-2*k**4*(k + 1)/5
Let p(w) be the third derivative of -w**8/26880 - w**7/10080 + w**6/1440 - w**4/6 - 3*w**2. Let l(g) be the second derivative of p(g). Factor l(n).
-n*(n - 1)*(n + 2)/4
Factor 14/5*w**2 - 8/5 - 24/5*w.
2*(w - 2)*(7*w + 2)/5
Suppose -v = -8 + 4. Factor 0*p + v - 3 - p**2 - 2*p + 2*p**2.
(p - 1)**2
Let z be 0/2 - (1 - 1). Let q = -133/33 + 48/11. Determine d, given that -1/3 + q*d**2 + z*d = 0.
-1, 1
Let r(l) be the third derivative of -l**6/160 + l**5/40 + 7*l**2. Factor r(i).
-3*i**2*(i - 2)/4
Let a(m) be the second derivative of m**7/14 - 23*m**6/30 + 16*m**5/5 - 6*m**4 + 8*m**3/3 + 8*m**2 + 8*m. Determine c so that a(c) = 0.
-1/3, 2
Suppose -176 + 176 + w**3 - w = 0. What is w?
-1, 0, 1
Factor -122*t**3 - 18*t + 118*t**3 - 20*t**2 - 6*t.
-4*t*(t + 2)*(t + 3)
Let -8/5 + 26/5*b - 6/5*b**2 = 0. Calculate b.
1/3, 4
Suppose 3*o - 61 - 308 = 0. Let n = o + -859/7. Let 0 - n*g**4 + 2/7*g**3 + 2/7*g**2 - 2/7*g = 0. What is g?
-1, 0, 1
Let o(j) be the first derivative of j**6/42 + 3*j**5/35 + j**4/14 - 2*j**3/21 - 3*j**2/14 - j/7 + 5. Factor o(d).
(d - 1)*(d + 1)**4/7
Suppose 18*m = 17*m + 4. Suppose m = 11*y - 10*y. Factor 2/9 + 4/9*t**3 - 4/9*t + 0*t**2 - 2/9*t**y.
-2*(t - 1)**3*(t + 1)/9
Let t(j) = 4*j**3 - 3*j**2 + 6*j + 2. Let a(u) = 3*u**3 - 3*u**2 + 5*u + 1. Let m(h) = -6*a(h) + 4*t(h). Factor m(s).
-2*(s - 1)**3
Let j(n) be the first derivative of -n**4/6 - 4*n**3 - 36*n**2 - 144*n - 11. Find a such that j(a) = 0.
-6
Solve 3/4*z**2 + 0*z**3 + 0 + 3/8*z - 3/4*z**4 - 3/8*z**5 = 0 for z.
-1, 0, 1
Let b(a) be the second derivative of -a**4/4 + a**3 - 3*a**2/2 + 6*a. Determine w, given that b(w) = 0.
1
Let l = -30 - -25. Let d(o) = 7*o**2 - 3*o. Let x(j) = -j**2 + 3*j + 2*j**2 - 4*j. Let s(u) = l*x(u) + d(u). Factor s(q).
2*q*(q + 1)
Let j(v) be the second derivative of 27*v**6/50 + 99*v**5/50 + 157*v**4/60 + 22*v**3/15 + 2*v**2/5 - 12*v. Factor j(f).
(f + 1)**2*(9*f + 2)**2/5
Suppose 5*g - k - 11 = -3*k, -3*g + 11 = -k. Let z(x) be the second derivative of -3/10*x**5 - 1/10*x**6 + 3/2*x**2 - x + 0 + 0*x**4 + x**g. Factor z(i).
-3*(i - 1)*(i + 1)**3
Let p(n) = 2*n**2 - 4*n + 2. Let k be p(2). Suppose k*x = 2*o + 4*x + 8, -28 = -3*o + 5*x. Determine y, given that 1 - o + y**4 + 1 - 2*y**2 = 0.
-1, 1
Let n be ((-4)/(-12))/(-1)*(-2)/1. Factor -n - 2/3*v**2 + 4/3*v.
-2*(v - 1)**2/3
Solve 4*s**3 - 8*s**2 + 0*s + s + 8*s**3 + 2*s**5 - 8*s**4 + s = 0 for s.
0, 1
Suppose 5*y + 20 = 0, y + 3*y = 3*s - 16. Let k(p) be the second derivative of -1/12*p**4 + 0*p**3 + 0 - 2*p + s*p**2. Factor k(w).
-w**2
Suppose -y - b = -2*b, 0 = -y - 2*b + 6. Suppose -p - y*u = 3*u - 24, -4*p - 4 = -5*u. Factor 1/4*i**p + 0*i**2 - 1/4*i**3 + 0*i + 0.
i**3*(i - 1)/4
Suppose -12 = 4*z - 5*z - 2*y, -16 = -3*z - 2*y. Factor 1/2*m**2 - z + 0*m.
(m - 2)*(m + 2)/2
Let -75 - 27/4*o**2 - 45*o = 0. What is o?
-10/3
Let t(a) be the second derivative of -a**6/75 - 3*a**5/50 + 4*a**3/15 - 4*a. Determine p so that t(p) = 0.
-2, 0, 1
Let s(o) = -10*o**3 + 10*o**2 - 5. Let v(i) = -11*i**3 + 11*i**2 - i - 5. Let a(b) = -6*s(b) + 5*v(b). Factor a(k).
5*(k - 1)**2*(k + 1)
Let x(f) be the third derivative of 1/8*f**4 + 0*f - f**2 + 0*f**3 + 1/20*f**5 + 0. Factor x(u).
3*u*(u + 1)
Let s(h) be the third derivative of 0 + 0*h**3 + 0*h**5 + 0*h + 1/60*h**4 - 1/300*h**6 + 7*h**2. Determine f so that s(f) = 0.
-1, 0, 1
Determine u, given that 3 + u**2 + 2*u**2 - 8*u**2 + 2*u**2 = 0.
-1, 1
Suppose -3*i + 4*t = 25 - 3, -3*i = 2*t + 16. Let x be (40/(-18))/(i/9). Factor 4/3*s + x*s**2 + 0.
2*s*(5*s + 2)/3
Suppose -8*f + 210 = -3*f. Let l = -124/3 + f. Factor 2/3*o - l*o**3 + 0*o**2 + 0.
-2*o*(o - 1)*(o + 1)/3
Let -1/2*v**3 + 1/2*v + 0 + 0*v**2 = 0. Calculate v.
-1, 0, 1
Let l be (-28)/36*(-1)/3. Let f(k) be the first derivative of -8/15*k**5 + 4/27*k**3 + 1/6*k**4 + l*k**6 + 0*k**2 + 0*k - 2. Factor f(h).
2*h**2*(h - 1)**2*(7*h + 2)/9
Factor -1 + 2*z**2 + z**3 - 6*z - 3 + 5*z**3 + 2*z**4.
2*(z - 1)*(z + 1)**2*(z + 2)
Let j(k) = -k + 13. Let n be j(5). Solve -4*m**4 + 3*m**5 - n*m**2 + m**5 - 4*m + 12*m**4 = 0 for m.
-1, 0, 1
Suppose -15*r + 9*r + 12 = 0. Let s(a) be the second derivative of 9/20*a**4 - 3*a + 9/25*a**5 + 0 + 1/10*a**6 + 1/5*a**3 + 0*a**r. Find m such that s(m) = 0.
-1, -2/5, 0
Find u, given that 1 + 2*u**2 + 5/2*u + 1/2*u**3 = 0.
-2, -1
Let g(o) = o**2 - 6*o + 2. Let t be 36/10*(-5)/(-3). Let z be g(t). Determine k, given that 4/3*k + 8/3*k**3 + 0 + 2/3*k**4 + 10/3*k**z = 0.
-2, -1, 0
Let z be -1 - ((-264)/27)/8. Let m(c) be the second derivative of -1/9*c**4 + 0 + 0*c**2 - z*c**3 + c - 1/60*c**5. Factor m(x).
-x*(x + 2)**2/3
Let -1/4*z**2 - 1/4 + 1/2*z = 0. Calculate z.
1
Let m(t) = t**3 - 6*t**2 - 5*t - 10. Let o be m(7). Find w such that -3*w**4 + w**o + w**4 + w**2 = 0.
-1, 0, 1
Suppose 6*o = 4*o + 10. Let w(q) be the second derivative of 0*q**2 - 1/63*q**7 + 1/15*q**o - 1/9*q**3 + 0*q**6 + 0 + 0*q**4 + q. Find d, given that w(d) = 0.
-1, 0, 1
Determine d so that 82*d**2 - 68*d**2 + 2*d**3 - 26*d - 2*d**4 + 3 + 9 = 0.
-3, 1, 2
Let m = -20/7 + 22/7. Let n = -1/461 + 3695/3227. Solve 10/7*b - n*b**2 - m = 0.
1/4, 1
Let f(n) = -2*n**3 - n**2 - 3*n - 9. Let r(d) = -5 - d**2 - d**3 + 4*d - 19*d + 13*d. Let w(b) = 3*f(b) - 5*r(b). Factor w(p).
-(p - 2)*(p - 1)*(p + 1)
Let i = 15 + -12. Suppose 55*u**2 - u**i - 52*u**2 + 4*u**3 = 0. Calculate u.
-1, 0
Suppose -4*y + 3 + 13 = 0. Suppose 5*f = 2*t + 6, -y*f - t = -3*t - 4. Solve -32/5*b - 4/5 - 49/5*b**3 - 77/5*b**f = 0 for b.
-1, -2/7
Let i = 0 - 0. Suppose 4*l - 7 - 5 = i. Factor -3*m**3 + m**l - 7*m**4 - 3*m**5 - 2*m**5.
-m**3*(m + 1)*(5*m + 2)
Suppose 3*i - 4*i + 5 = 0. Suppose -3*d - 2*d - 5*j + 40 = 0, -i*d - 2*j = -31. Let 3*f**5 + 0*f**3 - 2*f**d - 2*f**3 + f = 0. What is f?
-1, 0, 1
Let w = -4 + 11. What is m in -3*m + 2*m - m**2 - 3*m**2 + w*m = 0?
0, 3/2
Let t = 808/2681 - 6/383. Factor 6/7 - t*g**2 + 4/7*g.
-2*(g - 3)*(g + 1)/7
Suppose p = v - 5, 5*v = -0*p + 4*p + 25. Suppose p*m - 3 = -m. Factor 4/7 - 4/7*h**2 - 6/7*h + 6/7*h**m.
2*(h - 1)*(h + 1)*(3*h - 2)/7
Let k(d) = d**2 + 9*d + 8. Let a(h) = h**2 + 6*h + 5. Let g(z) = 8*a(z) - 5*k(z). Suppose g(t) = 0. What is t?
-1, 0
Factor 0*x**2 + 6/5 + 9/5*x - 3/5*x**3.
-3*(x - 2)*(x + 1)**2/5
Let t(y) be the third derivative of -y**6/10 + 11*y**5/15 - 5*y**4/6 - 2*y**3 - 25*y**2. Let t(o) = 0. What is o?
-1/3, 1, 3
Let s(q) be the second derivative of 0*q**2 + 0*q**4 + q - 1/2*q**3 - 1/30*q**5 + 0 - 1/180*q**6. Let a(m) be the second derivative of s(m). Factor a(t).
-2*t*(t + 2)
What is z in -10/7*z**3 + 0 - 6/7*z + 16/7*z**2 = 0?
0, 3/5, 1
Let t(m) be the third derivative of -2*m**2 + 0*m**4 + 0*m - 1/210*m**7 + 0*m**3 + 0 + 1/120*m**6 - 1/336*m**8 + 1/60*m**5. Factor t(b).
-b**2*(b - 1)*(b + 1)**2
Let n(m) be the third derivative of m**6/900 - m**4/60 + 2*m**3/45 - 6*m**2. Factor n(y).
2*(y - 1)**2*(y + 2)/15
Find u, given that 7/2*u**2 - 9/4 + 1/4*u**5 + 1/2*u**3 - 3/4*u - 5/4*u**4 = 0.
-1, 1, 3
Suppose -1 = -w + 1. Factor -5/2*g**4 - 1/2*g**w - 4*g**3 + g + 0.
-g*(g + 1)**2*(5*g - 2)/2
Factor 3 - 5 - 6*j**2 + 4 + 3*j**4 + 1.
3*(j - 1)**2*(j + 1)**2
Suppose 3*h - 5*h = -6. Suppose h*i + 22 = 5*l, 8 - 2 = -3*l - 3*i. Solve 0*n - 2/3*n**3 + 0*n**l + 2/3*n**4 + 0 = 0 for n.
0, 1
Let c(t) = -t**2 + 3*t - 2. Let l(q) = 15*q**2 - 48*q + 33. Let b(o) = 33*c(o) + 2*l(o). Factor b(m).
-3*m*(m - 1)
Let v(f) = 2*f**2 - 95*f - 46. Let a be v(48). Factor 2/5*j + 2/5*j**a - 4/5.
2*(j - 1)*(j + 2)/5
Factor -4/3 + 2/3*d**2 - 2/3*d.
2*(d - 2)*(d + 1)/3
Let w be 4/2 + (5 - 4). Factor 1 + 2*i**w + 2 - 6 + 2*i**2 + 1 - 2*i.
2*(i - 1)*(i + 1)**2
Let h(n) = -2*n**2 - 8*n + 4. Let l(o) be the first derivative of 17/2*o**2 + 5/3*o**3 + 1/4*o**4 - 8*o - 2. Let b(g) = 5*h(g) + 2*l(g). Factor b(s).
2*(s - 1)**2*(s + 2)
Suppose -16 = -0*v - 4*v. Suppose 4*t = 3*n - 17, 0 = n - v*t - 3 - 8. Factor -4*g**3 + 3 + 4*g**3 + n*g**4 - 6*g**2.
3*(g - 1)**2*(g + 1)**2
Let x(w) be the third derivative of 0*w**4 + 0*w - 3/40*w**6 + 1/35*w**7 + 0 + 6*w**2 + 1/20*w**5 + 0*w**3. Factor x(n).
3*n**2*(n - 1)*(2*n - 1)
Solve -8*k - 18 - 4*k**2 + 15 + k**4 - 2*k**2 = 0.
-1, 3
Let n(w) be the second derivative of 0*w**2 - 2/21*w**3 + 3*w - 1/10*w**5 - 3/14*w**4 + 0. Factor n(o).
-2*o*(o + 1)*(7*o + 2)/7
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