culate x.
-1, 0, 2
Suppose b - 11 = p, -4*b + b + 32 = -2*p. Suppose b = 5*r - 5. Factor -1/3*w**r + 1/3 + w**2 - w.
-(w - 1)**3/3
Let g(o) be the first derivative of o**8/5040 - o**7/2520 - o**3/3 + 4. Let b(t) be the third derivative of g(t). Factor b(s).
s**3*(s - 1)/3
What is y in -2/9*y**3 - 2/9*y**4 + 0 + 2/9*y**2 + 2/9*y = 0?
-1, 0, 1
Let t(r) be the second derivative of -r**6/90 - r**5/60 + r**4/36 + r**3/18 - 3*r. Factor t(a).
-a*(a - 1)*(a + 1)**2/3
Let y(a) be the third derivative of a**5/60 - a**3/6 + 19*a**2. Let y(q) = 0. What is q?
-1, 1
Factor -36/7*a - 8/7 + 16/7*a**3 - 12/7*a**2.
4*(a - 2)*(a + 1)*(4*a + 1)/7
Let r(x) = -14*x**2 + 7*x - 9. Let f(j) = j**2 + j + 1. Let w(a) = 20*f(a) + 4*r(a). Find i such that w(i) = 0.
2/3
Let j(n) be the first derivative of n**7/1680 - n**6/360 - n**5/80 + n**3 + 6. Let k(l) be the third derivative of j(l). Suppose k(a) = 0. Calculate a.
-1, 0, 3
Let b(a) be the second derivative of 1/6*a**3 - 1/20*a**5 + 5*a + 1/2*a**2 - 1/12*a**4 + 0. Factor b(m).
-(m - 1)*(m + 1)**2
Let j be 33/(-44) + (-6)/(-8). What is t in 2/5*t**2 + 0*t - 2/5*t**4 + j + 0*t**3 = 0?
-1, 0, 1
Let g(x) be the second derivative of -x**7/56 + x**6/40 + 3*x**5/80 - x**4/16 + 28*x. Factor g(q).
-3*q**2*(q - 1)**2*(q + 1)/4
Let v(u) = -42*u + 2 - 4 + 43*u. Let l be v(2). Find g, given that 1/5*g + 1/5*g**2 + l = 0.
-1, 0
Let a(v) = -18*v**5 - 84*v**4 - 50*v**3 - 3*v**2 - 5*v. Let s(y) = 18*y**5 + 84*y**4 + 50*y**3 + 2*y**2 + 6*y. Let b(w) = 6*a(w) + 5*s(w). Factor b(n).
-2*n**2*(n + 4)*(3*n + 1)**2
Let i = -55/8 - -193/28. Let h = 15/56 + i. Factor -2/7*y + 0 + h*y**2.
2*y*(y - 1)/7
Let k be 1 + (4 - 2/2). Suppose -l + k = l. Suppose 34*j**2 + 4*j + 109*j**3 + 2*j**l + 126*j**4 - 6*j**5 + 55*j**5 = 0. What is j?
-1, -2/7, 0
Let f(i) be the third derivative of 0 - 1/20*i**5 - 2*i**2 - 1/480*i**6 + 0*i - 8/3*i**3 - 1/2*i**4. Factor f(q).
-(q + 4)**3/4
Let b = 102 - 508/5. Suppose -5*d + 0*w + 3*w = -32, 4*w = -d - 12. Factor 0*u - 2/5*u**d + 0 + b*u**2 + 0*u**3.
-2*u**2*(u - 1)*(u + 1)/5
Solve 3/5*g - 3/5 - 3/5*g**3 + 3/5*g**2 = 0 for g.
-1, 1
Suppose -2*m = -p + 6*p - 5, -m = 3*p - 1. Suppose 4*i = -i + m. Find c such that 0 + 2/11*c**i + 2/11*c**4 + 0*c + 4/11*c**3 = 0.
-1, 0
Let o(i) be the third derivative of 6*i**2 - 1/84*i**8 + 0 + 2/105*i**7 - 1/15*i**5 + 0*i**3 + 0*i**4 + 0*i + 1/30*i**6. Let o(w) = 0. What is w?
-1, 0, 1
Factor -7*a**5 - 6*a**2 + 2*a**5 - 9*a - 3 + 2*a**5 + 6*a**3 + 6*a**5 + 9*a**4.
3*(a - 1)*(a + 1)**4
Let h(l) = l + 1. Let r be h(4). Factor 3*w**2 + 2*w**3 + 0*w**2 - r*w**3.
-3*w**2*(w - 1)
Let k(i) = -i**3 - 9*i**2 - 2*i - 6. Let o be k(-9). What is p in -4*p**4 - 2*p**5 - 8*p + 4*p**2 - 5*p**5 + 0*p**4 + 3*p**5 + o*p**3 = 0?
-2, -1, 0, 1
Let b(p) be the first derivative of 2*p**5/25 + p**4/2 + 4*p**3/5 - 4*p**2/5 - 16*p/5 - 23. What is s in b(s) = 0?
-2, 1
Suppose 4*k - 2 = 3*k. Let q(j) be the first derivative of k + 0*j - 2/3*j**3 + j**2. Find t, given that q(t) = 0.
0, 1
Let r = -37 + 37. Let k(m) be the third derivative of 0*m + 0*m**4 + 1/105*m**7 + 0*m**3 + r*m**6 + 0 + m**2 - 1/30*m**5. Let k(q) = 0. What is q?
-1, 0, 1
Let u(b) be the first derivative of 2/75*b**5 - 1/30*b**4 - 4/45*b**3 + 0*b + 2 + 0*b**2. Factor u(w).
2*w**2*(w - 2)*(w + 1)/15
Factor -4*p**3 + 0 + 4*p + 6 - 2 - 4*p**2 + 0.
-4*(p - 1)*(p + 1)**2
Let n(w) = -w**4 + w**3 - w**2 + w. Let m(p) = -2*p**3 + 2*p**2. Let f(a) = 2*m(a) - 2*n(a). Suppose f(d) = 0. Calculate d.
0, 1
Let v(a) = 20*a**2 - 17. Let k(d) = -5*d**3 - d**2 + d - 1. Let n be k(1). Let l = 1 + -18. Let s(x) = -7*x**2 + 6. Let r(q) = l*s(q) + n*v(q). Factor r(j).
-j**2
Let t be (1/2)/((-1)/(-4)). Let p(w) be the second derivative of 1/15*w**3 + 0 + 0*w**t - w + 1/30*w**4. Factor p(s).
2*s*(s + 1)/5
Suppose 0 + 10*y**5 + 0*y + 53/2*y**4 + 2*y**2 + 14*y**3 = 0. Calculate y.
-2, -2/5, -1/4, 0
Suppose -3*z = -z + 4. Let a be (-2)/z + 2/(-2). Suppose 4/3*s + 2/3*s**3 + 2*s**2 + a = 0. What is s?
-2, -1, 0
Let m = -6 + 8. Factor -4 + x**2 - 2 + 5*x**m - 3*x**4 + 3.
-3*(x - 1)**2*(x + 1)**2
Factor 9*o**2 - 301 - 6*o + 301 - 3*o**3.
-3*o*(o - 2)*(o - 1)
Let q(h) = -h**3 - h**2 - h + 1. Let f(k) = k**3 + 2*k**2 + 2*k - 2. Suppose 0 = -2*t + t - 6. Let x(w) = t*q(w) - 4*f(w). Find n such that x(n) = 0.
-1, 1
Suppose -3*r - 3*b = -b - 4, -3*r - 31 = -5*b. Let n = r + 7. What is d in 12*d**2 + 6 - n*d**3 + 3*d**3 - 24*d + 10 = 0?
2
Let u be (-64)/(-6)*(7 + -5). Let m = u - 21. Factor 0*f**3 - 1/3*f**5 + 0*f + m*f**4 + 0 + 0*f**2.
-f**4*(f - 1)/3
Let c(x) = -x**2 - 8*x - 3. Let y be c(-7). Suppose -19 = -3*n - y*r, -5*r + 9 = -11. Factor -2*i**2 + 1 - n.
-2*i**2
Let q(h) be the second derivative of -h**4/12 - 5*h**3/6 - 2*h**2 + 13*h. Factor q(i).
-(i + 1)*(i + 4)
Let z = -3773 + 11176/3. Let l = z - -51. Find v, given that -2/3 - 8/3*v**2 - l*v = 0.
-1, -1/4
Let t = 20 + -16. Suppose 0 = -w - 3*g - 12, -2*w + 13 + 8 = -3*g. Factor 2*y**2 - t*y**3 + 2*y**w + 3 - 5 + 2*y.
-2*(y - 1)**2*(y + 1)
Solve -2*d**2 + 8/7*d - 17/7*d**3 + 5/7*d**4 + 0 = 0 for d.
-1, 0, 2/5, 4
Let y(o) be the first derivative of -5 - 4/45*o**3 - 1/30*o**4 + 0*o - 1/15*o**2. Factor y(k).
-2*k*(k + 1)**2/15
Let r = 31 + -31. Let d(y) be the third derivative of 0*y**3 + 0*y**5 + r*y**4 + 1/70*y**7 + 0*y + 1/40*y**6 + 3*y**2 + 0. Factor d(m).
3*m**3*(m + 1)
Let t(n) be the first derivative of -n**3/4 + 3*n**2/8 + 1. Factor t(a).
-3*a*(a - 1)/4
Let q(c) = -80*c**5 - 40*c**4 + 402*c**3 - 378*c**2 + 100*c - 4. Let a(u) = -u**5 + u**4 - u + 1. Let y(z) = 5*a(z) - q(z). Suppose y(l) = 0. Calculate l.
-3, 1/5, 1
Let s(b) = -b**3 - 6*b**2 + b + 6. Let k be s(-6). Suppose -3*a + 6 = -k*a. Determine f, given that a*f**2 + 0*f**4 - 2*f**4 + 0*f**2 = 0.
-1, 0, 1
Let l = 1/1792 + -9729/1792. Let m = 40/7 + l. Factor 0 + m*o + 2/7*o**4 + 6/7*o**3 + 6/7*o**2.
2*o*(o + 1)**3/7
Suppose 10 = 3*x - 2*j, -1 + 7 = -3*j. Factor -6*q**3 + 0*q**2 - x*q**4 + 2*q**3 - 2*q**2.
-2*q**2*(q + 1)**2
Let h(w) be the second derivative of -w**6/19 + 47*w**5/190 - 17*w**4/38 + 7*w**3/19 - 2*w**2/19 + 36*w. Let h(t) = 0. What is t?
2/15, 1
Let g(p) be the third derivative of -11/140*p**7 - 1/8*p**4 - 3*p**2 + 0*p**3 - 33/160*p**6 - 1/4*p**5 - 5/448*p**8 + 0*p + 0. What is a in g(a) = 0?
-2, -1, -2/5, 0
Suppose -3*b - 4*t = 1 + 3, 3*b = 3*t + 24. Let m(k) be the third derivative of 0*k**3 + 1/135*k**5 - 1/108*k**b + 0*k - 1/540*k**6 + 0 + 3*k**2. Factor m(i).
-2*i*(i - 1)**2/9
Let x be 20/70 + 30/(-154). Let a = x - -85/33. Factor -14/3*p**2 + 0*p - 2*p**3 + a.
-2*(p + 1)*(p + 2)*(3*p - 2)/3
Let u(m) = 8*m**3 + 13*m**2 - 3*m - 3. Let b(l) = -52*l**3 - 84*l**2 + 20*l + 20. Let t(q) = 5*b(q) + 32*u(q). Factor t(w).
-4*(w - 1)*(w + 1)**2
Let x(k) = 2*k + 0 - 1 - k**2 + 5 - 2. Let f be x(2). Factor 0 + 0*w**f + 1/4*w - 1/4*w**3.
-w*(w - 1)*(w + 1)/4
Let i(t) be the first derivative of 9/5*t**5 + 9/2*t**2 - 3/2*t**4 - 1/2*t**6 - 2*t**3 + 6 - 3*t. Let i(k) = 0. What is k?
-1, 1
Let r(g) = -13*g**3 - g**2 + 3*g. Let t(x) = x**3 - x**2 - x. Let h(d) = r(d) + 3*t(d). Factor h(b).
-2*b**2*(5*b + 2)
Let c(z) be the first derivative of z**3 - 3*z**2 + 3*z - 8. Solve c(u) = 0 for u.
1
Let m(r) be the first derivative of -2*r**5/35 - 3*r**4/14 - 4*r**3/21 + 11. Factor m(q).
-2*q**2*(q + 1)*(q + 2)/7
Let i be (11/2)/(6/(-60)). Let n = i - -276/5. Factor 4/5*y**2 - n - 3/5*y.
(y - 1)*(4*y + 1)/5
Suppose m = -y - 3, -15 = y - 0*y + 5*m. Let o = 10 + -7. Factor 2/5*q**5 + 2/5*q**o + 4/5*q**4 + 0 + y*q**2 + 0*q.
2*q**3*(q + 1)**2/5
Suppose 2*j = 5 + 7. Let s be 2/3 + (-192)/(-36). Factor -10*t - s*t + t**2 + 4 + j*t**2.
(t - 2)*(7*t - 2)
Let d be 1*(-8)/4*-1. Let m(a) be the first derivative of -1 + 1/3*a**3 + a + a**d. Let m(l) = 0. What is l?
-1
Let s = 173 - 71. Solve s*b**3 - 99*b**3 - b**4 - 2*b**4 = 0 for b.
0, 1
Let b(z) = z + 3. Let k be b(0). Suppose k*t - 2 = 2*t. Let 0 + 1/4*a**3 - 1/4*a**t + 0*a = 0. What is a?
0, 1
Suppose -12 = -v - 4*q, 0*v - 5*q = v - 15. Factor -1/3*l**3 + v + 2/3*l + 1/3*l**2.
-l*(l - 2)*(l + 1)/3
Factor -1 - 10*x - 4*x**2 - 5 + 2*x**3 + 2*x**2.
2*(x - 3)*(x + 1)**2
Let q(z) = -3*z**4 - 3*z**3 + 6*z**2 + 6*z - 3. Let y(t) = -3*t**4 - 4*t**3 + 5*t**2 + 6*t - 4. Let s(j) = 4*q(j) - 3*y(j). Factor s(d).
-3*d*(d - 2)*(d + 1