38*a**4 + 14*a**4 + 17*a**4 = 0.
-2/3, 0, 3
Let k(v) be the first derivative of -v**6/2 - 9*v**5/5 - 3*v**4/4 + 3*v**3 + 3*v**2 + 35. Determine o, given that k(o) = 0.
-2, -1, 0, 1
Let k(f) be the third derivative of 0*f**3 + 2*f**2 + 0*f**4 + 0 + 1/240*f**5 + 1/120*f**6 + 0*f. Let k(w) = 0. Calculate w.
-1/4, 0
Let m(y) be the first derivative of 15*y**6/2 + 24*y**5 + 20*y**4 - 10*y**3 - 45*y**2/2 - 10*y - 55. Determine p, given that m(p) = 0.
-1, -1/3, 2/3
Let r be 4/22 + (-60)/(-33). Factor r*i**2 + 0*i + 2*i - i**3 - i**3 - 2*i**4.
-2*i*(i - 1)*(i + 1)**2
Let o(h) = h**2 - 9*h - 22. Let b be o(11). Factor 0*w**3 - w**2 + 1/2*w**4 + b*w + 1/2.
(w - 1)**2*(w + 1)**2/2
Let o(m) be the third derivative of 1/14*m**7 + 0*m**3 + 0*m + 0 + 3/40*m**6 - 5*m**2 - 1/20*m**5 + 1/56*m**8 - 1/8*m**4. Factor o(v).
3*v*(v + 1)**3*(2*v - 1)
Let t(c) = -5*c**2 - 2*c + 4. Let b(a) be the first derivative of -a**3/3 + a + 1. Let h be (-42)/(-7)*(-2)/3. Let y(m) = h*b(m) + t(m). Factor y(k).
-k*(k + 2)
Let b be 2/4 + 55/(-10). Let s = -3 - b. Factor 0*o - 1/4*o**3 + 0*o**s + 0 + 1/4*o**5 + 0*o**4.
o**3*(o - 1)*(o + 1)/4
Let h(b) be the third derivative of 243*b**8/56 - 324*b**7/35 - 9*b**6/4 + 139*b**5/15 + 23*b**4/3 + 8*b**3/3 - 8*b**2. Factor h(n).
2*(n - 1)**2*(9*n + 2)**3
Let g(u) be the second derivative of 0 - 1/10*u**5 + u + 0*u**2 + 0*u**3 + 1/6*u**4. Factor g(m).
-2*m**2*(m - 1)
Let i(n) be the third derivative of -n**5/40 + n**4/8 - 4*n**2. Solve i(j) = 0.
0, 2
Let z(b) be the second derivative of -5*b**4/48 - 25*b**3/24 + 15*b**2/4 - 44*b. Factor z(j).
-5*(j - 1)*(j + 6)/4
Let k(f) be the third derivative of -f**7/4200 + f**5/150 - f**3/6 - 8*f**2. Let r(u) be the first derivative of k(u). Factor r(y).
-y*(y - 2)*(y + 2)/5
Let j(p) be the second derivative of -3/20*p**5 + 0 + 7*p + 2*p**3 + 1/2*p**4 - 12*p**2. Factor j(r).
-3*(r - 2)**2*(r + 2)
Let g(j) = -j**2 + j - 1. Let k(w) = -6*w**4 - 16*w**3 - 6*w**2 - 12*w + 8. Let p(z) = -8*g(z) - k(z). Find u such that p(u) = 0.
-1, -2/3, 0
Let j(x) be the first derivative of x**3 + 24*x**2 + 192*x - 27. Determine k so that j(k) = 0.
-8
Let s be 1/(-5) - 17/(-85). Let b(g) be the third derivative of -g**2 + s*g**3 - 1/120*g**6 + 0*g - 1/210*g**7 + 1/24*g**4 + 1/60*g**5 + 0. Factor b(x).
-x*(x - 1)*(x + 1)**2
Let n be (-3 - -31)*6/8. Suppose -5*m + 4*p - 6 = -n, 5*m - 15 = -p. Factor 2/7*i**m + 4/7 + 8/7*i**2 + 10/7*i.
2*(i + 1)**2*(i + 2)/7
Let -a**3 - 3*a**4 - a**2 + 3*a**3 + 9*a + 4*a**4 - 11*a = 0. What is a?
-2, -1, 0, 1
Factor -4*d + d**3 + 1/3*d**4 - 2/3*d**2 - 8/3.
(d - 2)*(d + 1)*(d + 2)**2/3
Let b(r) = r**2 + 2*r - 3. Let o be b(3). Solve -6 - 6*a**4 - 21*a**5 + 54*a**3 - o*a**3 - 27*a + 6*a + 12*a**2 = 0 for a.
-1, -2/7, 1
Suppose 0 = 37*v - 31*v. Factor 0 - 4/3*b**3 - 14/3*b**4 + v*b + 0*b**2.
-2*b**3*(7*b + 2)/3
Let z(g) be the second derivative of g**5/120 + g**4/16 + g**3/6 + 3*g**2/2 - g. Let j(k) be the first derivative of z(k). Factor j(m).
(m + 1)*(m + 2)/2
Let j be 0/(-1) + -2 + 4. Let y(q) be the first derivative of -2*q**3 - 1/2*q**4 - j*q**2 + 0*q - 2. Factor y(d).
-2*d*(d + 1)*(d + 2)
Let t(f) = -f**2 - 5*f + 3. Let b be t(-5). Solve g**2 - b + g**2 - 1 - 2*g = 0.
-1, 2
Let v(w) = -2*w**2 + 59*w + 32. Let k be v(30). What is l in -3/4 + 1/2*l - 1/2*l**3 - 1/4*l**4 + l**k = 0?
-3, -1, 1
Let m be 1/(1/2 + -1). Let f = 0 - m. Suppose f*w + 2*w**2 + 0*w**2 + 2 + 2*w = 0. What is w?
-1
Determine i so that 8/9*i**2 + 2/9 - 10/9*i = 0.
1/4, 1
Let r(c) be the first derivative of 15*c**4/4 + 12*c**3 + 6*c**2 - 7. Factor r(q).
3*q*(q + 2)*(5*q + 2)
Suppose 0*c - 3*c + 5*l = -29, 4*c - 2*l = 20. Suppose -1/4*t**2 + 1/4*t**4 + 0 - 1/4*t**5 + 1/4*t**c + 0*t = 0. What is t?
-1, 0, 1
Let u(q) = -5 + 7 + 1 - 4. Let v(b) = -2*b**3 - 6*b**2 - 6*b - 6. Let i(l) = 4*u(l) - v(l). Factor i(y).
2*(y + 1)**3
Let u = 22 + -18. Let p(j) be the second derivative of 0*j**3 - j + 0 + 0*j**2 - 1/48*j**u. Factor p(s).
-s**2/4
Let m be 0/8*(-1)/2. Factor -12*i**2 - 6 + 6 + m - 3*i.
-3*i*(4*i + 1)
Let g(z) be the third derivative of z**8/112 + z**7/70 - 3*z**6/40 - z**5/20 + z**4/4 + 5*z**2. Factor g(t).
3*t*(t - 1)**2*(t + 1)*(t + 2)
Let o(n) = n**2 - 17*n + 32. Let w be o(15). Find r such that -2/3*r**4 + 0 + 2/3*r**w - 1/3*r**5 + 1/3*r + 0*r**3 = 0.
-1, 0, 1
Let s(o) be the second derivative of -o**5/130 + 2*o. Factor s(h).
-2*h**3/13
Let i(v) be the first derivative of -v**4/8 - v**3/3 + 7. Let i(n) = 0. What is n?
-2, 0
Suppose 8 = 5*y - 12. Factor 5*n**2 - n - 5 + y - 1 - 2*n**3.
-(n - 2)*(n - 1)*(2*n + 1)
Factor 3/2*g + 0 - 1/2*g**2.
-g*(g - 3)/2
Suppose -160*u**2 - 3*u - 8 - 30*u + 100*u**3 - 12*u - 31*u = 0. What is u?
-1/5, 2
Let g(v) be the second derivative of v**9/15120 + v**8/6720 - v**7/2520 - v**6/720 - 7*v**4/12 + v. Let b(u) be the third derivative of g(u). Factor b(q).
q*(q - 1)*(q + 1)**2
Let c(y) be the third derivative of -y**11/166320 + y**10/37800 - y**9/30240 - y**5/20 - 3*y**2. Let h(a) be the third derivative of c(a). Solve h(o) = 0 for o.
0, 1
Let h(v) = 8*v**4 - 6*v**3 + 20*v**2 + 6*v + 2. Let m(o) = o**4 - o**3 + 2*o**2 + o. Let x(z) = 2*h(z) - 20*m(z). What is d in x(d) = 0?
-1, 1
Let y(n) be the second derivative of 1/55*n**5 + 0 + 0*n**4 + 0*n**2 + 6*n - 1/231*n**7 + 0*n**6 - 1/33*n**3. Factor y(z).
-2*z*(z - 1)**2*(z + 1)**2/11
Let r(g) be the first derivative of 2*g**3/39 + 5*g**2/13 + 12*g/13 + 9. Factor r(f).
2*(f + 2)*(f + 3)/13
Let m = 225 + -390. Let p be (-162)/m + 20/(-25). Factor -6/11*n - 4/11 - p*n**2.
-2*(n + 1)*(n + 2)/11
Let h(b) be the first derivative of 11/6*b**3 - 3/4*b**4 + 2 - b**2 + 2*b. Let r(k) be the first derivative of h(k). Factor r(f).
-(f - 1)*(9*f - 2)
Solve -6/5*b + 3/5*b**2 + 0 = 0.
0, 2
Let v(z) be the second derivative of -z**5/160 + z**4/32 - z**3/16 + z**2/16 - 5*z. Find q such that v(q) = 0.
1
Let d be (2 - 4)/(-2) - -1. Let g be (2/(-4))/((-2)/24). Solve g*c**3 - 5*c**3 + c - d*c = 0 for c.
-1, 0, 1
Factor -8/9*c + 10/9 - 2/9*c**2.
-2*(c - 1)*(c + 5)/9
Factor -4*w - 28*w**5 - 5*w**3 + 13*w**3 + 13*w**5 + 11*w**5.
-4*w*(w - 1)**2*(w + 1)**2
Let o be ((-12)/(-20))/(-3)*-3. Let -2/5 - 1/5*q**2 - o*q = 0. Calculate q.
-2, -1
Let f = -3/14 + 19/14. Factor 2/7*r**4 + 12/7*r**2 - 8/7*r**3 + 2/7 - f*r.
2*(r - 1)**4/7
Let d(k) be the second derivative of -k**5/120 + 5*k**4/72 + k**3/6 - 13*k. Factor d(l).
-l*(l - 6)*(l + 1)/6
Let p(l) be the third derivative of -l**11/831600 + l**9/151200 + l**5/20 - 2*l**2. Let h(a) be the third derivative of p(a). Factor h(j).
-2*j**3*(j - 1)*(j + 1)/5
Let l(x) be the second derivative of -2*x**7/7 - 31*x**6/15 - 27*x**5/5 - 6*x**4 - 8*x**3/3 + 15*x. Let l(c) = 0. What is c?
-2, -2/3, -1/2, 0
Let s be ((-30)/(-18))/(2/(-36)). Let u be s/4*16/(-140). Find c, given that 0 - u*c**4 + 6/7*c**3 - 2/7*c**2 + 0*c + 2/7*c**5 = 0.
0, 1
Let n(k) = k**4 + k**2 - k - 1. Let a(h) = -4*h**4 + 3*h**3 - 2*h**2 + h + 2. Let r(o) = -a(o) - 2*n(o). Suppose r(i) = 0. Calculate i.
-1/2, 0, 1
Let z be (16/(-54))/(-2 - 12/(-9)). Find n, given that 2/9*n**2 + 2/3*n + z = 0.
-2, -1
Let q(d) be the second derivative of -3*d**5/20 - d**4/4 + 2*d**3 + 6*d**2 + 6*d. What is p in q(p) = 0?
-2, -1, 2
Suppose v - w = -2*w - 60, v = 2*w - 45. Let u be (-7)/(-22) + (-10)/v. Solve 0 - 1/2*p**3 + u*p + 7/4*p**4 - 7/4*p**2 = 0.
-1, 0, 2/7, 1
Let z(p) = p**2 + 7*p + 6. Let x be z(-8). Let b be 6/x - (-24)/(-56). Factor -14*a**4 + 0*a - 8*a**3 - 8/7*a**2 + b.
-2*a**2*(7*a + 2)**2/7
Factor -3/5*v + 1/5*v**3 - 2/5*v**2 + 0.
v*(v - 3)*(v + 1)/5
Let x = 20/193 + 11440/1351. Let 0 - 38/7*o**4 + 16/7*o + 24/7*o**2 - x*o**3 + 30/7*o**5 = 0. What is o?
-1, -2/5, 0, 2/3, 2
Determine s, given that 1/4*s**5 + 0*s**2 + 0*s + 0 + 0*s**3 - 1/2*s**4 = 0.
0, 2
Let m be 0/(-2) - 20/(-10). What is q in 0*q + m*q**3 + 4 - 2*q - 4*q = 0?
-2, 1
Let i = -4 - -2. Let o be (0 - 1) + i + 5. Factor 4*u + 4 - 4*u**2 + o*u**2 - 6.
-2*(u - 1)**2
Let j(p) be the second derivative of 25*p**4/48 + 5*p**3/6 + p**2/2 - 6*p. Factor j(d).
(5*d + 2)**2/4
Let p(r) = -3*r**5 + 11*r**4 - 36*r**3 + 31*r**2 - 7. Let k(i) = i**5 - 4*i**4 + 12*i**3 - 10*i**2 + 2. Let u(z) = 14*k(z) + 4*p(z). Find l such that u(l) = 0.
0, 2
Factor 4/3*j + 16/3*j**3 + 0 - 14/3*j**2 - 2*j**4.
-2*j*(j - 1)**2*(3*j - 2