a**3 + 0 - 2/3*a**4.
-2*a*(a - 1)**2*(a + 1)/3
Let b(i) = -2*i**5 - 2*i**4 + 9*i**3 - i**2 - 3*i - 1. Let h(m) = m**5 - m**4 + m**3 - m**2. Let q(r) = b(r) - 2*h(r). Let q(v) = 0. What is v?
-1, -1/2, 1
Let -46*z**2 + 8 + 31*z**2 - 3 + 10*z = 0. What is z?
-1/3, 1
Let z(p) = p + 1. Let g be z(2). Let c be 9/6 - g/(-6). Factor -3*o**2 - 3*o + 12*o - 2 + o**2 - 2*o**c.
-(o - 2)*(4*o - 1)
Let p(j) be the third derivative of j**5/240 + 13*j**2. Factor p(t).
t**2/4
Let j(m) be the first derivative of -m**7/420 - m**6/90 - m**5/60 + 2*m**3/3 + 2. Let k(b) be the third derivative of j(b). Factor k(x).
-2*x*(x + 1)**2
Let q(w) = 12*w**4 + 36*w**3 - 8*w**2 + 16*w. Let b(h) = -h**3 - h. Let z(m) = 16*b(m) + q(m). What is g in z(g) = 0?
-2, 0, 1/3
Let p(x) be the first derivative of -2/5*x**5 + 2/3*x**3 - 3 + 1/3*x**6 + 0*x**2 - 1/2*x**4 + 0*x. Solve p(j) = 0.
-1, 0, 1
Let a be 15/4 - 5/(-20). Let q be 0/(0 - (-1 - 1)). Factor -12/7*p**2 + 2/7*p + 24/7*p**3 - 20/7*p**a + q + 6/7*p**5.
2*p*(p - 1)**3*(3*p - 1)/7
Let b be 2/(-8) - (-66)/8. Let z(j) be the third derivative of 0 + 1/168*j**b - j**2 - 1/30*j**5 - 1/60*j**6 + 0*j**3 + 0*j**4 + 1/105*j**7 + 0*j. Factor z(h).
2*h**2*(h - 1)*(h + 1)**2
Let w = 667/9 - 74. Let c(a) be the third derivative of 0*a + 1/180*a**5 + 0 + 1/24*a**4 + a**2 + w*a**3. Let c(k) = 0. Calculate k.
-2, -1
Let m(l) = -l**2 + 8*l + 4. Let t be m(8). Let b(w) be the first derivative of 0*w + 0*w**2 + 4/27*w**3 + 1/18*w**t - 5. Factor b(y).
2*y**2*(y + 2)/9
Let m = -725 + 727. Solve 21/5*h**m - 6/5 + 3*h = 0 for h.
-1, 2/7
Suppose 0 + 1/3*v**3 - 2/3*v + 1/3*v**2 = 0. Calculate v.
-2, 0, 1
Let t(h) be the third derivative of 0*h**3 + 0*h**4 + 3*h**2 + 0*h**5 + 0 + 1/480*h**6 - 1/840*h**7 + 0*h. Factor t(a).
-a**3*(a - 1)/4
Let c be 3/27*(-30)/(-5). Let v(b) be the second derivative of 2*b + 5/18*b**4 + 1/3*b**3 - c*b**2 + 0. Factor v(l).
2*(l + 1)*(5*l - 2)/3
Suppose -s + 11 = -0*s. Let z = s - 7. Factor -2*n**2 + 4*n**5 - 2*n**z - n**3 - 3*n**5 + 4*n**4.
n**2*(n - 1)*(n + 1)*(n + 2)
Solve 0*k - 2/5*k**4 + 1/2*k**3 + 0 - 3/10*k**5 + 1/5*k**2 = 0.
-2, -1/3, 0, 1
Let g be (-4)/(-2) - (-1 + 1). Suppose 12 = 4*m - 8*m, -5*s + 5*m + 25 = 0. Factor -2*a**3 + 0*a**g + 7*a**2 - s*a - 3*a**2.
-2*a*(a - 1)**2
Let k(x) be the first derivative of -x**6/60 - x**5/30 + 3*x**2/2 - 3. Let s(l) be the second derivative of k(l). Suppose s(p) = 0. What is p?
-1, 0
Suppose o - 30 = -4*w - 0*o, 0 = 2*w - o - 18. Let s be (3/5)/(12/w). Determine g so that s - 14/5*g - 26/5*g**3 + 6*g**2 + 8/5*g**4 = 0.
1/4, 1
Factor 5/3*g**4 + 0 + 1/3*g**3 + 4/3*g**5 + 0*g + 0*g**2.
g**3*(g + 1)*(4*g + 1)/3
Let d be 4*2/(-12)*(-1)/2. Let q(f) be the third derivative of 0*f + 0 - 1/60*f**6 + f**2 + 1/30*f**5 + 1/12*f**4 - d*f**3. Find w such that q(w) = 0.
-1, 1
Let n(w) be the third derivative of -1/40*w**6 + 0*w**3 + 0*w + 0 + 7/120*w**5 + 3*w**2 - 1/24*w**4. Determine k so that n(k) = 0.
0, 1/2, 2/3
Factor -k**5 + 0*k + 3*k**4 - 5*k**3 + 3*k**3 + 0*k.
-k**3*(k - 2)*(k - 1)
Suppose -8 = -2*u - 2. Solve 5*i**3 - 2 + 0*i**2 - 2*i - 3*i**2 + 5*i**2 - u*i**3 = 0 for i.
-1, 1
Let t be ((-15)/50)/(6/(-72)). Factor 4/5 + t*z**2 + 22/5*z.
2*(z + 1)*(9*z + 2)/5
Factor 9*c**2 + 4*c - 10*c**4 + 9*c**3 - c + 13*c**4.
3*c*(c + 1)**3
Let d(g) be the third derivative of g**10/90720 + g**9/22680 - g**7/3780 - g**6/2160 - g**4/12 - 2*g**2. Let f(t) be the second derivative of d(t). Factor f(h).
h*(h - 1)*(h + 1)**3/3
Let g(t) be the third derivative of -t**7/2520 - t**6/180 - t**5/30 - t**4/9 - 4*t**3/3 + 3*t**2. Let l(f) be the first derivative of g(f). Solve l(y) = 0.
-2
Let q(d) be the second derivative of -d**8/10752 + d**7/2520 - d**6/5760 - d**5/480 - 3*d**4/4 + 4*d. Let y(s) be the third derivative of q(s). Factor y(z).
-(z - 1)**2*(5*z + 2)/8
Let d be (-5)/(-15) - 1/3. Factor 2/9*l**4 + 0*l**3 + d + 0*l + 0*l**2 + 2/9*l**5.
2*l**4*(l + 1)/9
Let b(g) be the third derivative of g**7/140 - g**5/40 + 12*g**2. Solve b(c) = 0.
-1, 0, 1
Let t(k) be the first derivative of -k**3/24 - 3*k**2/8 - 9*k/8 - 5. Factor t(o).
-(o + 3)**2/8
Let j = -1 - -1. Let 0 + 2*q**3 + j - 11*q**2 + 6*q**4 + 7*q**2 = 0. Calculate q.
-1, 0, 2/3
Let h be 2/(-20) + (-252)/(-120). Find c, given that 0*c - 1/3*c**3 + 0 + 0*c**h + 1/3*c**4 = 0.
0, 1
Let a(t) = 2*t**3 + 14*t**2 + 9*t - 18. Let u be a(-6). Find r such that -2/9*r**3 + 0*r - 2/9*r**4 + 0 + u*r**2 = 0.
-1, 0
Let h(v) be the first derivative of -9*v**6/10 - 12*v**5/5 - 5*v**4/4 + v**3 - v - 6. Let x(c) be the first derivative of h(c). Suppose x(g) = 0. What is g?
-1, 0, 2/9
Suppose 5*n = 4*c + 12, -4*n - 29 = 5*c - 55. Determine a, given that 2/7*a**c - 16/7*a + 32/7 = 0.
4
Factor -12/7*a - 2/7*a**2 - 18/7.
-2*(a + 3)**2/7
Let u = -11 - -15. Factor u*f - 3*f - 4*f**2 + 3*f**2.
-f*(f - 1)
Let f(q) be the first derivative of 0*q - q**2 + 2/3*q**3 + 3. Factor f(p).
2*p*(p - 1)
Factor -27*k + 20*k**2 - 16*k - 9*k - 24.
4*(k - 3)*(5*k + 2)
Let w(s) be the first derivative of -7/20*s**5 - 1 - 1/8*s**4 + 7/12*s**3 + 0*s + 1/4*s**2. Solve w(t) = 0 for t.
-1, -2/7, 0, 1
Let z(g) = -g**3 + 6*g**2 - 3*g - 6. Suppose 2*o + 3 = 1, -2*a + 2*o = -12. Let p be z(a). Factor w - 4*w + 12*w**p - 3*w**5 + 21*w**2 - 9*w**2 - 18*w**3.
-3*w*(w - 1)**4
Factor 3/4*p**4 + 1/2*p + 0 - 1/2*p**3 - 3/4*p**2.
p*(p - 1)*(p + 1)*(3*p - 2)/4
Let j(w) be the second derivative of w**4/3 + 8*w**3/3 + 6*w**2 - 5*w. Suppose j(a) = 0. What is a?
-3, -1
Solve 0*p + 2/7*p**3 - 2/7*p**5 - 4/7*p**2 + 4/7*p**4 + 0 = 0.
-1, 0, 1, 2
Let v(i) be the first derivative of -i**3/5 + 3*i**2/5 - 3*i/5 + 33. Determine m so that v(m) = 0.
1
Let f(z) be the third derivative of -z**6/1620 - z**5/270 - z**4/108 - z**3/6 - 3*z**2. Let g(t) be the first derivative of f(t). Factor g(r).
-2*(r + 1)**2/9
Let p be 1*(-3)/(3/5). Let y = -3 - p. Factor -8*f**3 + 7*f**3 - 3*f**2 + 4*f**y.
-f**2*(f - 1)
Solve -2/5*x**3 + 4/5*x - 2/5*x**5 - 6/5*x**2 + 0 + 6/5*x**4 = 0.
-1, 0, 1, 2
Let v be (4 + -5)*0/(-3). Let m(n) be the first derivative of -1/15*n**5 - 2 + 0*n + 1/6*n**4 - 1/9*n**3 + v*n**2. Let m(t) = 0. Calculate t.
0, 1
Let p(l) = 8*l**3 - 5*l**2 - 14*l. Let k(u) = 3*u**3 - 2*u**2 - 5*u. Let n(f) = -11*k(f) + 4*p(f). Find z such that n(z) = 0.
0, 1
Let c(y) = y**3 + 9*y**2 + 9*y + 1. Let i(s) = s**3 + 5*s**2 + 5*s + 1. Let p(k) = 3*c(k) - 5*i(k). Solve p(f) = 0 for f.
-1, 1
Let r(a) = 2*a + 10. Let h(i) = 3*i + 19. Let x(f) = -3*h(f) + 5*r(f). Let l be x(7). Factor -4/3*p**2 + 2/3*p**5 - 2/3*p + 4/3*p**4 + l + 0*p**3.
2*p*(p - 1)*(p + 1)**3/3
Let b = -29 + 29. Suppose 3*k + i = 1, -5*k + b*i + 15 = -i. Factor n - 1/2*n**3 + 0 - 1/2*n**k.
-n*(n - 1)*(n + 2)/2
What is i in 2*i**3 - 3*i**2 + 23*i + i**3 - 22*i - i**4 = 0?
0, 1
Let n(b) = 24*b**2 - 10*b - 34. Let v(t) = -5*t**2 + 2*t + 7. Suppose -21 + 6 = -5*l. Let s = -23 - -37. Let y(j) = l*n(j) + s*v(j). Factor y(q).
2*(q - 2)*(q + 1)
Factor 3*v + 0 + 11/2*v**2 + 3/2*v**3.
v*(v + 3)*(3*v + 2)/2
Let d(s) be the second derivative of -s**3/6 + 4*s. Let m be d(-3). Solve -2/7*h**2 + 2/7 + 2/7*h - 2/7*h**m = 0.
-1, 1
Let a(c) = -3*c**2 + 23*c + 1. Let d(z) = -z**3 + 5*z**2 + 7*z + 1. Let m be d(6). Let o(p) = 2*p**2 - 11*p - 1. Let n(v) = m*o(v) + 3*a(v). Factor n(b).
(b - 2)*(5*b + 2)
Let k(s) = -s**2 - 7*s - 6. Let v be k(-6). Let r be (3/(-27))/(2/(-6)). Solve 0 - r*i**4 + v*i + 0*i**3 + 1/3*i**2 = 0 for i.
-1, 0, 1
Let s(t) = -t**2 + 23*t - 40. Let l be s(21). Factor 0 + 1/2*u**3 - 3/2*u**l + u.
u*(u - 2)*(u - 1)/2
Let r = 443 - 1763/4. Find o such that 0 + 3/4*o**5 + 9/4*o**3 + 0*o - 3/4*o**2 - r*o**4 = 0.
0, 1
Let w(f) be the first derivative of 0*f**2 - 1/30*f**6 + 1/30*f**4 - 3/100*f**5 - 4*f + 0*f**3 + 3. Let t(q) be the first derivative of w(q). Factor t(l).
-l**2*(l + 1)*(5*l - 2)/5
Let y be (8/10)/(8/20). Suppose g**2 + 15 - 17 + g**y = 0. Calculate g.
-1, 1
Let a(s) be the first derivative of 16*s**5/5 + 7*s**4 + 8*s**3/3 - 2*s**2 - 7. Find x, given that a(x) = 0.
-1, 0, 1/4
Determine i so that 0 - 2/5*i**3 + 2/5*i + 0*i**2 = 0.
-1, 0, 1
Let c(w) = -w**2 - 8*w - 4. Let f be c(-7). Let f - y + 3*y**2 - 2*y**2 - 3*y = 0. What is y?
1, 3
Suppose 5*u + d - 29 + 8 = 0, 4 = 2*u - 4*d. Suppose -g = -0 - 3. Factor 1/4*w**2 + 0*w + 0*w**g - 1/4*w**u + 0.
-w**2*(