Suppose m = 5*h + 5*m - 8, -5*m = 3*h - 10. Let b = -514 + 2578/5. Suppose -2/5*u**3 - b*u**2 - 8/5*u + h = 0. What is u?
-2, 0
Suppose -2*i + 0 = -6. What is o in -3*o**2 + 2*o**i - 4 + 6 + o**2 - 2*o = 0?
-1, 1
Let z(i) be the third derivative of -i**6/40 + 9*i**5/20 - 27*i**4/8 + 27*i**3/2 - 16*i**2. Solve z(g) = 0.
3
Let v be (-4 - 0)*1/(-1). Suppose 0*y - y = -2. Factor f**4 - 4*f**v + 2*f**2 + y*f**3 - 3*f**3.
-f**2*(f + 1)*(3*f - 2)
Let x(z) be the third derivative of -z**7/105 + z**2. Suppose x(p) = 0. Calculate p.
0
Let h(k) = 5*k**4 + 4*k**3 + 4*k**2 + 4*k + 4. Let w(r) = -6*r**4 - 5*r**3 - 5*r**2 - 5*r - 5. Let j(u) = -5*h(u) - 4*w(u). Factor j(l).
-l**4
Let f(q) be the third derivative of -q**7/735 + q**6/140 - q**5/105 - 43*q**2. Suppose f(l) = 0. Calculate l.
0, 1, 2
Let g(h) = 4*h**4 + 4*h**3. Let t be -3*(2 + -5 + 0). Let f(m) = 17*m**4 + 17*m**3. Let s(r) = t*g(r) - 2*f(r). Suppose s(u) = 0. Calculate u.
-1, 0
Let o(y) = y**2 - 9*y + 9. Let s be o(8). Let l be (-4)/((-2)/s)*2. Factor -10*i**3 - 7*i + 6*i - i**5 + l*i**3 + 4*i**2 + 4*i**4.
-i*(i - 1)**4
Suppose -4*f = 5*h + 51, -2*h + 2*f - 4 - 2 = 0. Let k be ((-1)/14)/(h/224). Factor k - 40/7*b + 36/7*b**2 + 2/7*b**4 - 2*b**3.
2*(b - 2)**3*(b - 1)/7
Let v(l) be the first derivative of l**4/12 + l**3/6 + 8*l + 3. Let z(x) be the first derivative of v(x). Find t such that z(t) = 0.
-1, 0
Suppose -2*w - 3*w + 20 = 0. Factor 4 - w - o + o**2.
o*(o - 1)
Let c(t) be the first derivative of -t**5/20 - t**4/8 - t**3/12 + 3. Factor c(x).
-x**2*(x + 1)**2/4
Factor 4/3*a**2 + 8/3*a + 0.
4*a*(a + 2)/3
Suppose -2*r = -4*j - r + 5, 0 = -3*j + 3*r - 3. Factor 3*u**2 + 0*u**2 - 5*u + j - 2*u**2 + 2*u.
(u - 2)*(u - 1)
Let z(g) be the first derivative of -2*g**3/15 - 2*g**2 - 10*g - 5. Let z(r) = 0. What is r?
-5
Factor 12/5 + 0*s - 3/5*s**3 - 9/5*s**2.
-3*(s - 1)*(s + 2)**2/5
Let h = 605 - 2871/5. Find r, given that -h*r**2 - 8/5 + 64/5*r + 98/5*r**3 = 0.
2/7, 1
Factor 27/7*z**4 + 3/7*z**5 + 48/7 + 144/7*z + 96/7*z**3 + 24*z**2.
3*(z + 1)*(z + 2)**4/7
Let f(j) be the third derivative of 1/40*j**5 + 0 + 0*j - 1/8*j**4 - 6*j**2 + 0*j**3. Solve f(s) = 0.
0, 2
Let g(l) be the second derivative of -l**4/15 - 2*l**3/15 + 4*l**2/5 + 2*l - 10. What is r in g(r) = 0?
-2, 1
Let c be (14/4 - 2)/(2/4). Let s(t) be the second derivative of 1/2*t**4 + t**c - 2*t + t**2 + 1/10*t**5 + 0. Suppose s(v) = 0. What is v?
-1
Let o = 881/15 - 214/3. Let m = o + 13. What is z in -4/5 - m*z + 8/5*z**2 + 6/5*z**3 = 0?
-1, 2/3
Let y be 2*(-1)/6*9. Let b = y - -4. Factor b - x**4 - 4*x**3 + 4*x**2 - 3 - x**4 + 2*x + 2*x**5.
2*(x - 1)**3*(x + 1)**2
Let u(s) = 7*s**4 + 3*s**3 + 5*s**2 + 9*s + 5. Let a(b) = b**4 - b**3 - b**2 + b + 1. Let v(j) = 5*a(j) - u(j). Suppose v(i) = 0. What is i?
-2, -1, 0
Let r = 59 - 117/2. Factor 0*u**3 + 0 - 1/2*u**4 + r*u**2 + 0*u.
-u**2*(u - 1)*(u + 1)/2
Suppose w - 4 = 4*t - 0*t, -2 = -4*w + 2*t. Let b(f) be the third derivative of f**2 - 1/60*f**5 + w*f + 1/6*f**3 + 0*f**4 + 0. Factor b(i).
-(i - 1)*(i + 1)
Let c(k) be the first derivative of 11*k**5/5 - 35*k**4/4 + 13*k**3 - 17*k**2/2 + 2*k + 11. Factor c(f).
(f - 1)**3*(11*f - 2)
Let c = -950/3 + 318. Let v = 10/21 - 1/7. Factor 0 + c*d**2 - 4/3*d - v*d**3.
-d*(d - 2)**2/3
Suppose -30*t + 54 = -3*t. Factor -4/9*u - 2/9*u**t + 0.
-2*u*(u + 2)/9
Solve 0 + 2/3*n**5 + 0*n**2 + 0*n**4 + 2/3*n - 4/3*n**3 = 0.
-1, 0, 1
Let y = 3086 + -21869/7. Let z = y - -39. Suppose 2/7 + z*u**2 + 6/7*u + 2/7*u**3 = 0. What is u?
-1
Suppose 14 = -2*s - 4*i - 0*i, 8 = s - i. Determine m, given that 1/4 - 1/4*m**s - 1/4*m**2 + 1/4*m = 0.
-1, 1
Let l(j) be the third derivative of j**8/546 - j**7/195 - 3*j**6/130 + 2*j**5/195 + 7*j**4/78 + j**3/13 + 12*j**2. Solve l(b) = 0 for b.
-1, -1/4, 1, 3
Suppose -23 = 3*x + 2*i + 2*i, -5*i - 24 = -x. Let d be (-12 + 14)/(x/(-2)). Factor -1/5*m**5 + 0 + 0*m - 3/5*m**3 + 1/5*m**2 + 3/5*m**d.
-m**2*(m - 1)**3/5
What is h in -1 + 4*h**5 - 28*h**3 - 4*h**2 + 4 + 1 + 12*h**5 + 12*h = 0?
-1, -1/2, 1
Let o be (-49)/(-14)*12/14. Let x(u) be the first derivative of 2*u + 11/2*u**2 + 3*u**o - 3. Factor x(q).
(q + 1)*(9*q + 2)
Let v(y) be the first derivative of -y**4/6 - 2*y**3/3 + y - 3. Let x(p) be the first derivative of v(p). Determine i, given that x(i) = 0.
-2, 0
Factor -2/3 - 4/3*x**2 + 3*x.
-(x - 2)*(4*x - 1)/3
Let b(w) be the second derivative of 0*w**5 - 1/12*w**3 + 1/30*w**6 - 1/12*w**4 + 1/84*w**7 + 0 + 3*w + 0*w**2. Factor b(c).
c*(c - 1)*(c + 1)**3/2
Let f(g) be the first derivative of 25*g**3/3 - 65*g**2/2 - 30*g - 28. Factor f(q).
5*(q - 3)*(5*q + 2)
Let y(q) = q**2 - 6*q + 11. Let d be y(5). Let c(f) = f**3 - 5*f**2 - 8*f + 12. Let t be c(d). What is k in 4/3*k**2 + 10/3*k**3 + t*k + 0 - 14/3*k**4 = 0?
-2/7, 0, 1
Let f(g) be the first derivative of 2*g**5/5 - 5*g**4 + 24*g**3 - 54*g**2 + 54*g + 13. Factor f(r).
2*(r - 3)**3*(r - 1)
Let y = 753/7 + -107. Factor y*j**3 - 6/7*j**5 - 10/7*j**4 + 0*j + 0*j**2 + 0.
-2*j**3*(j + 2)*(3*j - 1)/7
Let l = 10 - 10. Let w(t) be the second derivative of -2*t - 1/15*t**6 - 4/63*t**7 + 1/6*t**4 + 1/6*t**5 + 0 - 1/9*t**3 + l*t**2. Find n such that w(n) = 0.
-1, 0, 1/4, 1
Suppose z - 4 = -w - 1, 26 = 4*z - 3*w. Let l(g) be the second derivative of 0*g**2 + 0 + 0*g**4 + 0*g**3 + 1/20*g**z - g. Factor l(d).
d**3
Let a(u) be the second derivative of 7/4*u**3 + 0 + u + 3/8*u**5 + 1/20*u**6 + 3/2*u**2 + 9/8*u**4. Factor a(z).
3*(z + 1)**3*(z + 2)/2
Let k(y) = -y**3 - y**2. Let m(q) = -q**4 - 2*q**3 - 4*q**2. Let j(h) = -4*k(h) + m(h). Solve j(f) = 0.
0, 2
Let c(d) be the first derivative of -5*d**7/189 - 7*d**6/135 - d**5/45 - 5*d - 7. Let w(a) be the first derivative of c(a). Factor w(p).
-2*p**3*(p + 1)*(5*p + 2)/9
Solve 0 + 16/3*u**4 + 8/3*u**2 + 20/3*u**3 + 4/3*u**5 + 0*u = 0.
-2, -1, 0
Let h(x) be the first derivative of -2*x**5/25 + 11*x**4/5 - 94*x**3/5 + 44*x**2 - 40*x + 13. Factor h(f).
-2*(f - 10)**2*(f - 1)**2/5
Let z(v) be the second derivative of v + 1/30*v**5 + 0*v**3 + 0 + 1/6*v**2 - 1/12*v**4. Suppose z(p) = 0. Calculate p.
-1/2, 1
Factor 0*o - 8/9*o**4 + 7/9*o**3 - 2/9*o**2 + 0 + 1/3*o**5.
o**2*(o - 1)**2*(3*o - 2)/9
Let d(m) be the second derivative of 0*m**3 - 1/168*m**7 + 0 - 1/40*m**6 - 1/48*m**4 + 5*m - 3/80*m**5 + 0*m**2. What is l in d(l) = 0?
-1, 0
Let x = -9/2 + 6. Factor 0 + 5/2*c**2 + 7/2*c**3 + x*c**4 + 1/2*c.
c*(c + 1)**2*(3*c + 1)/2
Let n = -171 - -859/5. Factor 0*a**2 - 2/5*a**5 + 0 - 2/5*a**3 + n*a**4 + 0*a.
-2*a**3*(a - 1)**2/5
Suppose -s - 4 = -5*s. Let i = s + 1. What is a in 3*a + 0 - 3/2*a**i = 0?
0, 2
Suppose 0*d**4 + 0 + 0*d**2 + 2/5*d**5 - 4/5*d**3 + 2/5*d = 0. Calculate d.
-1, 0, 1
Let r(b) be the second derivative of -4*b**5/5 - b**4/3 - 7*b. Factor r(z).
-4*z**2*(4*z + 1)
Let r(d) = 3*d**2 + 2*d - 1. Let u(v) = 5*v**2 + 4*v - 1. Let a(s) = -7*r(s) + 4*u(s). Let l be a(3). Factor l*x - 1/3*x**2 + 1/3.
-(x - 1)*(x + 1)/3
Let d(a) be the first derivative of 2*a**3/3 + 4*a**2/5 - 2*a/5 - 3. Suppose d(z) = 0. Calculate z.
-1, 1/5
Let w = -1 - -2. Let l = 5 + -6. Let x(g) = -2*g**2 + g + 2. Let z(h) = h. Let v(t) = l*z(t) + w*x(t). Factor v(s).
-2*(s - 1)*(s + 1)
Let s = -3698/67 + -181479/469. Let c = s - -443. Determine b, given that -8/7*b**3 + 2/7*b + 0 - c*b**2 = 0.
-1, 0, 1/4
Factor 15*s**2 + 6*s**3 + s - 36*s**2 + 2*s + 12*s**2.
3*s*(s - 1)*(2*s - 1)
Factor 3/2*b**2 - 1 + 1/2*b.
(b + 1)*(3*b - 2)/2
Let z be (7 + -5)/((-12)/21). Let m = z + 4. Factor -1/2*j**2 + 0 - j + m*j**3.
j*(j - 2)*(j + 1)/2
Factor -2/15*r**4 + 0 + 0*r**3 + 0*r + 0*r**2.
-2*r**4/15
Let j(b) = -2*b**3 + b**2 - b. Let f(x) = 5*x**4 - 60*x**3 + 70*x**2 - 45*x. Let m(d) = -f(d) + 15*j(d). Factor m(i).
-5*i*(i - 3)*(i - 2)*(i - 1)
Let y(p) be the second derivative of p**4/12 + p**3/3 + p**2/2 + 3*p. Let y(z) = 0. Calculate z.
-1
Let k = 199/3 - 66. Suppose 0*w - 2*w = 0. Solve -1/3*t**2 + w*t + k = 0.
-1, 1
Let c(m) = m + 3. Let d be c(-3). Let q = 1/258 + 343/258. Determine l so that d - 4/3*l**4 + 2/3*l**5 + 0*l**3 + q*l**2 - 2/3*l = 0.
-1, 0, 1
Let i(b) be the third derivative of b**8/1008 + b**7/630 - 3*b**2. Find j, given that i(j) = 0.
-1, 0
Let v = -30 - -64. Suppose 0 = -5*o + v + 11. What is z in 9*z - 2*z**5 - 2*z**4 - o*z = 0?
-1, 0
Factor -4/7*o**2 + 0 - 2/7*o**