*2*(m + 2)/6
Let z = 567/8 + -71. Let y = 3/8 + z. Factor -1/4*h**2 + y*h**3 + 0 - 1/2*h.
h*(h - 2)*(h + 1)/4
Let c be 4/(-5)*(-4 - 266/(-84)). Let c*k + 4/3 - 2/3*k**2 = 0. What is k?
-1, 2
Factor -5*z**4 + 5*z**2 + 5*z**5 - 112*z**3 + 107*z**3 - 2*z + 2*z.
5*z**2*(z - 1)**2*(z + 1)
Let w be -33*(-4)/120 - (-2)/5. Factor -1/2*q**4 + 0*q + 0 - q**2 - w*q**3.
-q**2*(q + 1)*(q + 2)/2
Suppose -p = -5*o - 68, -2*o + 63 = 2*p - 61. Let l be (54/p)/(9/14). Factor l*w + 4/3*w**2 + 1/3*w**3 + 0.
w*(w + 2)**2/3
Let w be (-4)/(-6)*(-36)/(-8). What is c in -w*c**3 + 4*c**3 - 2*c**4 - 3*c**3 = 0?
-1, 0
Let d be 138/18 - 2/3. Suppose -3*w = -2*j, 3*w = d*w - 3*j. Factor -2/5*m**2 + 2/5*m**3 + 0*m + w.
2*m**2*(m - 1)/5
Factor -6/7*q + 15/7*q**2 - 6/7*q**3 + 0.
-3*q*(q - 2)*(2*q - 1)/7
Let q(b) = b - 3. Let s be q(4). Let z be s/2 - (-9)/(-42). Factor 0 + 2/7*y + z*y**2.
2*y*(y + 1)/7
Suppose -3*d - d + 20 = 0. Let v(x) be the first derivative of 1 + 0*x + 1/9*x**3 + 0*x**2 + 1/15*x**d + 1/6*x**4. Factor v(z).
z**2*(z + 1)**2/3
Let j = 16 - -74. Let n be ((-8)/(-14))/(j/35). Determine d so that -n*d**4 - 4/9*d**3 + 2/9*d + 4/9*d**2 - 2/9 + 2/9*d**5 = 0.
-1, 1
Let m(z) be the first derivative of 1/8*z**4 - 1/3*z**3 + 1/4*z**2 + 2 + 0*z. Suppose m(k) = 0. Calculate k.
0, 1
Let q(i) be the third derivative of i**9/1134 - i**8/2520 - i**7/315 + i**6/540 - 4*i**3/3 + 5*i**2. Let l(v) be the first derivative of q(v). Solve l(h) = 0.
-1, 0, 1/4, 1
Let f(p) = 9*p**3 + 4*p**2 + 5. Let i(t) = 10*t**3 + 4*t**2 + 6. Let s(j) = -6*f(j) + 5*i(j). Factor s(u).
-4*u**2*(u + 1)
Let y(r) be the second derivative of r**6/105 - r**4/28 - r**3/21 + 2*r**2 + 4*r. Let j(m) be the first derivative of y(m). Factor j(z).
2*(z - 1)*(2*z + 1)**2/7
Suppose -4*b = -25 - 47. Suppose 0 = -q + 3*q, 2*q - b = -y. Suppose -41*i - 8 + 30*i**5 + 120*i**4 - 38*i**4 + 9*i - y*i**2 + 58*i**3 = 0. Calculate i.
-1, -2/5, 2/3
Suppose -3*i - 4*i = -5*i. Determine d, given that 4/7*d**3 - 2/7*d + 0*d**2 + 0*d**4 - 2/7*d**5 + i = 0.
-1, 0, 1
Let v(m) be the second derivative of 1/16*m**4 - 1/120*m**6 + 0*m**5 + 0 - 3*m - 1/12*m**3 + 0*m**2. Factor v(x).
-x*(x - 1)**2*(x + 2)/4
Factor -x + 7 + 22*x - 1 + 15*x**2.
3*(x + 1)*(5*x + 2)
Let h(m) = -m**3 + 10*m**2 - 9*m + 2. Let x be h(9). Suppose -1/2*p - 1/2*p**5 - 1/2*p**4 - 1/2 + p**3 + p**x = 0. Calculate p.
-1, 1
Let f(i) = -i**5 + i**3 - i**2 + i - 1. Let q(h) = -h**5 + h**4 - h**3 - 5*h**2 + 6*h - 4. Let b(z) = -4*f(z) + q(z). Factor b(n).
n*(n - 1)*(n + 1)**2*(3*n - 2)
Let t = -3 - -7. Let s(m) = -7*m**2 + 6*m - 7. Let u(i) = 8*i**2 - 6*i + 8. Let x(l) = t*u(l) + 5*s(l). Factor x(o).
-3*(o - 1)**2
Let b be ((-1)/(-48))/(9/12). Let m(w) be the third derivative of -1/27*w**3 - b*w**4 + w**2 - 1/90*w**5 + 0*w + 0 - 1/540*w**6. Factor m(k).
-2*(k + 1)**3/9
Let a be ((-18)/(-16))/((-3)/10). Let b = 53/12 + a. Solve 1/3*m**3 + 0 - 1/3*m**2 - b*m = 0 for m.
-1, 0, 2
Let a(t) be the second derivative of -2*t**6/15 - 2*t**5/5 + t**4 - 17*t. Factor a(w).
-4*w**2*(w - 1)*(w + 3)
Let b(f) be the third derivative of -f**9/60480 - f**8/5040 - f**7/1260 - 7*f**5/60 - 5*f**2. Let n(x) be the third derivative of b(x). Factor n(i).
-i*(i + 2)**2
Factor -20*z**2 + 37*z - 24 - 30*z + 61*z.
-4*(z - 3)*(5*z - 2)
Let o(c) be the second derivative of c**6/360 + c**5/90 + c**4/72 + c**2/2 - 3*c. Let i(h) be the first derivative of o(h). Let i(v) = 0. Calculate v.
-1, 0
Let f(c) be the first derivative of c**5/40 + c**4/12 + c**3/12 - 2*c - 1. Let r(p) be the first derivative of f(p). Find k, given that r(k) = 0.
-1, 0
Suppose -4*n = -2*l - 8, -8 = -4*l - 0*n + 2*n. Suppose 3*o - 5*m + 14 = 0, -l*m + 9 = -2*o - 3. Find q such that 8/3 + 8/3*q + 2/3*q**o = 0.
-2
Factor 5*l**5 + l**4 + 36*l**3 - 16*l + 2*l**3 + 10*l**3 - 29*l**4 - 16*l**2.
l*(l - 2)**3*(5*l + 2)
Let q(m) = -m**3 - 3*m**2 + 2. Let k(n) = -4*n**3 - 10*n**2 + 7. Suppose 10 = 4*u + 2. Let b(j) = u*k(j) - 7*q(j). Factor b(w).
-w**2*(w - 1)
Suppose 3*v = 4*v - 36. Suppose 2*z - v = -7*z. Determine d, given that -8*d**z + 0 - 14/3*d**3 + 4/3*d + 14/3*d**2 = 0.
-1, -1/4, 0, 2/3
Let h(z) be the second derivative of -3*z + 1/27*z**3 + 0*z**2 + 1/27*z**4 + 0 + 1/90*z**5. Factor h(w).
2*w*(w + 1)**2/9
Let x(w) be the third derivative of -25*w**6/144 - 5*w**5/12 - 5*w**4/12 - 2*w**3/9 + 24*w**2. Factor x(n).
-(5*n + 2)**3/6
Factor -95*o**3 + 10 + 0*o - 5*o - 30*o**2 + 23*o**2 - 35*o**4 - 68*o**2.
-5*(o + 1)**3*(7*o - 2)
Let f = -127 + 130. Factor -3/4*l**3 + 0 + f*l**2 - 3*l.
-3*l*(l - 2)**2/4
Let y(r) be the first derivative of 4*r**3/3 + 8*r**2 + 16*r + 1. Let y(j) = 0. What is j?
-2
Let j = 27 - 19. Solve 24*o - 8*o**2 + 3*o**3 - 6*o**4 + 2*o**2 + j - 18*o**3 - 5*o**3 = 0 for o.
-2, -1/3, 1
Let t(b) be the third derivative of -b**7/280 + b**6/40 - b**5/20 - 7*b**2. Factor t(i).
-3*i**2*(i - 2)**2/4
Suppose 0*a**2 - 1/2*a**5 + a**3 - 1/2*a + 0 + 0*a**4 = 0. Calculate a.
-1, 0, 1
Let x = -1 + 5. Factor -2*m - 5*m**3 - 4*m**2 + x + 3*m**3 + 0*m**3 + 4*m**3.
2*(m - 2)*(m - 1)*(m + 1)
Let y = 140 - 137. Let m(g) be the third derivative of -1/36*g**4 + 2/9*g**3 + 0*g + 0 + y*g**2 - 1/30*g**5. Factor m(a).
-2*(a + 1)*(3*a - 2)/3
Let k(r) = -2*r**2 + 2. Let m be k(-2). Let n be 1/(((-9)/m)/3). Factor -12*d**n - 1/4 - 16*d**3 - 3*d.
-(4*d + 1)**3/4
Solve 0 + 1/2*s**3 - s**2 - 3/2*s = 0.
-1, 0, 3
Let j(s) be the first derivative of 7*s**5/90 + s**4/4 + 2*s**3/9 - s**2 - 4. Let o(v) be the second derivative of j(v). Solve o(q) = 0 for q.
-1, -2/7
Factor 2 - o**2 - 951*o**3 + 946*o**3 - 6 + o**5 + o**4 + 8*o.
(o - 1)**3*(o + 2)**2
Let j(c) = -6*c - 4. Let u be j(-1). Let q(z) be the first derivative of 0*z**u + 0*z**5 + 0*z + 1/9*z**6 - 1/6*z**4 + 2 + 0*z**3. Solve q(w) = 0 for w.
-1, 0, 1
Let k be (-6)/10 - (0 + -1). Let x = -18 + 21. Factor -4/5*c**x - 4/5*c**2 + 2/5*c**5 + 2/5*c + 2/5*c**4 + k.
2*(c - 1)**2*(c + 1)**3/5
Let l(m) = -m**3 - 8*m**2 + 2. Let f be l(-8). Let d(u) be the second derivative of 0 - 1/4*u**f - u - 5/24*u**3 + 7/48*u**4. Factor d(g).
(g - 1)*(7*g + 2)/4
Suppose 6 = 2*i - i. Let a(h) be the second derivative of -1/15*h**3 + 0*h**2 - 2/15*h**4 + 4/75*h**i + 1/50*h**5 - h + 0. Let a(p) = 0. What is p?
-1, -1/4, 0, 1
Suppose -3*o - b = -4 - 1, b = 5*o - 11. Factor -x**o - 24*x**4 + x**2 + 22*x**4 - x**5.
-x**4*(x + 2)
Let a = -13/4 + 15/4. Factor 1/2*h - a*h**2 + 0.
-h*(h - 1)/2
Solve 3 + r + r**2 - 6*r + 2*r - r = 0 for r.
1, 3
Solve 0 - 1/7*o**2 - 1/7*o = 0 for o.
-1, 0
Let d(u) = 4*u**2 - 2*u. Suppose -3*m - 6 = 3*w, m + m - 4 = 2*w. Suppose x - 1 = -m. Let s(j) = -j**2. Let q(t) = x*s(t) + d(t). Factor q(p).
p*(3*p - 2)
Let u(y) = y**2 + y - 1. Let a(o) = o**4 - 2*o**3 + 11*o - 7. Let d(g) = 2*a(g) - 6*u(g). Determine v so that d(v) = 0.
-2, 1, 2
Let q(k) be the second derivative of -k**4/4 + k**3 + 9*k**2/2 + 25*k. Find u, given that q(u) = 0.
-1, 3
Factor 2*c + c - 23*c**2 - 4*c**3 + 24*c**2.
-c*(c - 1)*(4*c + 3)
Let w(b) be the third derivative of 0*b + b**4 + 2*b**3 + 1/4*b**5 - 3*b**2 + 0 + 1/40*b**6. Factor w(z).
3*(z + 1)*(z + 2)**2
Let t(l) = -2*l**4 - 13*l**3 - 10*l**2 + 7*l + 9. Let s(d) = -2*d**4 - 12*d**3 - 10*d**2 + 8*d + 10. Let f(u) = -6*s(u) + 4*t(u). Suppose f(o) = 0. What is o?
-3, -2, -1, 1
Let r be 236/(-8) - (-1)/(-2). Let c be r/(-8) - (4 - 1). Find l such that -c*l**3 + 3/4*l - 1/2 + 1/4*l**4 + 1/4*l**2 = 0.
-1, 1, 2
Let q(c) be the first derivative of -c**6/6 + 3*c**4/4 + 2*c**3/3 + 34. Factor q(l).
-l**2*(l - 2)*(l + 1)**2
Suppose 0 = -2*p - 2*p + 4*v + 20, 0 = p + 3*v - 1. Let 0*h + 0*h**p + 0 + 1/2*h**3 - 1/2*h**5 + 0*h**2 = 0. Calculate h.
-1, 0, 1
Let p(w) be the second derivative of 0*w**2 + 3/56*w**7 + 1/5*w**5 + 0 + 1/12*w**4 + 0*w**3 + 7/40*w**6 - w. Find d such that p(d) = 0.
-1, -2/3, 0
Find w, given that -18*w**5 - 14*w**2 + 13*w**5 + 15*w**4 - 5*w**3 + 10*w - w**2 = 0.
-1, 0, 1, 2
Let z(h) be the second derivative of -3*h**5/40 + h**4/4 + 3*h**3/4 + 16*h. Factor z(x).
-3*x*(x - 3)*(x + 1)/2
Let v be -1 + ((-13380)/(-2534) - 4). Let h = 1/181 + v. Suppose 4/7 + h*f - 2/7*f**2 = 0. Calculate f.
-1, 2
Let p(n) = -n**4 + n**3 - n**2 - 1. Let c(x) = 6*x**4 + 2*x**3 - 10*x**2 - 4*x + 10. Let h(g) = c(g) + 2*p(g). Factor h(v).
4*(v - 1)**2*(v + 1)*(v + 2)
Suppose -t + 5*t 