/4
Let u(s) be the first derivative of -s**6/360 + s**5/90 + s**2/2 - 2. Let f(b) be the second derivative of u(b). Factor f(y).
-y**2*(y - 2)/3
Let p(h) be the second derivative of -h**4/2 + 5*h**3/2 - 9*h**2/2 - 5*h. Factor p(b).
-3*(b - 1)*(2*b - 3)
Let h be 4/(-5) + (54/20)/3. Let d(r) be the second derivative of -1/3*r**4 + 0*r**2 + 0 + 0*r**3 + r + 1/15*r**6 + h*r**5. Factor d(b).
2*b**2*(b - 1)*(b + 2)
Factor 0 - 1/3*d + 1/3*d**2.
d*(d - 1)/3
Let r(p) = -p**2 - p. Let t(x) = x**3 + 7*x**2 + 7*x. Let v(b) = -3*r(b) - t(b). Solve v(c) = 0 for c.
-2, 0
Let j = -2 + 5. Suppose -3*b**j - 3*b**2 + 2 - 4*b**3 + 7*b + b**2 = 0. What is b?
-1, -2/7, 1
Let k(i) be the first derivative of 1/6*i**4 - 3 + 0*i - 2/3*i**2 + 2/9*i**3. Factor k(j).
2*j*(j - 1)*(j + 2)/3
Solve 4/5*g**2 + 0 + 3/5*g + 1/5*g**3 = 0.
-3, -1, 0
Factor 1/8*i + 1/8*i**2 + 0.
i*(i + 1)/8
Let z = -4651/5 + 935. Factor 0 + 0*k - z*k**3 - 3/5*k**5 - 3*k**4 - 12/5*k**2.
-3*k**2*(k + 1)*(k + 2)**2/5
Let n(p) = p**3 - 5*p**2 - 5*p. Let r be n(6). Factor -3*i - 2*i + 2*i**2 + r*i - i**2.
i*(i + 1)
Let 4*c + 0*c + 52*c**2 - 56*c**2 = 0. Calculate c.
0, 1
Find g, given that 0*g + 0 - 2/13*g**5 + 0*g**2 + 4/13*g**4 - 2/13*g**3 = 0.
0, 1
Let c(q) be the second derivative of -q**5/120 + q**3/12 - q**2 + q. Let v(i) be the first derivative of c(i). Factor v(d).
-(d - 1)*(d + 1)/2
Let d(w) be the second derivative of 1/3*w**3 - 4*w - 1/12*w**4 + 0 - 1/20*w**5 + 0*w**2. Suppose d(n) = 0. What is n?
-2, 0, 1
Suppose -1/2 + o**3 + 7/2*o - 9/2*o**5 + 15/2*o**4 - 7*o**2 = 0. Calculate o.
-1, 1/3, 1
Let i be 4/16 - 30/(-8). Let y be (2 + 0 - 0)*1. Factor o**3 - o - 2*o**y - 4*o**3 - o**i - o**2.
-o*(o + 1)**3
Let d(a) be the second derivative of a**4/24 - 5*a**3/2 + 225*a**2/4 + 20*a. Factor d(o).
(o - 15)**2/2
Factor 0 - 3/2*x**3 - 3/2*x**4 + 3/2*x**2 + 3/2*x**5 + 0*x.
3*x**2*(x - 1)**2*(x + 1)/2
Let j be 4/(-16) + 4/15. Let n(o) be the third derivative of 1/24*o**4 + 1/18*o**3 + 0*o + j*o**5 + 0 + 2*o**2 + 1/360*o**6. Factor n(d).
(d + 1)**3/3
Let g(u) be the third derivative of -3*u**2 + 1/210*u**7 + 0*u + 0 - 1/360*u**6 + 0*u**5 + 0*u**4 + 0*u**3. Let g(a) = 0. Calculate a.
0, 1/3
Let v(q) be the first derivative of 3/2*q + 9/8*q**2 + 2 - 5/4*q**3. Factor v(i).
-3*(i - 1)*(5*i + 2)/4
Let w(a) be the second derivative of -a**8/26880 + a**6/960 - a**5/240 - a**4/4 + 3*a. Let u(m) be the third derivative of w(m). Factor u(d).
-(d - 1)**2*(d + 2)/4
Let u(s) be the first derivative of 4*s**3/3 + 8*s**2 + 12*s - 46. Let u(g) = 0. Calculate g.
-3, -1
Let s(x) = -3*x - 1. Let m be s(0). Let l(g) = -3*g - 3. Let z be l(m). Factor z*q + 2/3*q**3 + 0 - 4/3*q**2.
2*q**2*(q - 2)/3
Factor 14/13*g + 6/13 + 4/13*g**2.
2*(g + 3)*(2*g + 1)/13
Let b be 30/12 + (-2)/4. Let a(h) be the third derivative of 1/6*h**3 + 1/12*h**4 - 3*h**b + 1/60*h**5 + 0 + 0*h. Let a(k) = 0. Calculate k.
-1
Let s be (-2)/(-4)*(-3694)/(-7). Let p = s - 263. What is t in 0*t + p*t**4 + 2/7*t**2 - 2/7*t**5 - 6/7*t**3 + 0 = 0?
0, 1
Let j = 47 - 45. What is x in 1/2*x**j - 1/2*x + 0 = 0?
0, 1
Let o(c) = -c**3 - 2*c**2 + 2*c - 1. Let j be o(-3). Suppose -a**2 + 4*a - a**2 + a**j - 4 = 0. Calculate a.
2
Let f(j) = 6*j**2 - 6*j - 5. Let r(o) = o**2 - o - 1. Let b(x) = f(x) - 2*r(x). Let m(t) = 4*t**2 - 4*t - 2. Let u(s) = 6*b(s) - 5*m(s). What is d in u(d) = 0?
-1, 2
Let d = -318 + 4128/13. Let a = 56/65 + d. Determine k so that 16/5 + 12/5*k**2 - 24/5*k - a*k**3 = 0.
2
Determine k so that -3/7*k**5 - 300/7*k**2 - 240/7*k**3 + 57/7*k**4 + 0 + 0*k = 0.
-1, 0, 10
Let j(p) = p**4 - p**3 + p**2 - p + 1. Let n(k) = -2*k**4 - 8*k**3 + 20*k**2 - 12*k - 4. Let z(s) = -4*j(s) - n(s). Find m such that z(m) = 0.
0, 2
Let a(i) = -9*i**3 - 3*i**2 + 4*i + 8. Let v(f) = -14*f**3 - 4*f**2 + 6*f + 12. Let g(p) = 8*a(p) - 5*v(p). Find s, given that g(s) = 0.
-2, -1, 1
Let -2*l**3 + 6 - 202 - 60*l**2 - 2*l**3 - 289*l + 37*l = 0. What is l?
-7, -1
Suppose 6 = 4*p + 2*h, p - 4*p = -3*h - 9. Let q be 3/(-7) + p/2. Find n, given that 4/7*n**3 - 2/7*n**4 - q*n + 0*n**2 + 2/7 = 0.
-1, 1
Let y(m) = m**3 - 6*m**2 + 4*m + 5. Let t be y(5). Suppose 0*c - 2/5*c**2 + t = 0. What is c?
0
Solve -459 + 3*p**2 - 449 + 896 - 9*p = 0.
-1, 4
Let r(d) be the third derivative of 0 + 1/12*d**5 + 0*d - 1/12*d**4 + 2*d**2 - 1/210*d**7 + 0*d**3 - 1/40*d**6 + 1/336*d**8. Determine n, given that r(n) = 0.
-2, 0, 1
Let g(k) be the first derivative of k**4/9 - 20*k**3/27 + 2*k**2/3 + 4*k + 15. Factor g(m).
4*(m - 3)**2*(m + 1)/9
Let u be 222/10 + (-9)/45. Suppose -24*q + u*q + 4 = 0. Let 2/7*p**3 + 2/7*p**q - 2/7*p - 2/7 = 0. What is p?
-1, 1
Let y(t) be the second derivative of 1/6*t**3 + 1/24*t**4 + 1/4*t**2 + 3*t + 0. Let y(w) = 0. What is w?
-1
Let l(a) be the third derivative of a**6/30 - a**4/6 + 9*a**2. Find p, given that l(p) = 0.
-1, 0, 1
Let b(j) be the third derivative of j**7/1260 - j**6/360 - j**4/12 - 3*j**2. Let t(w) be the second derivative of b(w). Find u, given that t(u) = 0.
0, 1
Let p(n) = -n**2 + 8*n + 9. Let a be p(9). Suppose a*o = -2*o + 4. Find m such that -m**2 + 3*m + 4 - m - m**o = 0.
-1, 2
Let j(u) be the second derivative of 2*u**5/5 + u**4 - 10*u. Factor j(x).
4*x**2*(2*x + 3)
Let h(s) = -s**3 - 3*s**2 - 3*s. Let v be h(-2). Suppose 0 = 2*g - v - 0. Solve m**2 + g + 1 - 4*m + m**2 = 0 for m.
1
Suppose 3 = 5*l - 2*l - 2*q, 0 = 5*q - 15. Suppose -18 = -2*b - 4*y, -b + 2*y = l*b - 6. Factor -b*i**4 - i**3 + 2*i**4 + 0*i**3.
-i**3*(i + 1)
Let x(m) be the first derivative of m**4/66 - 8*m**3/33 + 16*m**2/11 + 7*m + 3. Let g(c) be the first derivative of x(c). Factor g(b).
2*(b - 4)**2/11
Let n(t) = -t**2 - 6*t - 1. Let i be n(-5). Let g = -1 + i. Factor -3/4*b**g - 5/4*b**2 + b**4 + 3/4*b + 1/4.
(b - 1)**2*(b + 1)*(4*b + 1)/4
Let x(p) be the second derivative of -p**4/60 - p**3/10 - p**2/5 - 8*p. Suppose x(t) = 0. What is t?
-2, -1
Let h(l) = 17*l**5 - 16*l**4 + 26*l**3 - 8*l**2 + 5*l + 8. Let x(f) = -6*f**5 + 5*f**4 - 9*f**3 + 3*f**2 - 2*f - 3. Let s(g) = 3*h(g) + 8*x(g). Factor s(i).
i*(i - 1)**3*(3*i + 1)
Let l(c) be the third derivative of -c**8/420 + 4*c**7/105 - 4*c**6/15 + 16*c**5/15 - 8*c**4/3 + 64*c**3/15 + 8*c**2. Factor l(o).
-4*(o - 2)**5/5
Let s be 1/4*2 - 0. Let t(j) be the second derivative of -j - s*j**2 + 0 - 1/30*j**6 + 2/3*j**3 - 1/2*j**4 + 1/5*j**5. Factor t(r).
-(r - 1)**4
Suppose 6*y + 20 = 10*y. Suppose -5*t - y*b + 50 = 0, -b + 35 = 4*t + 2*b. Factor 6/7*x**4 - 2/7 - 6/7*x - 4/7*x**2 + 2/7*x**t + 4/7*x**3.
2*(x - 1)*(x + 1)**4/7
Let y(j) = -j**3 + 4*j**2 + j. Let c be y(3). Suppose -3*i + c = -0*i. Factor 0*u**i + u**5 + u**4 - u**3 + 0*u**3 - u**2.
u**2*(u - 1)*(u + 1)**2
Let r be 3/(-2)*(-8 - -6). Factor -2*w**2 - 3*w - 8 - 2*w - r*w.
-2*(w + 2)**2
Let p(m) = -2*m**3 + 2*m. Let o(a) = -a**3 + a. Let x(b) = -6*o(b) + 5*p(b). Determine w so that x(w) = 0.
-1, 0, 1
Let l(q) be the third derivative of -5*q**8/336 + q**7/21 + q**6/8 - 2*q**2. Let l(p) = 0. What is p?
-1, 0, 3
Let a be (-4)/6 + (-8)/(-3). Solve -3*w**3 - w**2 - 3*w**2 + 3*w**a + 2*w**4 + 2*w**4 = 0 for w.
-1/4, 0, 1
Let n(r) be the first derivative of 5*r**3/3 - 20*r**2 + 60*r + 19. Determine f, given that n(f) = 0.
2, 6
Let q(c) be the second derivative of 0*c**3 + 1/48*c**4 - 1/8*c**2 - c + 0. Factor q(z).
(z - 1)*(z + 1)/4
Let h(f) be the second derivative of -1/10*f**6 - 2*f**3 + 6*f**2 + 3/5*f**5 - 3*f + 0 - 3/4*f**4. Solve h(j) = 0.
-1, 1, 2
Suppose 0*f - 3*f = -36. Factor 0*n**2 + 12 + 2*n**2 + n**2 + f*n.
3*(n + 2)**2
Suppose -9 - 11 = 5*l, -16 = -5*t - l. Suppose -4*k = 2*b + 2 - 4, 0 = -b - t*k - 5. Solve b*w**2 + 3*w - 48*w**3 - 3*w**2 + 12*w**2 - 1 = 0 for w.
-1/4, 1/4, 1/3
Let c(j) be the first derivative of -2*j**5/45 + j**4/18 + 4*j**3/9 - 4*j**2/9 - 16*j/9 - 20. What is a in c(a) = 0?
-2, -1, 2
Suppose 7*a = a + 18. Suppose -6*y**a + 0*y + 2*y + 4*y + 3*y**4 - 3*y**2 = 0. Calculate y.
-1, 0, 1, 2
Let a(d) = 3*d**4 + 13*d**3 - 4*d**2 + 7*d - 7. Let k(g) = -g**4 - 4*g**3 + g**2 - 2*g + 2. Let r(u) = -2*a(u) - 7*k(u). Factor r(n).
n**2*(n + 1)**2
Let a be (1/3)/((-18)/(-162)). Let g(w) be the second derivative of 1/60*w**4 + 1/30*w**a + 0*w**2 + 0 - w. Let g(v) = 0. Calculate v.
-1, 0
Let i = 37 + -34. Let f(c) be the first derivative of 2*c**2 - 1/3*c**i - 3 -