-1, 0
Let s(u) be the second derivative of u**6/20 - u**5/15 + u**4/36 - u**2 - u. Let c(v) be the first derivative of s(v). Factor c(h).
2*h*(3*h - 1)**2/3
Let o(q) = q + 2. Let x(c) = c**2 + 4*c + 2. Let k be x(-4). Let a be o(k). Suppose 2*z + 14/3*z**2 - a*z**4 - 2/3 - 22/3*z**3 + 16/3*z**5 = 0. What is z?
-1, -1/2, 1/4, 1
Let h(f) = f**2 - 4*f + 2. Let j be h(10). Let w = j + -121/2. Find z such that 3/2*z**3 + 3/2 - 3/2*z - w*z**2 = 0.
-1, 1
Let f = -4245999/301 - -98746/7. Let p = f - -1/43. Factor 0 + p*x**3 - 2/7*x**2 + 2/7*x**4 - 2/7*x.
2*x*(x - 1)*(x + 1)**2/7
Let d(u) be the first derivative of -1/6*u**2 + 2/3*u - 8/9*u**3 - 5/12*u**4 + 1. Let d(j) = 0. What is j?
-1, 2/5
Let y(m) be the third derivative of -m**6/420 - 2*m**5/105 + 5*m**4/84 + 2*m**2 + 35. Solve y(w) = 0.
-5, 0, 1
Suppose -4*f + 7*t = 4*t - 11, f - 3*t - 5 = 0. Suppose -3*w + m + 3 = 0, -2*w + f*m = m - 1. Let -o**4 + 2*o**3 + o**w + 2*o**4 + 0*o**3 = 0. Calculate o.
-1, 0
Factor -1/2*l**2 + 0 + 0*l - 1/6*l**3.
-l**2*(l + 3)/6
Let j be ((-2)/(-4))/((-1)/(-12)). Suppose 0 = j*x - 2*x - 8. Factor 0 - n**2 + 4*n**3 - 5*n**3 - 1 + n + x.
-(n - 1)*(n + 1)**2
Let x be (18/10)/((-21)/(-14)). Factor 2/5*b**2 + 4/5 - x*b.
2*(b - 2)*(b - 1)/5
Let n(m) be the second derivative of m**5/30 + 5*m**4/18 + 7*m**3/9 + m**2 + 36*m. Factor n(x).
2*(x + 1)**2*(x + 3)/3
Let x(l) be the first derivative of -8/39*l**3 - 1/26*l**4 - 4/13*l - 5/13*l**2 - 8. Factor x(q).
-2*(q + 1)**2*(q + 2)/13
Let d(x) be the third derivative of x**7/630 - x**6/180 + x**5/180 + 47*x**2. Solve d(a) = 0 for a.
0, 1
Let h(r) be the third derivative of r**8/448 + r**7/420 - r**6/80 - r**5/60 + r**4/32 + r**3/12 - 9*r**2. Find x, given that h(x) = 0.
-1, -2/3, 1
Suppose -2*z - 3*z + 15 = 0. Factor 4*h**3 + 0*h**z + 8*h**2 + 24*h**4 - 28*h**4.
-4*h**2*(h - 2)*(h + 1)
Let a(d) be the third derivative of 7*d**5/30 + 2*d**4/3 + 16*d**3/3 + 8*d**2. Let s(l) = -9*l**2 - 11*l - 21. Let k(t) = 5*a(t) + 8*s(t). Factor k(o).
-2*(o + 2)**2
Let g(c) be the third derivative of -c**2 + 5/12*c**4 + 7/30*c**5 + 0 - 2/3*c**3 + 0*c. Determine x so that g(x) = 0.
-1, 2/7
Let c be (-1 - 1)*(-4 - -2). Suppose -c*f - 25 = -6*y + 3*y, 4*y = -5*f - 8. Solve 2/7*d**2 + 2/7*d**y - 2/7*d - 2/7 = 0.
-1, 1
Let a(o) = o**2 - 28*o + 3. Let m be a(28). Factor 1/3 + 1/3*g**m + g + g**2.
(g + 1)**3/3
Suppose -2*p + 8 = -4*g, p + 10 = 3*p - 5*g. Factor -2*t - 5*t**2 + 2*t**2 + p*t**2 + 8*t.
-3*t*(t - 2)
Let v(s) be the third derivative of -s**5/20 + 2*s**3 + 13*s**2. Factor v(k).
-3*(k - 2)*(k + 2)
Let r be (-12 - (-1432)/120)*-1*5. Factor 4/3 - 4/3*i + r*i**2.
(i - 2)**2/3
Let c(i) be the second derivative of i**6/15 - 4*i**5/15 + i**4/3 - i**2/3 + 3*i. Determine w, given that c(w) = 0.
-1/3, 1
Let v(a) = -a**3 + a**2. Let o be (3/6)/(2/4). Let d(y) = -9*y**3 - 3*y**2 + 24*y - 12. Let n(q) = o*d(q) - 12*v(q). Factor n(p).
3*(p - 2)**2*(p - 1)
Let b be 4/(-2) - 4*-1. Let d = 52 - 47. What is m in 3/4*m**3 + 0 + 3/4*m**d - 1/2*m + 3/4*m**b - 7/4*m**4 = 0?
-2/3, 0, 1
Let c(k) be the second derivative of k**7/2520 - k**6/1080 - k**5/360 + k**4/72 - k**3/2 + 3*k. Let i(q) be the second derivative of c(q). Factor i(m).
(m - 1)**2*(m + 1)/3
Let l(q) = q**3 - 6*q**2 - q + 6. Let a(j) = -j**2 + 1. Suppose 3*b + b + 2 = 5*y, 0 = 5*y + b - 12. Let r(g) = y*l(g) - 14*a(g). Factor r(k).
2*(k - 1)*(k + 1)**2
Let i(y) be the first derivative of -4*y**2 + 8*y + 2/3*y**3 + 1. Factor i(a).
2*(a - 2)**2
Let r = 7 - 5. Factor -3 - 1 + 2*h + 4 + 2*h**r.
2*h*(h + 1)
Let j(w) be the second derivative of w**6/60 - w**5/15 - w**4/12 + 2*w**3/3 - w**2 + 5*w. Let s(f) be the first derivative of j(f). Factor s(d).
2*(d - 2)*(d - 1)*(d + 1)
Let d be (-2 + 0 + 2)*1. Let r = 0 - d. Let 2*p**3 - 2*p**2 + r*p**2 + 0*p**3 = 0. Calculate p.
0, 1
Let o = -1759/525 - -84/25. Let w(v) be the third derivative of 0*v**3 + 0*v + 0 + 0*v**5 - o*v**7 - 4*v**2 + 0*v**4 - 1/60*v**6. Find i, given that w(i) = 0.
-1, 0
Let u be 10/4*44/55. Solve 7*b**3 - 19*b**3 + 3*b**4 + 12*b**2 + u*b - 2*b = 0 for b.
0, 2
Let u(q) = -q + 9. Let z be u(5). Factor -3*a**2 + 10*a + 6*a**2 + 6*a**3 + 3 + 9*a**2 + a**z + 0*a**4.
(a + 1)**3*(a + 3)
Let b be (-6)/(-15) - 14/10. Let o(n) = -n**2 - 2*n + 3. Let t(a) = -a**2 + 1. Suppose 0 = -2*y - y + 6. Let i(c) = b*o(c) + y*t(c). Factor i(d).
-(d - 1)**2
Let f = 5974/7 - 852. Factor f*j**2 - 4/7 - 4/7*j**3 - 2/7*j.
-2*(j - 2)*(j - 1)*(2*j + 1)/7
Let z(r) be the second derivative of -r**5/140 + r**4/42 - 38*r. Find t, given that z(t) = 0.
0, 2
Suppose 3*n - 4*u = 17, 6*n - 4*n - 2*u = 10. Factor -s**4 + 6/5*s**2 - 2/5*s**n + 3/5*s**5 - 1/5*s - 1/5.
(s - 1)**3*(s + 1)*(3*s + 1)/5
Let h(s) = -19*s**2 - 16*s - 21. Let u(t) = -t**2 - 4*t - 6. Let m be u(-4). Let x(c) = -9*c**2 - 8*c - 10. Let w(n) = m*h(n) + 13*x(n). Factor w(p).
-(p + 2)*(3*p + 2)
Factor l**2 + 3*l**4 - 3*l**2 - 6*l**3 + 9*l**2 - 4*l**2.
3*l**2*(l - 1)**2
Let p(c) = c**2 - 1 + 1 + 3*c + c**4 + 7*c**3. Let v(q) = -2*q**4 - 8*q**3 - 2*q**2 - 4*q. Let z(o) = 4*p(o) + 3*v(o). Factor z(l).
-2*l**2*(l - 1)**2
Let s(u) be the third derivative of u**6/360 + u**5/90 - u**4/72 - u**3/9 + 7*u**2. Factor s(y).
(y - 1)*(y + 1)*(y + 2)/3
Suppose p - w + 0*w + 14 = 0, -4*p + 2*w = 46. Let n = -7 - p. Solve 4*y**2 - 2*y**4 - 8*y**2 + 7*y**4 + n - 3*y**4 = 0 for y.
-1, 1
What is q in -3*q**4 + 26 - 26 - 12*q**2 + 15*q**3 = 0?
0, 1, 4
Let m(u) be the third derivative of u**5/18 + 2*u**4/9 - 4*u**3/9 - 10*u**2. Factor m(c).
2*(c + 2)*(5*c - 2)/3
Let z(x) be the second derivative of 0 - 1/3*x**3 - 1/6*x**4 + 0*x**2 - 7*x. Factor z(d).
-2*d*(d + 1)
Let s(j) be the first derivative of 5*j**6/6 - 2*j**5 - 5*j**4 + 40*j**3/3 - 16. Factor s(m).
5*m**2*(m - 2)**2*(m + 2)
Let l(w) = 5*w + 1. Let y be l(-1). Let z be 0*((-2)/y)/1. Factor 0*q**2 + z - 2/7*q + 2/7*q**3.
2*q*(q - 1)*(q + 1)/7
Let y be 6 - (-4)/(5 + -4). Factor -y*l + 10*l + 8*l**3 - 4*l - 4*l**5.
-4*l*(l - 1)**2*(l + 1)**2
Suppose 3/2*u**3 - 135/2*u**2 - 10125/2 + 2025/2*u = 0. What is u?
15
Let n(s) be the first derivative of 3*s**5/25 + 3*s**4/5 + 6*s**3/5 + 6*s**2/5 + 3*s/5 - 2. Factor n(q).
3*(q + 1)**4/5
Let a = -16 + 20. Let h(d) be the third derivative of 0*d**3 + 1/420*d**7 + 1/120*d**5 + 0 + 1/120*d**6 + 0*d**a - 2*d**2 + 0*d. Factor h(l).
l**2*(l + 1)**2/2
Let g(l) = -3*l**4 + 5*l**2 - 18*l + 14. Let t(k) = 19*k**4 + k**3 - 29*k**2 + 107*k - 85. Let f(i) = -39*g(i) - 6*t(i). Factor f(q).
3*(q - 2)**2*(q - 1)*(q + 3)
Suppose 0 = -7*l + 12*l. Let n(h) be the first derivative of 2 + 2/9*h**2 + l*h + 2/27*h**3. Factor n(g).
2*g*(g + 2)/9
Let d(m) = -5*m**2 - 10*m - 10. Let u(n) = -n**2 - n - 1. Let k(f) = d(f) - 10*u(f). Determine t, given that k(t) = 0.
0
Suppose 1/8*o**5 - 1/4*o**2 + 3/2*o - 7/8*o**3 + 0*o**4 + 1 = 0. What is o?
-2, -1, 2
Factor 18/7 + 2/7*z**2 - 12/7*z.
2*(z - 3)**2/7
Let t(r) = 6*r**3 - 6*r**2 - 4*r + 8. Let d(b) = 4*b**3 - 4*b**2 - 3*b + 5. Let p(g) = 8*d(g) - 5*t(g). Suppose p(a) = 0. What is a?
-1, 0, 2
Let i(q) be the third derivative of -1/54*q**4 - 8*q**2 - 1/270*q**5 + 0*q - 1/27*q**3 + 0. Determine k so that i(k) = 0.
-1
Let t(l) be the third derivative of -1/2352*l**8 + 0*l**4 + 0*l**3 + 7*l**2 + 0*l**7 + 0*l**5 + 0 + 1/840*l**6 + 0*l. Factor t(a).
-a**3*(a - 1)*(a + 1)/7
Let z(i) = -i**2 + 5*i - 4. Let d be z(4). Let j(l) be the third derivative of 1/2*l**4 + 0 - 1/3*l**3 + d*l - 3/10*l**5 + l**2 + 1/15*l**6. Factor j(f).
2*(f - 1)**2*(4*f - 1)
Determine c so that -9*c**2 + 2*c**4 + 6*c**3 + 4*c - c**2 - 6*c**5 + 4*c**5 = 0.
-2, 0, 1
Let s(u) = u**2 + u - 1. Let x(h) = -4*h**3 + 12*h**2 + 16*h - 8. Let a(j) = 8*s(j) - x(j). Solve a(w) = 0 for w.
-1, 0, 2
Let x = -14 + 14. Let v(t) be the third derivative of x*t**3 + 0 - 2*t**2 + 0*t + 1/300*t**6 + 1/60*t**4 - 1/75*t**5. Solve v(k) = 0.
0, 1
Let n(x) = -14*x**4 + 4*x**3 + 24*x**2 - 40*x - 8. Let j(b) = 5*b**4 - b**3 - 8*b**2 + 13*b + 3. Let g(u) = -8*j(u) - 3*n(u). Determine m, given that g(m) = 0.
-2, 0, 2
Let r(i) = -5*i**3 + i**2 + 11*i. Let b = -5 + 9. Let h(s) = s**3 - 2*s. Let x(m) = b*r(m) + 22*h(m). Suppose x(q) = 0. What is q?
-2, 0
Let z = 1208 - 1204. Factor 3/5*k**3 + 1/5*k**2 + 1/5*k**5 + 3/5*k**z + 0*k + 0.
k**2*(k + 1)**3/5
Let j**2 + j**2 + j**2 = 0. What