2*h**2*(h + 1)/7
Suppose 5*d - 5 = 5. Factor -57*o - o**d + 57*o.
-o**2
Factor 0*q**2 - 4/9*q**4 + 8/9*q**3 + 4/9 - 8/9*q.
-4*(q - 1)**3*(q + 1)/9
Let m(d) be the third derivative of 0*d**3 - 1/20*d**5 + 3/40*d**6 - 3/70*d**7 + 0*d**4 + 5*d**2 + 0*d + 1/112*d**8 + 0. Suppose m(z) = 0. What is z?
0, 1
Let t = -22/5 + 49/10. Solve -1/2*a**2 + 1/2*a**3 - t*a + 1/2 = 0.
-1, 1
Let q(h) be the second derivative of 5*h**4/12 + 5*h**3/3 + 5*h**2/2 - 20*h. Factor q(f).
5*(f + 1)**2
Let d(w) = 17*w + 1. Let n be d(1). Suppose -z - 5*h - n = -5, 5*h = -3*z - 9. Factor 4*j - 2*j**4 - 6*j + 4*j - z*j**3 + j**2 + j**2.
-2*j*(j - 1)*(j + 1)**2
Let x = 218 + -650/3. Factor -2/3 + 4/3*q**3 + 2/3*q**4 + 0*q**2 - x*q.
2*(q - 1)*(q + 1)**3/3
Determine p, given that -2/5*p + 0 + 2/5*p**2 = 0.
0, 1
Let l(d) be the third derivative of -d**6/1140 + d**4/76 - 2*d**3/57 + 12*d**2. What is q in l(q) = 0?
-2, 1
Let o(u) be the third derivative of 4*u**2 + 0 + 1/2*u**3 + 0*u + 1/20*u**5 - 1/4*u**4. Find r such that o(r) = 0.
1
Factor 3*c**5 - 4*c + c**2 - 8*c**4 + 7*c**2 + 0*c**5 + c**5.
4*c*(c - 1)**3*(c + 1)
Let o = -12 + 4. Let f(k) = k**2 + k - 1. Let d(g) = -6*g**2 - 24*g + 40. Let a(x) = o*f(x) - d(x). Let a(z) = 0. What is z?
4
Find c, given that -24/13 + 14/13*c**2 + 8/13*c + 2/13*c**3 = 0.
-6, -2, 1
Let u(y) be the first derivative of -y**6/120 + y**5/16 - 7*y**4/48 + y**3/8 + y + 2. Let k(o) be the first derivative of u(o). Factor k(x).
-x*(x - 3)*(x - 1)**2/4
Let n(j) be the first derivative of -j**6/21 + 4*j**5/35 + j**4/7 - 16*j**3/21 + j**2 - 4*j/7 + 32. Determine b, given that n(b) = 0.
-2, 1
Let r(k) be the first derivative of -8*k**3/3 - 4*k**2 - 6. Let w(s) = -23*s**2 - 23*s. Let c(l) = 17*r(l) - 6*w(l). Determine q, given that c(q) = 0.
-1, 0
Let j(k) be the second derivative of 1/600*k**5 + 1/1800*k**6 + 0*k**2 - 2*k + 0 - 1/2*k**3 + 0*k**4. Let w(u) be the second derivative of j(u). Factor w(b).
b*(b + 1)/5
Let a = -9/38 + 251/418. Factor 2/11*r**5 + 0*r**3 - 2/11*r + 0 - 4/11*r**2 + a*r**4.
2*r*(r - 1)*(r + 1)**3/11
Factor 603*a**2 + 17*a + a**4 + 21*a**3 - 65*a - 4*a**4 - 627*a**2.
-3*a*(a - 4)**2*(a + 1)
Let i = -8 - -8. Let g(y) be the second derivative of 2/105*y**6 - 1/21*y**3 + 2/21*y**4 - 1/14*y**5 + 0*y**2 + 2*y + i. Factor g(m).
2*m*(m - 1)**2*(2*m - 1)/7
Let r(c) be the second derivative of c**4/18 + c**3/3 + 18*c. Factor r(v).
2*v*(v + 3)/3
Factor -2/3 + 8/3*x**3 + 4*x - 6*x**2.
2*(x - 1)**2*(4*x - 1)/3
Let n(h) be the third derivative of -2*h**2 - 1/2*h**4 - 1/20*h**5 + 0 - 3/2*h**3 + 0*h. Factor n(a).
-3*(a + 1)*(a + 3)
Suppose 20 = -2*b - 4*t, -3*b + 4*t + 20 = b. Factor -18/7*d**3 - 24/7*d**4 + b - 10/7*d**5 + 0*d - 4/7*d**2.
-2*d**2*(d + 1)**2*(5*d + 2)/7
Suppose -3*b - y + 3 = 238, -3*b = -2*y + 223. Let w = -229/3 - b. Factor -w*v**2 - 4*v - 6.
-2*(v + 3)**2/3
Determine k so that 2/3*k**2 + 1/3*k**3 + 0*k + 0 = 0.
-2, 0
Let q(r) = 3*r - 46. Let b be q(16). Solve 3/5*s**b - 3/5 + 0*s = 0 for s.
-1, 1
Suppose 5*v - 4*t = 30, 2*v + 3*v - 2*t - 20 = 0. Suppose 0 = -2*i - v*i + 8. Factor -1/4*k**i + 0*k + 0 + 1/4*k**3.
k**2*(k - 1)/4
Let k = 5 - 1. Let v = k - 2. Suppose 0 + 32*i**5 - 13*i + 76*i**v - 21*i - 80*i**4 - 3*i**3 + 4 + 5*i**3 = 0. What is i?
-1, 1/4, 1, 2
Suppose 7*m + 324 = 6*m. Let r be (-9)/(m/(-56)) - -2. Factor r*p**2 + 0 - 2/9*p**3 - 2/9*p.
-2*p*(p - 1)**2/9
Let j(i) = 5*i**2 + i + 2. Let h(x) = 6*x**2 + x + 2. Let l(v) = -6*h(v) + 7*j(v). Factor l(a).
-(a - 2)*(a + 1)
Let y(f) = 4*f**2 - 9*f + 1. Let c(i) = -5*i**2 + 10*i - 2. Let z(l) = -5*c(l) - 6*y(l). Factor z(m).
(m + 2)**2
Let a(z) be the first derivative of -z**4/16 + z**3/12 + 9*z**2/8 - 9*z/4 - 5. Solve a(l) = 0.
-3, 1, 3
Let y(x) be the third derivative of -x**7/1680 + x**6/360 - x**5/240 + x**3/6 - x**2. Let q(k) be the first derivative of y(k). Suppose q(b) = 0. Calculate b.
0, 1
Let r(z) = z**2 + z + 1. Let n(j) = j**4 + 3*j**3 + j**2 - j - 2. Let k(o) = n(o) + 2*r(o). What is l in k(l) = 0?
-1, 0
Let u(b) be the third derivative of b**7/42 - b**6/6 + b**5/6 + 5*b**4/6 - 5*b**3/2 + 4*b**2. Factor u(z).
5*(z - 3)*(z - 1)**2*(z + 1)
Factor 0*z**2 + 2/7*z**3 + 0 - 2/7*z.
2*z*(z - 1)*(z + 1)/7
Let f(h) be the third derivative of 0 + 0*h**3 + 0*h**4 + h**2 + 0*h + 0*h**5 - 1/420*h**6. Determine i so that f(i) = 0.
0
Let c(z) be the second derivative of z**6/30 + 11*z**5/10 + 10*z**4 - 11*z**3/3 - 121*z**2/2 - 14*z. Solve c(q) = 0.
-11, -1, 1
Let n(u) = -u**2 + u - 4. Let z(a) = -3*a**2 + 2*a - 7. Let f(h) = -h**3 - 5*h**2 + 4. Let c be f(-5). Let s(i) = c*z(i) - 7*n(i). Suppose s(p) = 0. What is p?
0, 1/5
Let y(u) be the third derivative of -1/315*u**7 + 1/36*u**4 + 0*u + 0 + 0*u**3 + u**2 - 1/180*u**6 + 1/90*u**5. Factor y(g).
-2*g*(g - 1)*(g + 1)**2/3
Let f(o) be the second derivative of -o**7/14 + 3*o**5/20 - 7*o. Find a such that f(a) = 0.
-1, 0, 1
Let y = -161 + 163. Factor -2/7*k**y + 2/7 + 0*k.
-2*(k - 1)*(k + 1)/7
Let o(j) be the third derivative of j**6/120 + 3*j**5/40 + j**4/4 + j**3 - j**2. Let m(d) be the first derivative of o(d). Factor m(u).
3*(u + 1)*(u + 2)
Let t(q) be the second derivative of -q**6/90 - q**5/15 - q**4/12 + 2*q**3/9 + 2*q**2/3 + 17*q. Factor t(n).
-(n - 1)*(n + 1)*(n + 2)**2/3
Let x(z) be the first derivative of z**6/6 - z**4/4 + 2. Factor x(v).
v**3*(v - 1)*(v + 1)
Factor a**2 + 1/2*a - 1 - 1/2*a**3.
-(a - 2)*(a - 1)*(a + 1)/2
Let d be (3 - 2) + (-4)/12. Factor -1/3*m - 1/3*m**4 + 1/3*m**3 + m**2 - d.
-(m - 2)*(m - 1)*(m + 1)**2/3
Suppose -2*w + 7 = 1. Factor r + r**2 - 33*r**2 + 12*r**w - 4*r + 19*r.
4*r*(r - 2)*(3*r - 2)
Let a(z) = -4*z**2 + 6*z - 1. Let d(l) = -l. Suppose 2 + 3 = 5*x. Let q(b) = x*a(b) + d(b). Factor q(j).
-(j - 1)*(4*j - 1)
Suppose 0 = 8*o - 15*o. Let g be -2 - (-2 + -2*1). Find k, given that -1/2*k**3 + o*k - g*k**5 + 0 + 0*k**2 + 5/2*k**4 = 0.
0, 1/4, 1
Suppose 5*o + 3*g - g + 11 = 0, 3 = -g. Let n be (o/6)/(2/(-16)). Solve u**4 - 2/3*u**2 - 1/3 - n*u + 4/3*u**3 = 0 for u.
-1, -1/3, 1
Let v(j) be the second derivative of j**4/4 + 3*j**3 + 27*j**2/2 + 11*j. Determine x, given that v(x) = 0.
-3
Let g(x) = 9*x**2 + 4*x. Let i(j) be the second derivative of -j**4/3 - j**3/3 + 2*j. Let a(w) = -2*g(w) - 5*i(w). Find p, given that a(p) = 0.
-1, 0
Let i be (-5)/(-3) - 3/(5 - -4). Factor -i*t - 2/3*t**2 + 0.
-2*t*(t + 2)/3
Let g(w) be the third derivative of 0*w**6 + 0*w**7 + 0*w**3 + 0*w**4 + 0*w + 1/1848*w**8 + 4*w**2 + 0*w**5 + 0. What is c in g(c) = 0?
0
Let k(t) be the third derivative of 0*t**3 + 0 + 0*t + 5*t**2 - 1/60*t**6 - 1/30*t**5 + 0*t**4. Factor k(i).
-2*i**2*(i + 1)
Let f(t) be the second derivative of 3/50*t**5 - 1/15*t**3 - 4/75*t**6 + 0 - t + 1/15*t**4 - 4/105*t**7 + 0*t**2. Factor f(k).
-2*k*(k + 1)**2*(2*k - 1)**2/5
Suppose 0 = 6*g - 12*g. Suppose -3*q + 4*i + 26 = 0, 4*q + 4*i - 5*i = 13. Factor g - 2/5*k - k**q.
-k*(5*k + 2)/5
Factor 3/2*k**2 + 3/2*k**3 - 6 - 6*k.
3*(k - 2)*(k + 1)*(k + 2)/2
Let i(d) = d + 2. Let k be i(2). Find t, given that -8*t**k - 4*t**4 - 4*t**5 - t**3 - 9*t**3 - 3*t**3 - t - 6*t**2 = 0.
-1, -1/2, 0
Let b(s) = 8*s - 28. Let q be b(4). Let d(f) be the first derivative of -1/2*f**q + 5*f**2 + 4*f - 2/5*f**5 + 2*f**3 - 2. Factor d(a).
-2*(a - 2)*(a + 1)**3
Let m(t) be the third derivative of -t**5/30 + 7*t**4/12 + 6*t**3 + 34*t**2 + t. Solve m(x) = 0.
-2, 9
Let a(h) = -h**3 - 7*h**2 + 15*h - 13. Let r be a(-9). Suppose -2*t + 2 = 3*n - 9, -4*n + r = 2*t. Factor 1/2 - 1/2*w**n + 1/2*w - 1/2*w**2.
-(w - 1)*(w + 1)**2/2
Suppose 5*c + t + 0*t = -52, 0 = -3*t - 6. Let z = -6 - c. Factor -5/2*v**2 - v - 2*v**3 + 0 - 1/2*v**z.
-v*(v + 1)**2*(v + 2)/2
Suppose p + 7 = 4*i, 0 = i + i - p - 3. Factor 3*g**i - 6*g + 2*g - g**2.
2*g*(g - 2)
Suppose a - 3 = 0, 0*u - 2*u = 4*a - 16. Let m(x) be the first derivative of -1 - 1/8*x**u + 1/12*x**3 + 0*x. Factor m(z).
z*(z - 1)/4
Factor 491*s**2 + 16 + 8 + 252*s + 391*s**2 + 1029*s**3.
3*(7*s + 2)**3
Suppose 19 = 2*c + 7. Factor 0*f - 6*f**2 - 2*f**4 + c*f**3 - 4 + 2*f + 4.
-2*f*(f - 1)**3
Suppose 0 = a - 4*m - 11, -4*a + 2*m = -3*m. Let b(i) = -5*i**3 + i**2 + i - 5. Let x(u) = 3*u**3 - u**2 - u + 3. Let y(j) = a*b(j) - 8*x(j). Factor y(o).
(o + 1)**3
Let d(h) = -h**3 + 4*h**2 - 9*h + 10. Let k(o) = -6*o**3 + 27*o**2 - 63*o + 69. Let z(