. Factor -3*u**2 - g*u**4 + 5*u**2 + 2*u**3 - 2*u**5 + 0*u**3.
-2*u**2*(u - 1)*(u + 1)**2
Let z(q) be the third derivative of q**6/90 + q**5/30 - 5*q**3/6 + 5*q**2. Let u(g) be the first derivative of z(g). Factor u(j).
4*j*(j + 1)
Let y(n) = -6*n**4 - 15*n**3 + 6*n**2 + 15*n. Let v(g) = -g**4 - g**3 + g**2 + g. Let w(o) = 18*v(o) - y(o). Let w(l) = 0. What is l?
-1, -1/4, 0, 1
Let d(z) be the second derivative of 1/2*z**4 - 3*z + 0 + 5/3*z**3 + 2*z**2. Factor d(y).
2*(y + 1)*(3*y + 2)
Let m = -29 + 175/6. Let i(v) be the first derivative of -10/9*v**3 - m*v**2 + 1 - 11/4*v**4 + 0*v - 8/3*v**5 - 8/9*v**6. Factor i(h).
-h*(h + 1)**2*(4*h + 1)**2/3
Solve 0 - 8/9*z**3 - 2/9*z - 10/9*z**2 = 0 for z.
-1, -1/4, 0
Let y be 1 + (-1)/(-5)*-1. Let 2/5 - 6/5*o**4 - 2/5*o**5 - y*o**3 + 4/5*o**2 + 6/5*o = 0. What is o?
-1, 1
Let m(q) = -q**2 + 4*q - 2. Suppose 23 = -x + 5*c, c + 0*c - 5 = 0. Let l be m(x). Suppose -l*r**2 - 1 - 3*r + r - 1 - 2*r = 0. What is r?
-1
Let h(z) be the first derivative of 25*z**6/24 - 3*z**5/2 - 11*z**4/16 + z**3 + z**2/2 - 2. Solve h(r) = 0 for r.
-2/5, 0, 1
Let c(x) be the third derivative of 0*x**3 + 0 + 1/36*x**4 + x**2 - 1/90*x**5 - 1/180*x**6 + 1/315*x**7 + 0*x. Find g such that c(g) = 0.
-1, 0, 1
Let o be (-1)/(74/(-111)*1/2). What is b in -8762/5*b**o + 10816/5*b**4 + 16/5 + 2668/5*b**2 - 344/5*b - 4394/5*b**5 = 0?
2/13, 1
Let l(a) be the third derivative of a**5/510 - 5*a**4/204 + 2*a**3/17 - 59*a**2. Suppose l(s) = 0. Calculate s.
2, 3
Find a such that 5*a**2 + 34*a**3 + 26*a**3 - 61*a**3 - 4*a = 0.
0, 1, 4
Factor 1/9*u**4 - 2/9*u + 0 + 2/9*u**3 - 1/9*u**2.
u*(u - 1)*(u + 1)*(u + 2)/9
Solve 4/7*h**2 + 28 + 8*h = 0.
-7
Suppose 2 + 4 = 3*h. Let d be (0 - -4)*1/h. Factor -4*l + 3*l**2 + 5*l**d + 2*l**2.
2*l*(5*l - 2)
Let c = -10 + 13. Factor 2*o**c - 2*o**2 + 0 - 2/3*o**4 + 2/3*o.
-2*o*(o - 1)**3/3
Let y be (-1 + 0)*0 + -7. Let b(u) = -3*u**2 + 6*u + 9. Let t(s) = -4*s**2 + 9*s + 13. Let r(x) = y*b(x) + 5*t(x). Suppose r(q) = 0. What is q?
-2, -1
Let r(t) be the first derivative of -t**3 + 0*t**2 - 3/5*t**5 - 4 + 0*t + 3/2*t**4. Suppose r(b) = 0. What is b?
0, 1
Factor m**3 + 6/5*m**2 - 4/5*m + 1/5*m**4 - 8/5.
(m - 1)*(m + 2)**3/5
Let j(i) be the second derivative of i**4/16 + 3*i**3/4 + 27*i**2/8 + 5*i. Factor j(p).
3*(p + 3)**2/4
Let d be (-1)/2 - 14/(-4). Factor 0*n**2 + d*n**2 + 5*n**2 - n + 3*n.
2*n*(4*n + 1)
Let s(x) be the second derivative of x**5/30 + 5*x**4/36 + 2*x**3/9 + x**2/6 - 6*x. Factor s(v).
(v + 1)**2*(2*v + 1)/3
Let w(f) be the first derivative of -f**3/6 + f**2/2 - 6. Factor w(k).
-k*(k - 2)/2
Let z(t) = 4*t + 4. Let h be z(0). Let s(u) be the second derivative of 3/20*u**5 + 0*u**2 + 0*u**h + 2*u + 0 + 0*u**3. Suppose s(o) = 0. Calculate o.
0
Let i(c) = 5*c + 2. Let b(v) = v**2 + 6*v + 3. Let r(a) = 2*b(a) - 3*i(a). Let d(p) = 7*p + 0*p**2 - 7*p**2 + 2*p**2. Let o(k) = -3*d(k) - 7*r(k). Factor o(g).
g**2
Let n(j) be the second derivative of -1/40*j**5 - 1/4*j**3 - 1/8*j**4 + 0 - 1/4*j**2 + 2*j. Let n(u) = 0. Calculate u.
-1
Let l(g) be the third derivative of -1/8*g**4 + 0 + 0*g**5 + 1/120*g**6 + 0*g + 1/3*g**3 + 3*g**2. Factor l(h).
(h - 1)**2*(h + 2)
Factor 68*p**2 + 72*p**2 - 9*p**3 - 143*p**2.
-3*p**2*(3*p + 1)
Let p(u) be the first derivative of -1/7*u**4 + 0*u**3 + 2/7*u**2 + 2/7*u - 2/35*u**5 + 3. Factor p(b).
-2*(b - 1)*(b + 1)**3/7
Solve 10*a + 0*a + 0*a + a**2 - 3*a + 6 = 0 for a.
-6, -1
Let w(f) = 2*f**2 - 14*f + 12. Let t be w(6). Suppose 1/4*x**3 + t - 1/4*x - 1/4*x**2 + 1/4*x**4 = 0. Calculate x.
-1, 0, 1
Factor -4/7*h**3 - 2/7*h**5 + 6/7*h**4 + 0*h + 0*h**2 + 0.
-2*h**3*(h - 2)*(h - 1)/7
Let l = 6 + -1. Suppose 5 = 5*v - l. Factor v + b**3 - 2*b**3 + 0*b**3 + 3*b.
-(b - 2)*(b + 1)**2
Let k(u) = 8*u**2 - u - 2. Let q be k(2). Factor -5*o**2 + 3*o**5 - 4*o**4 - 31*o**3 + q*o**3 + 7*o**4 + 2*o**2.
3*o**2*(o - 1)*(o + 1)**2
Let y = -13 + 16. Suppose -m - 4*l = 3*m, -y*l = -5*m. Determine i, given that -1/4*i**3 + m*i**2 + 0*i + 0 - 1/4*i**4 = 0.
-1, 0
Let g(d) = -2 + 5*d**2 + 5 - 11*d**2. Let i(a) = -a**2 + a - 1. Let h(j) = g(j) + 3*i(j). Factor h(l).
-3*l*(3*l - 1)
Factor -8*r - 15*r**3 - 18*r**3 + r**3 - 28*r**2 - 12*r**4.
-4*r*(r + 1)**2*(3*r + 2)
Factor -36 - 4*c**2 - 11*c**2 + 4*c**2 - 24*c + 7*c**2.
-4*(c + 3)**2
Let m(u) be the second derivative of 1/6*u**4 + 0*u**3 + 1/21*u**7 + 1/5*u**6 + 3/10*u**5 + 0*u**2 + 0 - 2*u. Determine h, given that m(h) = 0.
-1, 0
Suppose 2*y - 18 = -4*t + 4*y, -2*t + 2*y = -14. Let a(v) = -2*v + 20. Let f be a(9). Solve -3*h**f - 6*h + 4*h + 5*h**t = 0 for h.
0, 1
Let q be (-4 - 4/(-8))*2. Let d = q - -10. Factor -3/2 - 3/2*j**2 + d*j.
-3*(j - 1)**2/2
Let w(y) be the second derivative of -y**5/130 + y**3/13 - 2*y**2/13 + 3*y. Factor w(n).
-2*(n - 1)**2*(n + 2)/13
Let c(x) = 6*x - 44. Let m be c(8). Let d(a) be the second derivative of 0*a**2 + 1/21*a**m + 1/70*a**5 - 2*a + 1/21*a**3 + 0. Factor d(r).
2*r*(r + 1)**2/7
Let o(d) be the first derivative of d**5/270 + d**2 + 1. Let h(t) be the second derivative of o(t). Find m such that h(m) = 0.
0
Suppose -3*k + 5 = 2*k. Let h be ((-15)/12)/(-5)*k. Find w, given that 0 - h*w**2 + 1/4*w = 0.
0, 1
Factor -2/3*o - 1/3*o**3 - 7/6*o**2 + 2/3.
-(o + 2)**2*(2*o - 1)/6
Determine a so that -8*a**4 - 580*a**2 - 20*a**3 - 12*a + 552*a**2 + 4*a**4 = 0.
-3, -1, 0
Let z be (5/(-5))/((-2)/(-4)). Let k = z - -2. Factor k*u**2 + u**2 - u**4 + 0*u**2.
-u**2*(u - 1)*(u + 1)
Let z(i) = -8*i**4 + 19*i**3 - 24*i**2 + 8*i + 5. Let b(y) = 12*y**4 - 28*y**3 + 36*y**2 - 12*y - 8. Let u(g) = 5*b(g) + 8*z(g). Let u(c) = 0. What is c?
0, 1
Let m = 15 - 14. What is s in -m + s + 6*s**4 + 2*s**3 + 9*s**4 - 14*s**2 - 7*s**5 - 2*s**5 + 6*s = 0?
-1, 1/3, 1
Let u = -2 + 1. Let a be (-2*(-2)/(-12))/u. Factor -a*d**3 + 0 - 1/3*d**2 + 1/3*d**4 + 1/3*d.
d*(d - 1)**2*(d + 1)/3
Factor 2 - 4*z**3 - 3 - 3 - 4 + 12*z.
-4*(z - 1)**2*(z + 2)
Factor 0*p**4 + 4*p**4 + 2*p**3 + 6*p**3 - 2*p**4.
2*p**3*(p + 4)
Determine n, given that 22*n**2 + 0*n**2 - 18 - n - n**2 + 4*n = 0.
-1, 6/7
Let b = 138 + -138. Let s(l) be the second derivative of b*l**3 - 1/120*l**6 + 0*l**2 + 1/48*l**4 + 1/80*l**5 + 0 - 3*l - 1/168*l**7. Let s(u) = 0. What is u?
-1, 0, 1
Determine g, given that -g**2 + 28*g - 73*g - 20 + 25*g - 4*g**2 = 0.
-2
Suppose 2*x - 50 = -3*k, 0 = -0*k + k - x - 10. Let f be (-21)/k + (-57)/(-30). Factor -f*j**2 + 0 + 2/5*j**3 + 0*j.
2*j**2*(j - 1)/5
Let x(h) be the first derivative of 1/5*h**2 + 0*h**3 - 2 + 0*h - 1/10*h**4. Determine n, given that x(n) = 0.
-1, 0, 1
Determine c so that 0*c + 15/2*c**4 + 0 - 2*c**2 + 6*c**3 + 2*c**5 = 0.
-2, 0, 1/4
Let i = 15597/320 + -9/64. Factor -324/5*c - 36/5*c**3 - i - 162/5*c**2 - 3/5*c**4.
-3*(c + 3)**4/5
Let t be 25/(-10)*-266*(-3)/(-10). Find h, given that 4 + 161*h**2 + 49*h**5 + t*h**4 + 547/2*h**3 + 42*h = 0.
-2, -1, -1/2, -2/7
Let b(z) be the second derivative of -z**7/77 - 4*z**6/165 + 13*z**5/55 - 4*z**4/11 + z**3/33 + 4*z**2/11 + 21*z. What is y in b(y) = 0?
-4, -1/3, 1
Suppose -a + 11 = -13*d + 9*d, 4*a + 5*d - 2 = 0. What is f in 1/5 - 2/5*f**a - 1/5*f**4 + 0*f**2 + 2/5*f = 0?
-1, 1
Let d be 170/45 + (-2)/(-9). Suppose -d = 5*v - 14. Solve 0*b**v + 2/5*b + 1/5*b**4 - 2/5*b**3 - 1/5 = 0.
-1, 1
Find m, given that 0 - 2/9*m**2 - 4/9*m + 2/9*m**3 = 0.
-1, 0, 2
Let x(t) = t + 7. Let z be x(-6). Let u be (z/6)/(2/40). Factor u*m**3 + 14/3*m + 2/3*m**4 + 4/3 + 6*m**2.
2*(m + 1)**3*(m + 2)/3
Suppose -1 = -4*w - 3*b + 31, -5*b + 20 = 0. Let f be (-5)/(-1)*2/w. Suppose j**4 - 1 - 5*j - 4*j**3 + 0*j**3 + f*j**3 + 7*j = 0. Calculate j.
-1, 1
Let m(y) be the first derivative of 2*y**5/5 - 7*y**4/2 + 4*y**3 - 34. Find p, given that m(p) = 0.
0, 1, 6
Let g(i) = i**3 - 11*i**2 + 12*i + 2. Let w be g(10). Solve 12 + 3*d**2 + 9*d - w + 16 = 0.
-2, -1
Let q = -8 - -10. Let l(z) be the first derivative of -1 + 0*z**2 - 2/3*z**3 + q*z. Factor l(x).
-2*(x - 1)*(x + 1)
Let w = -9 - -8. Let p(y) = -1. Let z(i) = -4*i**3 + 10*i**2 - 8*i - 10. Let b(j) = w*z(j) + 12*p(j). Let b(q) = 0. What is q?
1/2, 1
Let y(v) be the first derivative of -v**8/840 + v**7/210 - v**6/180 - v**3/3 + 4. Let f(a) be the third derivative of y(a). Suppose f(r) = 0. Calculate r.
0, 1
Solve 2*x**4 + 5*x**5 + 5*x**2 - 5*x**3 - 3*x**4 + x**4 - 5*x