-104368069/140721 - 2/46907. Let n = -731 - b. Factor -1/3*h**4 - 8*h**2 + n*h - 16/3 + 8/3*h**3.
-(h - 2)**4/3
Let g(b) be the first derivative of -2/15*b**5 - 3 + 1/3*b**2 - 1/3*b**4 + 4/9*b**3 + 1/9*b**6 - 2/3*b. Factor g(u).
2*(u - 1)**3*(u + 1)**2/3
Let r(p) be the second derivative of -2*p**4/9 - p**3/9 + 15*p. Determine s so that r(s) = 0.
-1/4, 0
Let i(x) be the second derivative of 0 + 0*x**2 + 0*x**3 + 1/18*x**4 - 3*x. Factor i(u).
2*u**2/3
Find q such that -3/2 + 3/2*q**5 - 3*q**2 + 3*q**3 + 9/2*q**4 - 9/2*q = 0.
-1, 1
Suppose 0 = -4*d + 6 + 2. Suppose -q**4 - q - 1 - 3*q**3 + 1 - 3*q**d + 0*q**2 = 0. Calculate q.
-1, 0
Let v be ((-9)/10)/(18/(-12)). Determine y so that -1/5*y**2 + v*y**5 + 0*y + 0 - 3/5*y**3 + 1/5*y**4 = 0.
-1, -1/3, 0, 1
Suppose -3*o - 5*v + 25 = 0, -3*v + 12 = -3. Suppose -4 = -2*x - 5*i + 5, o = -5*i + 5. Factor -2/9*k**x + 0*k + 2/9.
-2*(k - 1)*(k + 1)/9
Let j(b) = b**2 - 5*b - 3. Let n be j(-1). What is w in 1/4*w**n + 1/2*w**2 + 1/4*w + 0 = 0?
-1, 0
Let a(w) be the first derivative of -5*w**3/3 - 5*w**2 - 5*w - 2. Factor a(s).
-5*(s + 1)**2
Let b(x) be the first derivative of -x**3 - 3*x**2 + 9*x + 11. Factor b(z).
-3*(z - 1)*(z + 3)
Let -3/2*n - 1 - 1/2*n**2 = 0. What is n?
-2, -1
Let b be (-2 - 2)/(-2) + 3. Suppose 9*l - 8 = b*l. Factor -1/5*k**l - 1/5 + 2/5*k.
-(k - 1)**2/5
Let u = 119 + -355/3. Factor 1/3 + 1/3*w**4 - 1/3*w**5 - 1/3*w + 2/3*w**3 - u*w**2.
-(w - 1)**3*(w + 1)**2/3
Let 0*t - 4/5*t**2 + 0*t**3 + 4/5*t**4 + 0 = 0. Calculate t.
-1, 0, 1
Suppose -736 = -2*v - s - s, 4*v - 5*s = 1490. Let y = 3334/9 - v. What is q in y*q**2 + 10/9*q + 4/9 = 0?
-2, -1/2
Let g(o) be the third derivative of 2*o**7/35 - o**6/30 - 8*o**5/15 - 2*o**4/3 + 25*o**2. Factor g(j).
4*j*(j - 2)*(j + 1)*(3*j + 2)
Suppose 4*q + 2 = -5*h - 1, -18 = -3*q + 3*h. Factor -1/2*l**4 + 1/2 + 0*l**2 - l + l**q.
-(l - 1)**3*(l + 1)/2
Let d = -4 - -6. Suppose -d*i - i + 6 = 0. Determine t so that -2*t**3 - 8*t - 3*t**i - 2 - 3*t**2 + 2*t = 0.
-1
Let z(r) = -26*r**3 + 30*r**2 + 24*r - 14. Let n(w) = 5*w**3 - 6*w**2 - 5*w + 3. Let t(u) = 14*n(u) + 3*z(u). Factor t(b).
-2*b*(b - 1)*(4*b + 1)
Let s(j) be the second derivative of -j**5/10 + 5*j**4/12 + 2*j**3/3 - 3*j**2/2 + 45*j. Factor s(u).
-(u - 3)*(u + 1)*(2*u - 1)
Let s(t) be the third derivative of t**6/1440 + t**5/240 + t**4/96 + t**3/3 - 2*t**2. Let o(m) be the first derivative of s(m). Factor o(l).
(l + 1)**2/4
Let k(z) = 20*z**2 + 8*z - 12. Let q(w) = 7*w**2 + 3*w - 4. Let n(g) = -3*k(g) + 8*q(g). Let j(r) = -r**2 - r. Let y(c) = 8*j(c) - n(c). Factor y(b).
-4*(b + 1)**2
Let p be (4/6)/(3/(-18)). Let u(z) = -z - 1. Let d be u(p). What is m in -2 + 4*m**4 - 4*m**d - 2*m - 2*m**4 + 6*m = 0?
-1, 1
Let y(j) = j**4 - j**3 + j**2 + j. Let p(g) = g**5 - 9*g**4 + 20*g**3 - 22*g**2 + 6*g. Let z(u) = -3*p(u) - 6*y(u). Suppose z(o) = 0. Calculate o.
0, 1, 2
Let l(i) be the first derivative of -2*i**6/3 + i**4 + 14. Find z, given that l(z) = 0.
-1, 0, 1
Solve 2/17*v**5 + 0*v + 0 - 6/17*v**3 - 4/17*v**2 + 0*v**4 = 0.
-1, 0, 2
Let i = 4 + -4. Suppose -2*j + 10 = 2*h, 2*h = -i*h. Find n such that -10*n - 20*n**3 + 2 + 2*n**5 + 20*n**2 + 0 - 4*n**j + 10*n**4 = 0.
1
Factor 0*w**2 - 3*w**2 + 2*w - 4 + 5*w**2.
2*(w - 1)*(w + 2)
Let i(o) = o**3 - 12*o**2 + o - 10. Let r be i(12). Factor 1/3*d**4 + 0*d + 0*d**3 - 1/3*d**r + 0.
d**2*(d - 1)*(d + 1)/3
Let d(q) be the first derivative of -3*q**4/8 - 2*q**3 - 3*q**2 + 4*q + 3. Let r(m) be the first derivative of d(m). Determine i so that r(i) = 0.
-2, -2/3
Suppose i = -0 + 2. Let j be 5/(-25) + (-1)/(-5). Factor -4/9*y + j - 2/9*y**i.
-2*y*(y + 2)/9
Let m(p) be the second derivative of p**6/15 + p**5/10 + 7*p. Solve m(n) = 0.
-1, 0
Factor 2/5 - 7/5*c + 1/5*c**4 + 9/5*c**2 - c**3.
(c - 2)*(c - 1)**3/5
Find d such that 65 - 62 + d**2 + 2*d - 2*d**2 = 0.
-1, 3
Let p(z) = z**2 - 4*z - 2. Suppose -2*d + 5 = -d. Let b be p(d). Factor -2/7*r + 2/7 + 2/7*r**b - 2/7*r**2.
2*(r - 1)**2*(r + 1)/7
Let a = -17 + 24. Let h = a - 7. Factor 0*c + h - 1/4*c**2.
-c**2/4
Let i be (-14)/(-3)*(65/35 - 1). Let p(x) be the second derivative of -2/27*x**3 + i*x + 0 - 1/54*x**4 - 1/9*x**2. Factor p(h).
-2*(h + 1)**2/9
Let u be ((-5)/90)/(5/(-3)). Let l(n) be the third derivative of -u*n**5 + 0*n - n**2 + 1/120*n**6 + 1/24*n**4 + 0*n**3 + 0. Determine i so that l(i) = 0.
0, 1
Let g(z) = -110*z**2 + 615*z - 835. Let d(m) = -5*m**2 + 28*m - 38. Let p(h) = -45*d(h) + 2*g(h). Factor p(l).
5*(l - 4)*(l - 2)
Let j(n) be the second derivative of -n**7/12600 - n**4/12 + 2*n. Let c(o) be the third derivative of j(o). Factor c(h).
-h**2/5
Let -80 - 9*x**2 + 19*x**2 - 5*x**2 + 75*x = 0. Calculate x.
-16, 1
Let i be (-4)/(-10) - (-176)/10. Suppose -x - i = -4*x. Let 6 - 2*r**3 + 2*r**5 - x - 2*r**2 + 2*r**4 = 0. What is r?
-1, 0, 1
Suppose -24 = -2*c - 5*b, 18 = 5*c - b + 3*b. Let n(m) be the first derivative of -2/3*m - c + 0*m**2 + 2/9*m**3. Find j, given that n(j) = 0.
-1, 1
Let p(i) = 6*i**2 + 5. Let u(c) = c**2 + 1. Let a(o) = -p(o) + 5*u(o). Factor a(j).
-j**2
Let u(z) be the second derivative of -z**6/10 + 3*z**5/4 - 9*z**4/4 + 7*z**3/2 - 3*z**2 - 7*z. Factor u(s).
-3*(s - 2)*(s - 1)**3
Let r be 9/(3/1) - 0. Suppose -b + 2*x + 13 = r, 10 = -2*x. Factor -1/4*h**2 + 1/4*h**3 + 0*h + b.
h**2*(h - 1)/4
Let y(z) = -z**4 + 16*z**3 - 19*z**2. Let v(d) = -4*d**4 + 80*d**3 - 96*d**2. Let c(q) = -3*v(q) + 16*y(q). What is l in c(l) = 0?
0, 2
Let b(x) be the first derivative of 2*x**5/15 + x**4/2 - 4*x**3/9 - 4*x**2 - 16*x/3 + 29. Factor b(w).
2*(w - 2)*(w + 1)*(w + 2)**2/3
Let c = -36976/545 + 114/109. Let d = 68 + c. Find p such that 4/5*p**3 - 8/5*p**2 + 0 + 2/5*p + 8/5*p**4 - d*p**5 = 0.
-1, 0, 1/3, 1
Let q = -2/9 - -8/9. Let x(l) be the first derivative of -q*l**3 - 1 + 2*l + 0*l**2. Solve x(v) = 0 for v.
-1, 1
Let w(c) be the third derivative of -c**9/20160 - c**8/3360 - c**7/1680 + c**5/60 - 4*c**2. Let s(x) be the third derivative of w(x). Solve s(p) = 0.
-1, 0
Let y = -1 - -3/2. Let a(z) be the second derivative of y*z**5 - 3/2*z**4 + 7/15*z**6 - 5/3*z**3 + 2*z**2 + 3*z + 0. Factor a(t).
2*(t - 1)*(t + 1)**2*(7*t - 2)
Let w = -15758/459 + -1/459. Let c = -34 - w. Suppose -1/3*t**3 - 2/3*t**2 + c*t + 2/3 = 0. Calculate t.
-2, -1, 1
Let j(m) = -m**2 + m + 1. Let b(a) = -5*a**3 - a**2 + a + 1. Let g(f) = b(f) + 4*j(f). Factor g(c).
-5*(c - 1)*(c + 1)**2
Let q = -11/36 - -5/12. Let w(t) be the second derivative of t - 1/36*t**4 + q*t**3 - 1/6*t**2 + 0. Find i such that w(i) = 0.
1
Let w = -32 + 226/7. Let w*t + 0 - 4/7*t**2 + 0*t**3 + 4/7*t**4 - 2/7*t**5 = 0. What is t?
-1, 0, 1
Let q = -69 - 0. Let u = -617/9 - q. Suppose 2/9*a**2 + u*a + 2/9 = 0. What is a?
-1
Let a(z) be the second derivative of 2*z**4/27 + 2*z**3/27 - 21*z. Suppose a(o) = 0. Calculate o.
-1/2, 0
Let n = 70 + -50. Let p be 2/5 - 3/n. Find d, given that p*d**2 + 1/4*d**4 + 0 + 1/2*d**3 + 0*d = 0.
-1, 0
Let p = 7 + -3. Suppose 6*j = p*j. Determine b, given that 4*b + b**2 + b - 3*b + 1 + j*b = 0.
-1
Let u(w) be the third derivative of -w**7/8820 - w**6/1260 - w**5/420 - w**4/8 + 2*w**2. Let g(v) be the second derivative of u(v). Factor g(m).
-2*(m + 1)**2/7
Suppose 63 = 4*a - 29. Let b = -20 + a. Factor 0 + 0*c**2 + 3/5*c - 3/5*c**b.
-3*c*(c - 1)*(c + 1)/5
Let v be 6/9 - 8/(-6). Factor -2*u**2 + 2*u**2 + v*u - 4*u**2 + 3*u**2.
-u*(u - 2)
Let z(f) = 2*f**2 - 3*f + 5. Let d(g) = g**2 - g + 2. Let r(s) = 5*d(s) - 2*z(s). Let j(h) = 5*h**2. Let i(m) = -j(m) - 2*r(m). Factor i(l).
-l*(7*l + 2)
Suppose w + 0*w = 4*w. Let s(g) be the second derivative of 0 + 0*g**4 + 0*g**3 + w*g**2 + 2*g + 0*g**5 - 1/105*g**6. Factor s(h).
-2*h**4/7
Let t(a) be the second derivative of -a**6/45 + a**5/9 - 7*a**4/54 - 4*a**3/27 + 4*a**2/9 + 38*a. Let t(g) = 0. Calculate g.
-2/3, 1, 2
Let d(s) be the third derivative of s**9/20160 - s**7/1680 - s**5/30 - 4*s**2. Let v(t) be the third derivative of d(t). Determine p so that v(p) = 0.
-1, 0, 1
Let v(f) = f**2 - f - 1. Let i(a) = -3*a**3 + 2*a**2 + 10*a - 2. Let l(h) = i(h) - 2*v(h). Factor l(o).
-3*o*(o - 2)*(o + 2)
Let y(z) be the second derivative of 1/75*z**6 - 1/15*z**3 + 2/5*z**2 + 1/50*z**5 - 1/10*z**4 - 8*z + 0. Factor y(u).
2*(u - 1)**2*(u + 1)*(u + 2)/5
Let z(k) = -k**3 + k**2 - k - 30. L