) = 4*a**3 - 8*a**2 + 12*a + 36. Let f(b) = -r(b) + 6*s(b). What is j in f(j) = 0?
-3, 2
Let z be (-325)/(-45) - (3 - -2). Factor 10/9*c + 2/9 + 10/9*c**4 + 2/9*c**5 + 20/9*c**3 + z*c**2.
2*(c + 1)**5/9
Let p = 67/154 + 3/22. Factor -10/7*x**2 - p + 2*x.
-2*(x - 1)*(5*x - 2)/7
Let b(d) be the second derivative of -3*d - 1/480*d**6 - 1/2*d**2 + 1/96*d**4 + 0*d**3 + 0*d**5 + 0. Let k(f) be the first derivative of b(f). Factor k(n).
-n*(n - 1)*(n + 1)/4
Let d(k) be the third derivative of k**7/525 - 27*k**2. Solve d(y) = 0.
0
Suppose 49*l = 47*l + 4. Factor 4/3*o - 10/3*o**3 + 0 - l*o**2.
-2*o*(o + 1)*(5*o - 2)/3
Suppose -2*m - 4*u = -8, 32 = 5*m - u - u. Factor -m - 36*q**2 + 27*q + 15*q**3 + 2 - 2.
3*(q - 1)**2*(5*q - 2)
Let d = 183 - 181. Let o(i) be the first derivative of -4/5*i + 1/10*i**4 - d + i**2 - 8/15*i**3. Solve o(u) = 0 for u.
1, 2
Let a(b) be the first derivative of -b**4/20 + b**3/5 + 9*b**2/10 + 10*b + 1. Let c(w) be the first derivative of a(w). Find o, given that c(o) = 0.
-1, 3
Let l(i) = i**3 + 7*i**2 - i - 6. Let m be l(-7). Let g(p) be the first derivative of -m - 4*p - 9*p**2 - 8/3*p**3. Factor g(t).
-2*(t + 2)*(4*t + 1)
Let k(t) be the third derivative of 7*t**6/660 + 54*t**5/55 + 115*t**4/4 + 1058*t**3/33 - 45*t**2. Determine u so that k(u) = 0.
-23, -2/7
Factor 11/3*f**2 + 4/3 + 8*f.
(f + 2)*(11*f + 2)/3
Let s(t) be the first derivative of t**5/25 - 3*t**4/10 + 13*t**3/15 - 6*t**2/5 + 4*t/5 + 13. Factor s(g).
(g - 2)**2*(g - 1)**2/5
Let r(i) be the first derivative of -3*i**4/4 + i**3 + 3*i**2/2 - 3*i + 13. Find o, given that r(o) = 0.
-1, 1
Let l(q) be the second derivative of -q**4/21 - 2*q**3/3 + 16*q**2/7 + 2*q + 4. Factor l(r).
-4*(r - 1)*(r + 8)/7
Suppose -2*v + 1 + 3 = 0. Let p = -3859/12 - -1289/4. Factor 0*l**v - 1/3*l**5 + p*l**3 - 1/3*l + 0*l**4 + 0.
-l*(l - 1)**2*(l + 1)**2/3
Let z(x) = -x**3 - 2*x**2 - x - 5. Let l be z(-4). Let a be 3/6*(l + 1). Factor -10*b**4 - 6*b**2 + a*b**3 + 4*b**4 + b - 5*b.
-2*b*(b - 2)*(b - 1)*(3*b + 1)
Let t be 0 - (6/(-4) + 22/20). Factor 4/5*m**2 + t*m**3 + 0 + 2/5*m.
2*m*(m + 1)**2/5
Let n be 1 + 2 - (-7 + 1). Suppose -q**2 + q**5 - q**3 - 5*q**4 + n*q**3 - 3*q**2 = 0. What is q?
0, 1, 2
Let o(g) be the third derivative of g**8/112 + g**7/70 - g**6/20 - g**5/10 + g**4/8 + g**3/2 - 18*g**2. Find y, given that o(y) = 0.
-1, 1
Let o(t) be the third derivative of t**5/12 - 25*t**4/24 + 10*t**3/3 - 4*t**2 - t. Factor o(a).
5*(a - 4)*(a - 1)
Let 4/7*i + 5/7*i**2 + 0 + 1/7*i**3 = 0. Calculate i.
-4, -1, 0
Let u(w) be the third derivative of -w**11/166320 + w**10/75600 + w**5/60 - 2*w**2. Let p(l) be the third derivative of u(l). Factor p(q).
-2*q**4*(q - 1)
Let h(c) be the third derivative of -49*c**5/390 + 7*c**4/26 - 3*c**3/13 - c**2 + 4*c. Suppose h(r) = 0. Calculate r.
3/7
Suppose -u = 4*u - 10. Factor 4*n**5 - 5*n**5 + 2*n**3 - n - n**2 + n**u.
-n*(n - 1)**2*(n + 1)**2
Suppose g + 5 = 0, 0*u + 3*u + 4*g + 161 = 0. Let b = u + 145/3. Suppose -2/3*d**2 + b*d + 0 = 0. What is d?
0, 2
Let w(y) be the second derivative of 2/9*y**3 + 0 + 1/12*y**5 + 2/15*y**6 + 0*y**2 - 1/14*y**7 - 1/3*y**4 - 2*y. Suppose w(a) = 0. Calculate a.
-1, 0, 2/3, 1
Let p be 2/6 + 2/(-6). Let c(k) = -5*k**3 - 2*k**2 - 8*k - 7. Let g be c(-1). Factor 0*y - 2/5*y**g + 0*y**3 + p*y**2 + 0.
-2*y**4/5
Suppose -1/3*x**2 - 1 + 4/3*x = 0. What is x?
1, 3
Let x(w) be the third derivative of w**7/105 - w**6/15 + w**5/15 + w**4/3 - w**3 - 2*w**2. Factor x(g).
2*(g - 3)*(g - 1)**2*(g + 1)
Let w = 3/4 - 7/12. Let l(y) be the first derivative of w*y**3 + 1/24*y**4 + 0*y - 4 + 1/6*y**2. Factor l(o).
o*(o + 1)*(o + 2)/6
Let j(r) be the second derivative of -4*r**6/15 + 7*r**5/10 - r**4/3 - r**3/3 - 9*r. Factor j(g).
-2*g*(g - 1)**2*(4*g + 1)
Determine n, given that -3*n**2 - 194 + 194 - n**3 = 0.
-3, 0
Let b(g) be the first derivative of g**8/560 + g**7/280 - g**3/3 - 3. Let i(f) be the third derivative of b(f). Factor i(c).
3*c**3*(c + 1)
Suppose 0 = 4*l - 20, 2*l = -b + 4*b + 1. Suppose -3*k + 2 = -d - 2, 8 = -b*k - 2*d. What is h in 4/7*h**2 + k*h**3 - 2/7*h - 4/7*h**4 + 0 + 2/7*h**5 = 0?
-1, 0, 1
Let c(r) be the second derivative of -r**9/4320 - 3*r**8/4480 - r**7/2520 + r**4/4 + 2*r. Let s(m) be the third derivative of c(m). Let s(t) = 0. Calculate t.
-1, -2/7, 0
Solve 2*c**4 - 1/2*c + 0 + 1/2*c**3 - 2*c**2 = 0 for c.
-1, -1/4, 0, 1
Let r(l) = l**2 - 4*l + 6. Let g be r(3). Let v(q) be the first derivative of -2 + 1/6*q**4 - q**2 + 0*q**g - 4/3*q. Solve v(d) = 0.
-1, 2
Let s(y) = -2. Let h(f) = -50*f**2 - 40*f + 20. Let b(a) = -2*h(a) - 28*s(a). Factor b(m).
4*(5*m + 2)**2
Let n(f) be the third derivative of 0 + 1/660*f**6 + 4*f**2 + 0*f - 1/33*f**3 + 1/44*f**4 - 1/110*f**5. Factor n(u).
2*(u - 1)**3/11
Let i = 16/7 + -2. Factor -2/7*k**4 + 6/7*k**2 + 4/7 - i*k**3 + 10/7*k.
-2*(k - 2)*(k + 1)**3/7
Let d be (-1)/((-11)/(55/2)). Factor 3/2*k**2 + d*k**3 + 0 - k.
k*(k + 1)*(5*k - 2)/2
Let u be (-5)/(-5) - (-18)/(-20). Let l(z) be the first derivative of -2/15*z**3 + 0*z**2 + 0*z - 1 + u*z**4. Solve l(j) = 0.
0, 1
Let p(g) be the third derivative of g**8/756 - g**7/189 + g**6/270 + 2*g**5/135 - g**4/27 + g**3/27 + 25*g**2. Determine b so that p(b) = 0.
-1, 1/2, 1
Let o(g) be the first derivative of 2*g**3/57 + 10*g**2/19 + 50*g/19 + 10. Determine t so that o(t) = 0.
-5
Let z(s) be the first derivative of s**8/3360 - s**7/672 + s**6/480 + s**5/480 - s**4/96 + s**3/3 - 5. Let c(o) be the third derivative of z(o). Solve c(p) = 0.
-1/2, 1
Find c, given that 0*c**2 + 1/2 - 1/4*c**3 + 3/4*c = 0.
-1, 2
Let t(c) be the first derivative of 1/4*c**3 + 2 - 3/4*c + 0*c**2. Suppose t(f) = 0. What is f?
-1, 1
Let f(b) be the second derivative of b**6/3 + 7*b**5/10 + b**4/3 + b. Determine h so that f(h) = 0.
-1, -2/5, 0
Suppose -8*m + 72 = -2*m. Suppose 0 = m*s - 11*s. Determine n so that s*n - 1/5*n**2 + 0 = 0.
0
Let w be -5 - 8/((-8)/9). Factor -50/7*o**w + 0 + 20*o**3 + 16/7*o - 88/7*o**2.
-2*o*(o - 2)*(5*o - 2)**2/7
Let v = 7/124 - -6/31. Factor -3/4*b - v*b**2 + 1/2 - 1/4*b**4 + 3/4*b**3.
-(b - 2)*(b - 1)**2*(b + 1)/4
Let j(u) = 4*u**2 - 4*u + 2. Let z(c) = c**3 - c**2 + 1. Let v(l) = j(l) - 2*z(l). Factor v(k).
-2*k*(k - 2)*(k - 1)
Let g(l) = l**3 - 5*l**2 - 34*l - 18. Let o be g(9). Suppose o*a + 4/5*a**3 + 0 - 16/5*a**2 = 0. What is a?
0, 4
Let a(n) = -3*n**4 - 8*n**3 - 3*n**2 + 2. Let h(d) = 9*d**4 + 25*d**3 + 9*d**2 - 7. Let s be 4/26 - 72/(-39). Let c(o) = s*h(o) + 7*a(o). Factor c(l).
-3*l**2*(l + 1)**2
Suppose 2*d - 5*p - 6 = -1, 30 = 5*d + 5*p. Let w(n) be the first derivative of 1 + 0*n - 7/12*n**4 + 2/5*n**d + 2/9*n**3 + 0*n**2. Factor w(r).
r**2*(2*r - 1)*(3*r - 2)/3
Let c(m) be the third derivative of m**6/120 + m**5/30 - 22*m**2. Let c(t) = 0. What is t?
-2, 0
Let k(c) be the third derivative of c**8/112 + c**7/70 - 6*c**2. Factor k(h).
3*h**4*(h + 1)
Factor 0*u + 0*u**3 + 2/5 + 2/5*u**4 - 4/5*u**2.
2*(u - 1)**2*(u + 1)**2/5
Let m be (-1 + (-6)/(-5))*6. Let x(p) be the first derivative of 2 - 17/2*p**4 + 3*p**6 - 14/3*p**3 + 8*p**2 + m*p**5 + 8*p. Find o such that x(o) = 0.
-1, -2/3, 1
Let b(o) be the second derivative of -o**6/30 + o**5/10 - o**3/3 + o**2/2 - o. Solve b(q) = 0.
-1, 1
Let c(s) be the first derivative of -s**6/10 - 33*s**5/50 - 7*s**4/5 - 4*s**3/5 - s + 4. Let w(j) be the first derivative of c(j). Factor w(r).
-3*r*(r + 2)**2*(5*r + 2)/5
Let r(d) = -d**3 - d**2 + d. Let g(s) = -3*s**5 - 15*s**4 - 33*s**3 - 33*s**2 - 12*s - 3. Let q(l) = -g(l) + 3*r(l). Factor q(v).
3*(v + 1)**5
Let x = -10 - -19. Factor -9 + 3*a**2 + 6*a - 3*a**3 + x.
-3*a*(a - 2)*(a + 1)
Let q(o) be the second derivative of 0 - 1/10*o**5 - 1/2*o**2 + 1/4*o**4 + 0*o**3 + 2*o. Factor q(b).
-(b - 1)**2*(2*b + 1)
Let m(g) be the third derivative of -g**6/150 - 2*g**5/75 + 2*g**2. Factor m(k).
-4*k**2*(k + 2)/5
Let q(l) be the third derivative of l**5/300 - l**4/120 - l**3/15 + l**2. Suppose q(s) = 0. Calculate s.
-1, 2
Let c be 1*-9 + -2 + 3. Let p be 2/(-4)*c/3. What is i in -2*i**5 - p - 8/3*i**4 + 8/3*i**3 - 2/3*i + 4*i**2 = 0?
-1, 2/3, 1
Let x(y) be the second derivative of 0 + 3*y + 1/24*y**4 - 1/80*y**5 - 1/24*y**3 + 0*y**2. Factor x(p).
-p*(p - 1)**2/4
Let o(n) be the third derivative of 7*n**6/120 + n**5/2 + 3*n**4/2 + 4*n**3/3