2 + 8*k + 20. Let i be s(10). Let j(y) be the second derivative of -2*y + i - 4/15*y**5 - 2/9*y**3 - 7/18*y**4 - 1/15*y**6 + 0*y**2. Factor j(g).
-2*g*(g + 1)**2*(3*g + 2)/3
Suppose 3*f - 22 = -0*f + 5*d, 5*f - 4*d - 28 = 0. Factor 1 + 1 + 0*m**f + 5*m**3 - 2*m**5 - 2*m - 4*m**2 + 2*m**4 - m**3.
-2*(m - 1)**3*(m + 1)**2
Let n = 63 - 61. Let h(s) be the first derivative of -8/15*s**3 + 1/15*s**6 + 3 + 3/5*s**4 + 1/5*s**n + 0*s - 8/25*s**5. Suppose h(c) = 0. What is c?
0, 1
Let y(o) be the first derivative of o**5/80 - 5*o**4/48 + o**3/3 - o**2/2 - o + 2. Let g(l) be the first derivative of y(l). Let g(x) = 0. What is x?
1, 2
Suppose s - 3*s - 16 = -4*z, -4*s = -z + 18. Let k be 12 + -9 - (0 + 3). Suppose -2/5 + 2/5*o**z + k*o = 0. Calculate o.
-1, 1
Factor 0 + 0*k - 2*k**4 - 4/3*k**3 + 2/3*k**2.
-2*k**2*(k + 1)*(3*k - 1)/3
Let f(h) be the first derivative of h**3/9 - h**2 + 14. Solve f(c) = 0.
0, 6
Suppose 0*r + 9 = -r. Let a be ((-3)/(-5))/(r/(-45)). Factor 0*p - 1/3*p**a + 0*p**2 + 0.
-p**3/3
Let l(j) be the third derivative of -j**6/480 + j**4/32 - j**3/12 - 5*j**2. Factor l(z).
-(z - 1)**2*(z + 2)/4
Let x(w) be the first derivative of 4*w**3/3 + 3*w**2 + 2*w + 2. Determine t so that x(t) = 0.
-1, -1/2
Let s be (9/(-2))/((-14)/4). Factor -5/7*d**2 - 9/7*d**3 + s*d - 2/7 + d**4.
(d - 1)**2*(d + 1)*(7*d - 2)/7
Let y(g) be the second derivative of -g**5/30 - g**4/6 - g**3/3 - g**2/2 - g. Let m(p) be the first derivative of y(p). Find k, given that m(k) = 0.
-1
Let o(a) be the second derivative of a**9/7560 - a**8/1680 + a**7/1260 + a**4/4 + 2*a. Let j(t) be the third derivative of o(t). Let j(m) = 0. Calculate m.
0, 1
Solve -3*j**2 - 3/2 + 15/4*j + 3/4*j**3 = 0 for j.
1, 2
Let n(a) = a**5 - a**4 - a**3 - a. Let l(p) = 2*p**5 - 4*p**4 - 2*p**3 + p**2 - 3*p. Let m(f) = 5*l(f) - 15*n(f). Let m(s) = 0. Calculate s.
-1, 0, 1
Let n be 693/330 - 2/20. Factor 0*l**4 + 0 - 1/3*l**3 + 0*l**n + 1/6*l**5 + 1/6*l.
l*(l - 1)**2*(l + 1)**2/6
Let s be ((-57)/(-12))/((-9)/4) + 3. What is j in 2/9*j**3 + 0*j - 2/3*j**2 + s = 0?
-1, 2
Let m(d) be the third derivative of 0*d**5 + 0 - 2*d**2 + 1/540*d**6 + 0*d**4 + 0*d - 1/945*d**7 + 0*d**3. Factor m(s).
-2*s**3*(s - 1)/9
Let j = 329/129 + 5/43. Factor 8/3*c - j - 2/3*c**2.
-2*(c - 2)**2/3
Let d(w) be the second derivative of -w**4/24 - w**3/2 - 9*w**2/4 + 15*w. Factor d(x).
-(x + 3)**2/2
Let x(p) be the second derivative of -2*p + 1/105*p**6 - 1/35*p**5 - 1/7*p**2 + 0*p**4 + 2/21*p**3 + 0. Suppose x(d) = 0. Calculate d.
-1, 1
Let m(w) = -20*w**4 - 19*w**3 + 9*w**2 + 8*w - 13. Let q(s) = -10*s**4 - 10*s**3 + 4*s**2 + 4*s - 6. Let b(a) = 6*m(a) - 13*q(a). Solve b(d) = 0 for d.
-1, 0, 2/5
Let m = -87 - -175/2. Let i be 5/18 + 4/18. What is h in i*h**2 + 1/4*h**5 + m*h**3 - 3/4*h**4 - 3/4*h + 1/4 = 0?
-1, 1
Let c(k) be the first derivative of -5*k**3/3 + 20*k**2 - 80*k + 12. Let c(q) = 0. What is q?
4
Determine k, given that -2*k**5 - k**3 - k**5 + 4*k**5 = 0.
-1, 0, 1
Let d(u) be the first derivative of 6*u**5/35 + 5*u**4/42 - 2*u**3/7 + u**2/7 - 4*u - 2. Let i(b) be the first derivative of d(b). What is v in i(v) = 0?
-1, 1/4, 1/3
Find c, given that -10*c - 3*c**2 - 2*c**2 + 0*c**2 = 0.
-2, 0
Let x be (7/42)/(5/4 - 1). Let a(h) be the first derivative of 2/3*h + 4 + 2/9*h**3 + x*h**2. Factor a(o).
2*(o + 1)**2/3
Let i be -3*(-2)/(-6)*-4. Suppose 0 = -3*q + 6. Factor 0 - 3/2*z**3 + 1/2*z**i - 1/2*z + 3/2*z**q.
z*(z - 1)**3/2
Let z = -1807 + 9004/5. Let j = 7 + z. Determine a so that -j*a**3 - 2/5*a**4 + 0*a**2 + 2/5 + 4/5*a = 0.
-1, 1
Let b be 1*(-1)/((-8)/82). Let f = b + -197/20. Determine v so that 0 + 0*v + 6/5*v**4 - 2/5*v**5 + f*v**2 - 6/5*v**3 = 0.
0, 1
Let w(t) be the third derivative of -t**5/12 - 5*t**4/24 + 5*t**3/3 - 14*t**2. Factor w(z).
-5*(z - 1)*(z + 2)
Let h(r) be the second derivative of -r**5/240 + 3*r**2/2 - r. Let q(s) be the first derivative of h(s). Factor q(x).
-x**2/4
Let l(h) = h**2 + 5*h - 7. Let a be l(-8). Suppose -2 = 5*w - a. Factor 3*j - 2*j**w + j**4 - j + 1 - 2*j**4.
-(j - 1)*(j + 1)**3
Let f be (-4)/(-6)*105/(-10). Let l be 1/(-1)*(3 + f). Factor 0 + 0*k + 0*k**3 + 0*k**2 + 2/5*k**l.
2*k**4/5
Let y(o) = 30*o**2 - 180*o + 150. Let z(x) = 5*x**2 - 30*x + 25. Let j(b) = 4*y(b) - 25*z(b). Let j(r) = 0. What is r?
1, 5
Let c(q) be the third derivative of 0 + 0*q**3 - 1/12*q**4 + 1/60*q**5 - 1/210*q**7 + 1/60*q**6 - q**2 + 0*q. What is u in c(u) = 0?
-1, 0, 1, 2
Let k(s) be the third derivative of -4*s**2 + 7/80*s**5 + 0*s**3 + 1/16*s**4 + 0 + 0*s. Suppose k(y) = 0. Calculate y.
-2/7, 0
Let k(n) be the third derivative of -n**6/600 - n**5/300 + n**4/120 + n**3/30 - 14*n**2. Factor k(d).
-(d - 1)*(d + 1)**2/5
Let y(z) be the first derivative of -2/15*z**3 + 1/30*z**4 - z + 1/5*z**2 - 2. Let b(r) be the first derivative of y(r). Determine x so that b(x) = 0.
1
Let c(r) be the first derivative of -r**3 - 9*r**2/2 - 2. Suppose c(a) = 0. Calculate a.
-3, 0
Suppose 4*u = -0*u + 16. Let l be (-6 - -3) + (-5)/(-1). Factor -4*m**u + 2*m**3 + 3*m**4 + l*m**5 - 3*m**4.
2*m**3*(m - 1)**2
Suppose -u + 5*u - 22 = -2*a, -5*u + 3*a = 0. Suppose -14 = -5*v + 4*j, 5*v - 7 = -0*j - u*j. Suppose 0 - 3/2*z**4 + 3/2*z**v - 3/2*z**3 + 3/2*z = 0. What is z?
-1, 0, 1
Suppose -3*b + 12 = -6. Let y(u) = -u**3 + 88. Let z be y(0). Solve 206*w**3 + b*w**5 + 8*w**5 + 0 + 104*w + 182*w**2 + z*w**4 + 38*w**2 + 16 = 0 for w.
-2, -1, -2/7
Let j(d) be the first derivative of d**5/20 + 3*d**4/4 + 9*d**3/2 + 7*d**2/2 - 5. Let y(b) be the second derivative of j(b). Factor y(k).
3*(k + 3)**2
Let a(o) be the second derivative of -7*o**6/45 + 19*o**5/40 - 7*o**4/18 - o**3/12 + o**2/6 + 3*o. Solve a(i) = 0 for i.
-1/4, 2/7, 1
Let 4/7 - 995328/7*h**5 + 414720/7*h**4 - 69120/7*h**3 - 240/7*h + 5760/7*h**2 = 0. Calculate h.
1/12
Let u(z) be the third derivative of z**5/150 + z**4/15 + 4*z**3/15 - 13*z**2. Solve u(l) = 0 for l.
-2
Let o = -17 + 21. Factor 0*y**3 + 0*y**2 + 0 + 3/4*y**o + 0*y.
3*y**4/4
Let a = -4/5 + 6/5. Factor -4/5*k**2 - a*k + 2/5*k**3 + 4/5.
2*(k - 2)*(k - 1)*(k + 1)/5
Let k be 2/(-6) + 3488/(-24). Let a = k + 147. Factor -a + 5/6*d**3 + 1/6*d**4 - 2/3*d + d**2.
(d - 1)*(d + 2)**3/6
Let z = -295 - -300. Factor -1/3 - 2/3*c**2 + 2/3*c**3 - c + 1/3*c**z + c**4.
(c - 1)*(c + 1)**4/3
Let l(u) be the second derivative of 7*u**4/24 + 5*u**3/2 + 2*u**2 - 11*u. Factor l(y).
(y + 4)*(7*y + 2)/2
What is d in 144/5*d**3 + 729/5*d**5 - 12/5*d**2 + 0 - 567/5*d**4 + 0*d = 0?
0, 2/9, 1/3
Suppose -7/2*l + 5/2*l**2 + 3/2 - 1/2*l**3 = 0. Calculate l.
1, 3
Let t(m) be the third derivative of 1/9*m**3 + 0 - 1/12*m**4 + 1/30*m**5 - 1/180*m**6 + m**2 + 0*m. Suppose t(g) = 0. What is g?
1
Let v = 5 - 1. Let x be (v/14)/(50/70). Factor x*b**5 + 0*b + 2/5*b**4 + 0*b**2 + 0*b**3 + 0.
2*b**4*(b + 1)/5
Find p such that -12/5 + 2*p - 2/5*p**2 = 0.
2, 3
Let z(y) = 8*y**3 - 7*y**2 - 7*y. Let g(w) = -5*w**3 + 4*w**2 + 4*w. Let o(b) = -7*g(b) - 4*z(b). Factor o(x).
3*x**3
Let f(u) be the second derivative of -u**6/90 - u**5/30 - u**4/36 + 4*u. Find g such that f(g) = 0.
-1, 0
Factor 9*h**4 + 7*h**2 + 4*h**4 + h + 15*h**3 - 5*h**5 + 9*h**5.
h*(h + 1)**3*(4*h + 1)
Let p(k) = -2*k. Let m(v) = -4*v**2 + 40*v. Let l(t) = m(t) + 6*p(t). Find u, given that l(u) = 0.
0, 7
Let m be (-91)/174 + 3 + -2. Let t = m + 2/87. Solve 1/2*o**3 + 1/2*o**4 - 1/2*o**2 + 0 - t*o = 0 for o.
-1, 0, 1
Factor 15*h**3 - 11*h - 3*h - 5*h - 5*h**4 - h.
-5*h*(h - 2)**2*(h + 1)
Suppose -4*f + 20 = -12. Solve -7*s + 9*s - f*s + 15*s**2 = 0 for s.
0, 2/5
Let r(s) be the third derivative of -s**7/1470 - s**6/630 + s**3 + s**2. Let a(x) be the first derivative of r(x). Let a(n) = 0. Calculate n.
-1, 0
Let r be (-7)/(-3) - 14/42. Let h be 1 + 2 + (-4)/(-2). Determine s so that s**2 + 2*s**5 + 4*s**3 - 2*s**r - 3*s**3 - 3*s**h + s**4 = 0.
-1, 0, 1
Let b(v) = -v**3 + 6*