4 - 8/3 - 1/2*r**5 + 8/3*r = 0. What is r?
-2/3, 1, 2
Suppose 5*v - 6 = -3*n + 2*v, -5*n = -3*v - 34. Factor 6*l**4 + l**n - l**5 - 3*l**3 + 3*l**5 - 6*l**5.
-3*l**3*(l - 1)**2
Let a = 8 - 5. Factor -31*r**a - 4 + 11*r**3 + 14*r - r**2 - r**2.
-2*(r + 1)*(2*r - 1)*(5*r - 2)
Let s(n) = 13*n**4 - 69*n**3 + 87*n**2 - 38*n + 9. Let j(d) = 38*d**4 - 206*d**3 + 262*d**2 - 114*d + 28. Let r(a) = 3*j(a) - 10*s(a). Factor r(h).
-2*(h - 3)*(2*h - 1)**3
Let x(w) be the first derivative of 3/8*w**4 + 1/2*w**3 + 0*w - 3/10*w**5 - 3/4*w**2 - 2. Suppose x(m) = 0. Calculate m.
-1, 0, 1
Let m(b) be the third derivative of b**6/480 - b**5/240 - 5*b**4/96 - b**3/8 + 22*b**2. Find i, given that m(i) = 0.
-1, 3
Let x = -3 + 7. Factor -x*v**5 + 9*v**4 + 3*v**4 + 4*v**2 + 3*v**3 - 14*v**3 - v**3.
-4*v**2*(v - 1)**3
Let f(r) be the first derivative of -1/42*r**6 - 2/35*r**5 + 0*r**2 + 0*r + 0*r**3 - 1/28*r**4 + 1. Factor f(g).
-g**3*(g + 1)**2/7
Let h(z) be the first derivative of z**6/54 + 2*z**5/45 - z**4/18 - 8*z**3/27 - 7*z**2/18 - 2*z/9 + 7. Factor h(i).
(i - 2)*(i + 1)**4/9
Let n(q) be the third derivative of -q**7/525 - q**6/150 - q**5/150 + 8*q**2. Let n(v) = 0. What is v?
-1, 0
Suppose -3*j + 4*i = 14, 3*j - 1 = i - 0. Factor -2*p + 2*p**3 + p**3 + j*p - 2*p**4 - p.
-p*(p - 1)**2*(2*p + 1)
Let b = -31 - -33. Let i(n) be the first derivative of -4/5*n - 1/5*n**b + 3 + 2/15*n**3. Factor i(w).
2*(w - 2)*(w + 1)/5
Factor -u + 1/6*u**2 + 5/6.
(u - 5)*(u - 1)/6
Let h(l) be the first derivative of -4*l**5/5 + 11*l**4/4 - 5*l**3/3 - l**2 + 17. Determine r, given that h(r) = 0.
-1/4, 0, 1, 2
Let m(q) be the second derivative of q**5/38 + 3*q**4/19 + 4*q**3/19 - 8*q**2/19 + 23*q. Factor m(o).
2*(o + 2)**2*(5*o - 2)/19
Suppose 48*g - 41*g = 0. Factor 1/4*r**2 + g + 1/4*r.
r*(r + 1)/4
Let x(i) be the first derivative of 3 + 0*i - 2/27*i**3 + 2/9*i**2. Factor x(d).
-2*d*(d - 2)/9
Determine k so that k + 0 + 9*k**5 + 0 - 11*k**4 + 4*k**2 - k**4 - 2*k**3 = 0.
-1/3, 0, 1
Let m = 0 - 1. Let n(s) be the third derivative of s**6/120 + s**4/24 - 2*s**2. Let q(h) = 4*h**3 + 4*h**2 + 7*h. Let d(y) = m*q(y) + 3*n(y). Factor d(f).
-f*(f + 2)**2
Let f(n) be the second derivative of -n + 1/15*n**6 + 1/2*n**4 + 0 + 0*n**2 + 3/10*n**5 + 1/3*n**3. Factor f(c).
2*c*(c + 1)**3
Let k be 12/8*14/21. Factor 3/2*w + k - 1/2*w**3 + 0*w**2.
-(w - 2)*(w + 1)**2/2
Factor 2/9*b + 4/9 - 2/9*b**2.
-2*(b - 2)*(b + 1)/9
Suppose -12 = -4*x + 4. Factor -3*b**2 - 4 + x - 3*b**3 + 2 + 3*b + b**2.
-(b - 1)*(b + 1)*(3*b + 2)
Factor 1/6*m**2 + 0 + 0*m.
m**2/6
Factor 6*f**2 - 2*f**2 - 4*f - 2*f**2.
2*f*(f - 2)
Let q = -161/2 + 82. Suppose 46*s + 52 = 59*s. Suppose u**3 - 1/4 - q*u**2 + u - 1/4*u**s = 0. What is u?
1
Let j(y) = y**3 + y**2 - 1. Let x(w) = -12*w**3 - 10*w**2 + w + 10. Let v(a) = -44*j(a) - 4*x(a). Factor v(c).
4*(c - 1)**2*(c + 1)
Find n such that -6/7*n - 2/7*n**2 + 0 = 0.
-3, 0
Suppose 3*b = -2*b. Suppose -6*u + 7 + 11 = b. Find y, given that y**2 - y - 1/3*y**u + 1/3 = 0.
1
Let c be (-18)/99 - 3/((-66)/70). Factor -2/3 + 2/3*o**2 + 2/3*o**c - 2/3*o.
2*(o - 1)*(o + 1)**2/3
Let n(u) be the third derivative of 5*u**8/336 - u**6/12 + 5*u**4/24 - 31*u**2. Factor n(k).
5*k*(k - 1)**2*(k + 1)**2
Let k(a) = a**4 + 3*a**3 + 5*a - 5. Let h(p) = p**4 + 4*p**3 + 6*p - 6. Let z(l) = -5*h(l) + 6*k(l). Determine q, given that z(q) = 0.
0, 2
Let t(o) be the first derivative of 1/15*o**3 + 0*o + 0*o**2 + 5. Factor t(y).
y**2/5
Let n(b) be the second derivative of 11/6*b**4 + 2/3*b**3 + 1/12*b**6 + 0 + 0*b**2 + 33/20*b**5 + 6*b - 25/84*b**7. Solve n(f) = 0 for f.
-1, -2/5, 0, 2
Let u(j) be the third derivative of -j**7/70 - j**6/10 - 3*j**5/10 - j**4/2 - j**3/2 + 8*j**2. Factor u(t).
-3*(t + 1)**4
Find u such that -2/9*u + 0 + 0*u**2 + 2/9*u**3 = 0.
-1, 0, 1
Let j(c) be the third derivative of -2*c**7/21 + 17*c**6/30 - 7*c**5/5 + 11*c**4/6 - 4*c**3/3 + 5*c**2. Let j(i) = 0. What is i?
2/5, 1
Let t be (2 + -1)/(1/6). Let f be (4/(-6))/((-8)/t). Let -1/2*p - p**2 + 0 - f*p**3 = 0. Calculate p.
-1, 0
Let j(d) be the second derivative of d**8/23520 + d**7/4410 + d**6/2520 - d**4/4 + 2*d. Let u(n) be the third derivative of j(n). Solve u(z) = 0.
-1, 0
Let x(r) be the first derivative of -r**6/6 - r**5/15 + r**4/4 + r**3/9 + 14. What is q in x(q) = 0?
-1, -1/3, 0, 1
Suppose 4*n - 5*b - 6 = 0, n + 5*b = 9 + 5. Find i such that -i**n - 4*i + 3*i**3 + 1 - i**3 + 2*i = 0.
-1, 1
Let n be ((-2)/6)/(20/(-120)). Let y(u) be the second derivative of n*u + 0 - 1/7*u**2 - 1/7*u**3 - 1/14*u**4 - 1/70*u**5. Factor y(h).
-2*(h + 1)**3/7
Let c(n) = n**2 - n - 1. Let m(q) = -10*q**2 + 9*q + 6. Let f(v) = 5*c(v) + m(v). Let s(b) = -14*b**2 + 11*b + 3. Let y(j) = 17*f(j) - 6*s(j). Factor y(l).
-(l - 1)**2
Let n(z) = -4*z + 2*z**2 + z + z**2 + 0*z. Let j(u) = 7*u**2 - 7*u + 1. Let t(p) = -4*j(p) + 10*n(p). Factor t(s).
2*(s - 2)*(s + 1)
Let i(d) = d**2 - 2*d + 2. Let y be i(2). Determine f so that 5*f + 3 + 2 - 3 + 3*f**y = 0.
-1, -2/3
Let w = -8 + 6. Let a = -9 - -4. Let k(b) = -3*b**2 + 8*b + 8. Let p(l) = l**2 - 4*l - 4. Let z(s) = a*p(s) + w*k(s). Factor z(j).
(j + 2)**2
Let b(h) be the second derivative of -h**5/40 - h**4/24 + h**3/12 + h**2/4 - 4*h. Suppose b(j) = 0. Calculate j.
-1, 1
Let i(u) = u**2 + u. Let a be i(-2). Let p(k) be the first derivative of 1/8*k**4 + 1 + 0*k + 0*k**a + 1/12*k**3 + 1/20*k**5. Determine s, given that p(s) = 0.
-1, 0
Let t = 916/4041 + -2/449. Factor 0 - 4/9*b - t*b**3 - 2/3*b**2.
-2*b*(b + 1)*(b + 2)/9
Let c(v) = -7*v**2 + 9*v + 16. Let n(d) = -13*d**2 + 18*d + 31. Let l(m) = 7*c(m) - 4*n(m). What is h in l(h) = 0?
-1, 4
Let x(o) = 180*o**5 - 505*o**4 + 445*o**3 - 95*o**2 - 25. Let l(f) = 15*f**5 - 42*f**4 + 37*f**3 - 8*f**2 - 2. Let q(n) = 25*l(n) - 2*x(n). Factor q(m).
5*m**2*(m - 1)**2*(3*m - 2)
Suppose 2*v**4 - 5*v**4 + 161*v**5 - 158*v**5 = 0. Calculate v.
0, 1
Let l(u) be the first derivative of -8/3*u**3 + 2 - 11/5*u**2 - 4/5*u + 8/25*u**5 - 11/10*u**4 + 4/15*u**6. Find f, given that l(f) = 0.
-1, -1/2, 2
Suppose -2*t - 4*u = -u - 371, 3*t - 2*u = 576. Let c = t + -1326/7. Find k such that -4/7*k**3 + c*k - 2/7*k**4 + 0*k**2 + 2/7 = 0.
-1, 1
Let d(n) be the first derivative of -2*n**5/55 - 4*n**4/11 - 16*n**3/11 - 32*n**2/11 - 32*n/11 + 49. Let d(p) = 0. What is p?
-2
Let t(s) = -s**3 - 7*s**2 + 9*s + 12. Let b be t(-8). Factor 0 + 1/2*f**2 - f**3 - 1/2*f**b + f.
-f*(f - 1)*(f + 1)*(f + 2)/2
Let w be 5*3*26/(-15). Let t(z) = -4*z**3 + 5*z**2 - 9*z + 21. Let o(s) = -s**3 + s**2 - 2*s + 5. Let y(c) = w*o(c) + 6*t(c). Determine r so that y(r) = 0.
-2, -1, 1
Let g(f) be the first derivative of 1/24*f**4 + 2 + f - 1/6*f**3 + 1/4*f**2. Let w(y) be the first derivative of g(y). Factor w(o).
(o - 1)**2/2
Let v(m) = -m**2 + 19*m + 20. Let o be v(20). Factor 0*a + 1/2*a**5 - 1/2*a**3 - 1/2*a**4 + o + 1/2*a**2.
a**2*(a - 1)**2*(a + 1)/2
Factor 1/2 - 1/4*i - 3/4*i**2 + 1/4*i**3 + 1/4*i**4.
(i - 1)**2*(i + 1)*(i + 2)/4
Let w(i) = i**3 + 5*i**2 + 2*i - 2. Let n(c) = c**3 + c**2. Let j(y) = -6*n(y) + 2*w(y). Factor j(l).
-4*(l - 1)**2*(l + 1)
Let a(d) be the first derivative of d**5/15 + d**4/6 - d**3/9 - d**2/3 + 6. Factor a(w).
w*(w - 1)*(w + 1)*(w + 2)/3
Let x(v) be the third derivative of -v**7/105 + v**6/60 + v**5/6 + v**4/4 + 7*v**2. Find y, given that x(y) = 0.
-1, 0, 3
Let t(q) be the first derivative of -q**4/6 + 4*q**3/9 + q**2/3 - 4*q/3 + 29. Find d such that t(d) = 0.
-1, 1, 2
Let r be ((-28)/(-20) - (-12)/(-30))/3. Find o, given that 0*o + r*o**5 - 1/3*o**3 + 1/3*o**4 + 0 - 1/3*o**2 = 0.
-1, 0, 1
Let u(v) be the first derivative of 2/27*v**3 + 1 + 4/9*v**2 + 8/9*v. Suppose u(c) = 0. What is c?
-2
Suppose 4*f = u - 43, 0 = -3*f - 8*u + 3*u - 61. Let n be 0 - (8/f + -1). Factor n*j**2 + 1/3*j**3 + 4/3 + 8/3*j.
(j + 1)*(j + 2)**2/3
Let f be 258/(-3654) - (-2)/6. Let a = f - -2/87. Find o such that -a*o**3 - 2/7*o + 4/7*o**2 + 0 = 0.
0, 1
Let 0*b**3 + 8/11*b**2 - 6/11*b**4 + 0*b + 0 + 2/11*b**5 = 0. Calculate b.
-1, 0, 2
Let r be 0 + 0 - 16/(-4). Solve -r*o**2 + 2*o - 2 + 2 + 2*o = 0 for o.
0, 1
Let w(d) = 30*d**2 + 75*d + 30. Let n(r) = -20*r**2 - 50*r - 20. Let s(c) = -8*n(c) - 5*w(c). Factor s(k).
5*(k + 2)*(2*k + 1)
Suppose 0 = 4*u + 2*x - 26, 5*x - 41 = -7*u + 3*u. Suppose -2*p + 10 =