*n + 176/9*n**3 + 32/3*n**4 + 0.
2*n*(n + 2)**2*(3*n + 2)**2/9
Let i(g) = 2*g**3 - 2*g**2 + g + 3. Let j be i(3). Find v such that -13*v**3 - 40*v**3 + 120*v**4 + 32*v**3 - 45*v**2 - 6*v - j*v**3 + 144*v**5 = 0.
-1, -1/4, 0, 2/3
Let c(r) be the first derivative of 1/6*r**4 - r**2 - 1 - r + 1/20*r**5 - 1/6*r**3. Let f(x) be the first derivative of c(x). Let f(t) = 0. What is t?
-2, -1, 1
Let k = 19 + -13. Let l(t) be the first derivative of -1 + 0*t + 2/5*t**5 - 2/3*t**3 - 1/6*t**k + 1/2*t**2 + 0*t**4. Let l(b) = 0. Calculate b.
-1, 0, 1
Let o(k) be the first derivative of k**6/9 + 16*k**5/15 + 11*k**4/3 + 16*k**3/3 + 3*k**2 - 9. Suppose o(f) = 0. Calculate f.
-3, -1, 0
Let s(d) = d**5 + 2*d**4 + 8*d**3 + 6*d**2 + d + 2. Let y(f) = f**4 - f**3 - f**2 - 1. Let x = 0 + 2. Let b(h) = x*y(h) + s(h). What is m in b(m) = 0?
-1, 0
Let l(s) = 13*s**4 - 5*s**3 + 9*s - 9. Let g be (5*-3 - -3) + 3. Let r(i) = 3*i**4 - i**3 + 2*i - 2. Let u(p) = g*r(p) + 2*l(p). Factor u(q).
-q**3*(q + 1)
Let c(k) be the second derivative of k**4/30 + k**3/5 + 2*k**2/5 - 4*k. What is l in c(l) = 0?
-2, -1
Factor -42*v - 2 + 10 - 141*v**3 + 139*v**3 + 24*v**2 + 12.
-2*(v - 10)*(v - 1)**2
Let h be 6 + 1/1*-2. Suppose -p - h = -2*p. Factor -p*s - 6*s**3 - 9/5*s**4 - 4/5 - 37/5*s**2.
-(s + 1)**2*(3*s + 2)**2/5
Let j(o) be the first derivative of 2*o**6/3 + 8*o**5/5 + o**4 - 7. Find f, given that j(f) = 0.
-1, 0
Let x be ((-3)/6)/((-4)/8). Let n be -1 + x + (-4)/(-6). Let n*i**2 + 4/3 - 2*i = 0. Calculate i.
1, 2
Suppose -36 = -4*u - 4*i, 3*i - 9 = -4*u + 22. Solve 1/3*t**u + t**2 + 4/3*t - 4/3 - 4/3*t**3 = 0.
-1, 1, 2
Let k(l) be the first derivative of l**3/9 - 7*l**2/6 - 8*l/3 + 1. What is s in k(s) = 0?
-1, 8
Let l be 12/(-18) - (-4)/6. Suppose 0 = b - 0*b + f - 1, l = -4*f + 4. Factor -2/5*o + 2/5*o**5 - 4/5*o**4 + b*o**3 + 4/5*o**2 + 0.
2*o*(o - 1)**3*(o + 1)/5
Let a(t) be the first derivative of -12*t**4 - 3*t**2 + 21/5*t**5 + 0*t + 11*t**3 - 10. Factor a(m).
3*m*(m - 1)**2*(7*m - 2)
Let w(v) be the first derivative of 1/12*v**3 + 1/2*v**2 + 0*v**4 - 1/120*v**5 - 2 + 0*v. Let c(r) be the second derivative of w(r). Factor c(j).
-(j - 1)*(j + 1)/2
Let u(j) = -4 - 6 + 0*j**2 + 35*j + 14*j**4 - 3*j**2 - 29*j**3 - 1. Let g(k) = -k**3 - k**2 - k + 1. Let p(w) = 3*g(w) + u(w). Suppose p(s) = 0. Calculate s.
-1, 2/7, 1, 2
Let v be (-4)/54*6*-1. Let b = -799 - -801. Let 0*k + v*k**b + 0 - 2/9*k**3 = 0. What is k?
0, 2
Let v(g) be the third derivative of g**5/120 - g**4/16 + g**3/6 - 4*g**2. Find y, given that v(y) = 0.
1, 2
Suppose 4*z + 10 = 3*n - 10, 5*z + 25 = -4*n. Factor n + 1/2*w + 1/2*w**2.
w*(w + 1)/2
Let n be -9*2/(3 - 1). Let d(z) = 5*z**4 + 2*z**3 + z**2 - 2*z. Let p(g) = -21*g**4 - 7*g**3 - 4*g**2 + 9*g. Let b(k) = n*d(k) - 2*p(k). Factor b(q).
-q**2*(q + 1)*(3*q + 1)
Factor -40 + 660*s + s**2 + 0*s**2 - 650*s + 4*s**2.
5*(s - 2)*(s + 4)
Let i(v) be the second derivative of -5*v**4/6 + 8*v**3/3 + 4*v**2 - 8*v. Suppose i(s) = 0. What is s?
-2/5, 2
Let t(y) = -7*y - 143. Let k be t(-21). Factor 2/15*l**5 + 8/15*l**3 + 0 + 0*l**2 + 0*l + 8/15*l**k.
2*l**3*(l + 2)**2/15
Factor -2 - 28*r**2 - 31/2*r + 8*r**3.
(r - 4)*(4*r + 1)**2/2
Suppose -3*x + 3*i - 7*i + 4 = 0, -x + 4*i = 4. Let m = 5 - x. Find u such that u**3 - 2*u**3 - 2*u**2 + 2 + 6*u**2 - m*u = 0.
1, 2
Let s(g) be the second derivative of 0 - 1/120*g**6 + 4*g + 1/48*g**4 - 1/24*g**3 + 0*g**2 + 1/80*g**5. Determine u, given that s(u) = 0.
-1, 0, 1
Let y(z) be the first derivative of -3 + 0*z**2 + 0*z + 6/5*z**5 - 3/2*z**4 + 2/3*z**3 - 1/3*z**6. Factor y(m).
-2*m**2*(m - 1)**3
Let u = 1 - 1. Let f be (-2)/10 - (-21)/5. Factor -4/9*a**3 + 2/9*a**f + u*a + 2/9*a**2 + 0.
2*a**2*(a - 1)**2/9
Let o be 16/20*(-10)/(-2). Factor -h**2 - h**4 + 2*h**o - 2*h**3 + h**4 - h**2 + 2*h.
2*h*(h - 1)**2*(h + 1)
Let o(h) be the first derivative of -h**4/12 - 4*h**3/9 - 2*h**2/3 + 15. Find m such that o(m) = 0.
-2, 0
Let f(o) be the second derivative of o**5/70 - o**4/42 - o**3/21 + o**2/7 + 44*o. Factor f(y).
2*(y - 1)**2*(y + 1)/7
Factor 3*k + 11*k**2 - 14*k**2 + 3*k**5 + 3*k**4 - 3*k**3 - 3*k.
3*k**2*(k - 1)*(k + 1)**2
Suppose -4*i = -m - 23, 0 = 2*m - 6*i + 3*i + 21. Let s = m - -5. Determine c so that -3*c + 5*c - 4*c**2 + 5*c**s = 0.
-2, 0
Let z be 26/42 + 2/(-7). Solve 0*a**3 + 0*a + 1/3 + z*a**4 - 2/3*a**2 = 0.
-1, 1
Let c = 219 + -217. Solve 0*o + 2/5*o**3 + 0 + 2/5*o**4 + 0*o**c = 0 for o.
-1, 0
Find l, given that -3/4*l**2 + 1/4*l**3 + 3/4*l - 1/4 = 0.
1
Let n(c) = -2*c**2 + 2*c - 2. Let t(v) = v - 1. Let z(h) = 2*h**2 + 2*h - 1. Let l(p) = 3*t(p) - z(p). Let b(y) = -2*l(y) + 3*n(y). Factor b(m).
-2*(m - 1)**2
Let d(v) = v**2 + 8*v + 10. Let k be d(-7). Factor 3*u**4 - 5*u**4 + 4*u**k + 0*u**4.
-2*u**3*(u - 2)
Factor -1521/2*q**2 - 117*q - 6 - 6591/4*q**3.
-3*(13*q + 2)**3/4
Let d(l) be the first derivative of l**8/32 - 9*l**7/140 + l**6/40 - 2*l**2 - 3. Let o(h) be the second derivative of d(h). Factor o(a).
3*a**3*(a - 1)*(7*a - 2)/2
Solve 0*r**2 + 0 + 1/2*r**5 + 0*r + 0*r**4 - 1/2*r**3 = 0 for r.
-1, 0, 1
Suppose -8*r = -4*r. Let z = -23 - -27. What is a in 2*a**2 - z*a**4 - 3*a**4 + r*a**4 + 5*a**4 = 0?
-1, 0, 1
Let b(s) be the second derivative of -s**4/54 - 2*s**3/27 + 15*s. Factor b(p).
-2*p*(p + 2)/9
Let i(o) be the third derivative of -o**5/60 + o**3/6 - 17*o**2. Determine x so that i(x) = 0.
-1, 1
Let b be 3/(6/8 + 0). What is g in 5*g**2 - g**5 - 3*g**2 - 3*g**4 + 2*g - g**3 + b*g**2 - 3*g**2 = 0?
-2, -1, 0, 1
Let a(j) be the second derivative of 1/9*j**2 + 1/18*j**4 - 1/90*j**5 - 1/9*j**3 - j + 0. Suppose a(q) = 0. What is q?
1
Let d(h) = -h**2 + 8*h - 6. Suppose -v + 2 = 0, -q + 5*q + 6 = 5*v. Let l(i) = i - 1. Let w(x) = q*d(x) - 6*l(x). Let w(o) = 0. Calculate o.
0, 2
Let u be -1 + 1 + (-217)/(-936). Let b = u - 1/104. Suppose 0 + 0*v - b*v**2 = 0. Calculate v.
0
Suppose 0*y = 3*y - 9. Let k = -5 - -7. Solve s**k - s**5 + s**4 - 3*s**4 - y*s**3 + 5*s**4 = 0 for s.
0, 1
Let 1/5*y**4 - 1/5*y**3 + 0 + 1/5*y**5 + 0*y - 1/5*y**2 = 0. Calculate y.
-1, 0, 1
Let n(b) be the first derivative of b**8/168 - b**7/105 - b**2 + 1. Let w(u) be the second derivative of n(u). Factor w(v).
2*v**4*(v - 1)
Let g(j) be the first derivative of j**7/63 + j**6/45 - j**5/30 - j**4/18 + 2*j - 1. Let d(l) be the first derivative of g(l). Determine p, given that d(p) = 0.
-1, 0, 1
Let h = 59 - 56. Determine n so that 1/2*n**h + n**4 - 3/2*n**2 + 1/2 - 1/2*n = 0.
-1, 1/2, 1
Let u(t) be the third derivative of t**8/504 + t**7/315 - t**6/180 - t**5/90 - 13*t**2. Suppose u(k) = 0. What is k?
-1, 0, 1
Suppose -4*u = -3*k + 15, -2*u - 3*k - 25 = -8*k. Factor -14/5*i**3 - 4/5*i - 18/5*i**2 + u.
-2*i*(i + 1)*(7*i + 2)/5
Find y, given that -2*y**3 + y**4 - 2*y**2 + 4 - y**2 - y + 5*y = 0.
-1, 2
Suppose -7*v = -5*v. Find u such that v + 1/4*u**3 + 1/4*u + 1/2*u**2 = 0.
-1, 0
Determine o, given that -o**3 + 57 + o - 57 = 0.
-1, 0, 1
Let k(q) = 3*q + 3. Let u be k(4). Suppose 5*i = -0*i + u. Factor -g**4 - g**4 - 2*g**i + 0*g**2 + 2*g**2 + 2*g**5.
2*g**2*(g - 1)**2*(g + 1)
Let w = -19 - -25. Let f(k) = 17*k**2 + k + 6. Let l(q) = 9*q**2 + 3. Let m(o) = w*f(o) - 11*l(o). Factor m(p).
3*(p + 1)**2
Let v(h) be the second derivative of 0 + 13/30*h**3 - 1/5*h**2 - 11/60*h**4 - 9*h. Factor v(q).
-(q - 1)*(11*q - 2)/5
Let h = 12/37 + 235/74. Suppose 3*q - 16 = -q. Factor -1/2*z**2 + 0 - h*z**q + 0*z + 3/2*z**5 + 5/2*z**3.
z**2*(z - 1)**2*(3*z - 1)/2
Suppose 0 = q + 22*q - 207. What is j in -3/2*j**2 - q*j - 27/2 = 0?
-3
Let k(d) be the second derivative of -1/15*d**6 + 0 - 1/42*d**7 + 0*d**2 + 3*d + 0*d**4 - 1/20*d**5 + 0*d**3. Factor k(t).
-t**3*(t + 1)**2
Let u(m) = m - 7. Let y be u(7). Let p(h) be the second derivative of 1/48*h**4 + 0*h**2 + y + 3*h + 1/12*h**3. Determine d so that p(d) = 0.
-2, 0
Let z be (-2898)/(-4320) - (-4)/(-6). Let w(c) be the third derivative of 0*c**4 + 0*c + 3*c**2 + 0 - z*c**5 + 0*c**3. Determine x so that w(x) = 0.
0
Let y(k) = -4*k**3 + 3*k**2 + 6*k - 1. Let b(l) = l**3 - l**2 - l + 1. Let r(p) = 3*b(p) + y(p). Factor r(w).
-(w - 2)*(w + 1)**2
Factor 0*r**3 + 2*r**4 + 0 + 0*r - 2/3*r**2 - 4/3*r**5.
-2*r**2*(r - 1)**2*(2*r + 1)/3
Let w = 18 + -12. Suppose w*v = 3*v. Determine q so that -2/7*q**3 + v + 2/7*q + 0*q**2 