3*a(g) + 8*h(g). Let c be y(0). Factor 4/3 + 1/3*x**c + 4/3*x.
(x + 2)**2/3
Let m(r) = r**2 - r - 4. Let i be m(3). Let k be -2*(3/(-1) + i). Factor 2*d**4 - k*d**2 - 2*d**2 + 2 + 0*d**2.
2*(d - 1)**2*(d + 1)**2
Let 63/2*c**3 + 258*c - 36 - 477*c**2 + 147/2*c**4 = 0. Calculate c.
-3, 2/7, 2
Let x be 12/15 - (-2)/10. Suppose x - 7 = -2*j. Factor -1/3*y**4 + 0 - 1/3*y**j + 1/3*y + 1/3*y**2.
-y*(y - 1)*(y + 1)**2/3
Factor 16*o**2 + 20 + 25*o - 17*o**2 + 6*o**2.
5*(o + 1)*(o + 4)
Factor 3*r**5 - 6*r**2 - 5*r**4 + 22*r**4 - 3*r**3 - 11*r**4.
3*r**2*(r - 1)*(r + 1)*(r + 2)
Let u be (-7 - -3) + (-8)/(-2). Let w(l) be the third derivative of 0 + 0*l + 0*l**4 + 0*l**6 + 1/30*l**5 + u*l**3 - 1/105*l**7 + l**2. Factor w(q).
-2*q**2*(q - 1)*(q + 1)
Solve -14*l - 21*l**3 + 26*l**3 + 40*l**2 + 30 + 79*l = 0.
-6, -1
Factor -3/2 - 81/2*j**2 - 81/2*j**3 - 27/2*j.
-3*(3*j + 1)**3/2
Let x(y) = -y**2 - 10*y - 4. Let n(u) = u**2 + 9*u + 5. Let h(a) = -4*n(a) - 5*x(a). Factor h(r).
r*(r + 14)
Let g(p) = -6*p**4 - 9*p**3 + 8*p**2 + 9*p + 3. Suppose -9*m = -4*m + 25. Let b(r) = -r**2. Let o(u) = m*b(u) - g(u). Factor o(f).
3*(f - 1)*(f + 1)**2*(2*f + 1)
Let r(l) be the second derivative of -l**7/70 - 9*l**6/25 - 183*l**5/100 + 9*l**4 - 10*l**3 - 44*l. Factor r(h).
-3*h*(h - 1)**2*(h + 10)**2/5
Let t(m) = 2*m**3 + 9*m**2 - 18*m + 2. Let k(s) = 3*s**3 + 19*s**2 - 35*s + 3. Let v(g) = 6*k(g) - 11*t(g). Let v(p) = 0. What is p?
-1/4, 2
Let s(c) be the first derivative of 2*c**3/9 + c**2/3 - 4*c + 1. Factor s(v).
2*(v - 2)*(v + 3)/3
Let k(l) = -8*l**4 - 6*l**3 - 4*l**2 - 6. Let o(d) = 15*d**4 + 11*d**3 + 7*d**2 + 11. Let m(j) = -11*k(j) - 6*o(j). Factor m(p).
-2*p**2*(p - 1)*(p + 1)
Let 4/7*f - 2/7 - 2/7*f**2 = 0. What is f?
1
Let h = -154 - -2311/15. Let a(i) be the second derivative of 2*i**2 + 1/3*i**3 - 1/2*i**4 + 2*i + 0 - 1/10*i**5 + h*i**6. Determine f, given that a(f) = 0.
-1, 1, 2
Suppose 4*x = -4*p + 4, -p + 2*x - 5 = -4*p. Let o(u) = -u + 5. Let d be o(p). Solve -1 + 3*m + d*m + 0*m**3 + m**2 + m**3 - 6*m = 0 for m.
-1, 1
Suppose -9 = 3*o - 18. What is g in 12/11*g**2 - 2/11*g**o - 24/11*g + 16/11 = 0?
2
Let b(y) = -y**5 - 12*y**4 + 21*y**3 - 8*y**2 - 3*y - 3. Let f(m) = -12*m**4 + 20*m**3 - 8*m**2 - 2*m - 2. Let w(g) = -4*b(g) + 6*f(g). Solve w(i) = 0 for i.
0, 1, 4
Let k(n) be the second derivative of -n**4/54 + n**3/27 + 29*n. Factor k(s).
-2*s*(s - 1)/9
Find u such that -2/7 + 8/7*u - 8/7*u**2 = 0.
1/2
Let f(g) = -2*g**3 - 2*g**2 + 7*g + 7. Suppose 5*m = 17 + 18. Let u(t) = -t**3 - 2*t**2 + 6*t + 6. Let y(j) = m*u(j) - 6*f(j). Factor y(c).
c**2*(5*c - 2)
Let f(d) be the third derivative of -d**5/90 - 5*d**4/36 + 2*d**3/3 - 2*d**2 - 9. Suppose f(z) = 0. What is z?
-6, 1
Let o(d) = d**2 - 3*d + 5. Let u(g) = -2*g**2 + 4*g - 6. Let y(q) = 4*o(q) + 3*u(q). Let y(s) = 0. What is s?
-1, 1
Let d be (2/(-3))/((-2)/18). Factor 3*q + 2*q**4 + 8*q**3 + 12*q**2 + d*q - q + 2.
2*(q + 1)**4
Suppose 0 = -0*v - v - o - 2, -8 = -4*v + 4*o. Let c(z) be the third derivative of 1/6*z**3 + z**2 - 1/120*z**5 + 1/48*z**4 + v + 0*z. What is x in c(x) = 0?
-1, 2
Let n be (-18)/12*(-8)/66. Let c be 8/(-44) + 16/22. Factor -n*j**2 - 4/11 + c*j.
-2*(j - 2)*(j - 1)/11
Let r(v) = -v**3 + 6*v**2 - 4*v - 5. Let h be r(5). Suppose 2*z + h - 2 = 0. Solve -3*o**3 - o**2 + 4*o**3 - o + 0*o + z = 0.
-1, 1
Let t(k) be the first derivative of 1/16*k**4 + 0*k**2 + 2*k + 2 - 1/12*k**3. Let x(z) be the first derivative of t(z). Factor x(m).
m*(3*m - 2)/4
Let a(g) be the second derivative of g**6/45 + g**5/5 + 13*g**4/18 + 4*g**3/3 + 4*g**2/3 + 8*g. Factor a(i).
2*(i + 1)**2*(i + 2)**2/3
Let v(w) = -w**2 + 13*w + 19. Let z be v(14). Let o(l) be the second derivative of -1/12*l**4 + 0 + 0*l**2 + 0*l**3 + l - 1/20*l**z. Factor o(b).
-b**2*(b + 1)
Determine l so that 8/3*l**2 - 4*l + 0*l**4 + 16/3*l**3 - 4/3*l**5 - 8/3 = 0.
-1, 1, 2
Let y(m) be the first derivative of m**4/10 - 2*m**3/3 + 3*m**2/5 + 18*m/5 + 7. Factor y(g).
2*(g - 3)**2*(g + 1)/5
Let t(o) be the third derivative of -o**5/15 - o**4/6 - 9*o**2. Factor t(g).
-4*g*(g + 1)
Let k(h) be the second derivative of -h**8/168 + 2*h**7/105 - h**5/15 + h**4/12 + h**2/2 - 2*h. Let r(f) be the first derivative of k(f). Factor r(z).
-2*z*(z - 1)**3*(z + 1)
Let c(t) be the third derivative of -t**6/360 + t**4/72 + t**2. Solve c(m) = 0.
-1, 0, 1
Let i(y) be the second derivative of -2/27*y**4 - 1/135*y**6 + 2*y + 0*y**2 + 2/45*y**5 + 0 + 0*y**3. Solve i(b) = 0 for b.
0, 2
Let p(q) be the first derivative of q**6/9 - 2*q**4/3 - 4*q**3/9 + q**2 + 4*q/3 - 7. Factor p(s).
2*(s - 2)*(s - 1)*(s + 1)**3/3
Let w = 30 + -28. Let l(y) be the second derivative of y + 1/21*y**3 + 2/7*y**w - 1/42*y**4 + 0. Solve l(d) = 0.
-1, 2
Suppose -33 = -3*b - 9. Suppose 0 = 3*c + 2*r - 1, -b*c + 4*c = r - 8. What is j in 0 + 1/2*j - 1/2*j**c + j**4 - j**2 = 0?
-1, 0, 1/2, 1
Determine a so that 12/7*a**3 - 26/7*a**2 + 24/7*a - 8/7 - 2/7*a**4 = 0.
1, 2
Suppose -3*c - f = f - 8, 12 = -4*c + 3*f. Let b be c + (0 + 2 - 0). Factor -b*v**5 + 3*v**5 + v**5.
2*v**5
Let q(h) be the first derivative of -h**5/10 - h**4/8 - 4. Determine w so that q(w) = 0.
-1, 0
Let z be (1 - 2) + 0 - -1. Let a(b) be the second derivative of 2*b**3 - 3/8*b**4 - 3*b**2 + 3*b + z. Factor a(h).
-3*(h - 2)*(3*h - 2)/2
Let p(d) be the second derivative of -d**4/18 - d**3/9 + 2*d**2/3 + 6*d. Find w such that p(w) = 0.
-2, 1
Let j be (-345)/(-60) - 3/4. Suppose 0 - 8*p**3 + 2/3*p**2 + 32/3*p**j + 8/3*p**4 + 2/3*p = 0. What is p?
-1, -1/4, 0, 1/2
Let f(l) be the second derivative of -l**4/3 + 8*l**3/3 - 6*l**2 - 4*l. Find m, given that f(m) = 0.
1, 3
Let p(m) = -m**3 + 6*m**2 - 4*m - 2. Let l be p(5). Factor 0*w - w + l*w - 2*w**5 - 4*w**2 + 4*w**4.
-2*w*(w - 1)**3*(w + 1)
Let p(m) = -m**2 + 11*m - 6. Let o be p(10). Find f such that -2 + f**4 - 2*f - f**4 + 2*f**o + 6*f - 4*f**3 = 0.
-1, 1
Let o be 20/18*(-12)/(-20). Let n(l) be the first derivative of 4*l - o*l**3 + 2 + l**2. Let n(k) = 0. Calculate k.
-1, 2
Let a be 4/14 - (-2584)/4284. Find r, given that -26/9*r**3 + 16/9 + 40/9*r + 4/3*r**2 + 2/3*r**5 - a*r**4 = 0.
-1, -2/3, 2
Let m(p) be the second derivative of p**6/105 + 2*p**5/35 + 5*p**4/42 + 2*p**3/21 - p. Suppose m(x) = 0. Calculate x.
-2, -1, 0
Let i(c) be the second derivative of c**8/6720 - c**7/2520 - 5*c**4/12 - 7*c. Let u(s) be the third derivative of i(s). Solve u(v) = 0 for v.
0, 1
Let q be 28/24 - (12/4)/6. Solve q*f**4 + 0 - 2/3*f**2 - 2/3*f**3 + 2/3*f**5 + 0*f = 0 for f.
-1, 0, 1
Let u(w) be the third derivative of -w**7/1260 - w**6/120 - w**5/40 + w**4/36 + w**3/3 + 53*w**2. Factor u(h).
-(h - 1)*(h + 2)**2*(h + 3)/6
Let u be -6 + (-4)/(4*(-2)/16). Suppose -1/2 - y - 1/2*y**u = 0. Calculate y.
-1
Let y(h) be the second derivative of -3*h - 5/12*h**3 - 1/40*h**5 - 1/6*h**4 - 1/2*h**2 + 0. Factor y(p).
-(p + 1)**2*(p + 2)/2
Suppose 5*h + 2*v - 20 = 0, 0*v - 2*v = 0. Let y(m) be the first derivative of 0*m**2 - 3/16*m**h + 1 - 3/4*m**3 + 3*m. Factor y(d).
-3*(d - 1)*(d + 2)**2/4
Let q(n) = -2*n**3 - 7*n**2 + 9*n. Let i(m) = 3*m**3 + 8*m**2 - 8*m. Let w(s) = 5*i(s) + 4*q(s). Suppose w(o) = 0. Calculate o.
-2, 0, 2/7
Let w(q) = 3*q**4 - 2*q**3 + 2*q**2 - 3*q. Let k(i) = 5*i**3 - 8*i**2 + 4*i - i**4 + 6*i**2 - 3*i**4 - 3*i**3. Let m(p) = 5*k(p) + 6*w(p). Factor m(f).
-2*f*(f - 1)*(f + 1)**2
Suppose -1 = -4*n + 15. Factor -c**2 + 2*c**3 - n*c**3 + 0*c**4 - c**4.
-c**2*(c + 1)**2
Suppose 4*g = 4*n + g - 21, 5*g - 23 = -3*n. Suppose -3*b + 25 - 8 = 4*x, 2*x = -b + 5. Solve -r**2 + 2 + n - b = 0 for r.
-1, 1
Let n(p) be the first derivative of -p**7/35 + 11*p**6/180 - p**5/18 + p**4/36 + 4*p**3/3 + 2. Let g(r) be the third derivative of n(r). Factor g(f).
-2*(3*f - 1)**2*(4*f - 1)/3
Let p(a) be the second derivative of a**7/126 - a**5/30 + a**3/18 + a. Solve p(q) = 0 for q.
-1, 0, 1
Let d(n) be the second derivative of 3/40*n**5 + 7/40*n**6 + 0*n**2 + 0*n**3 + 0 + 1/14*n**7 - 1/16*n**4 - 4*n. Factor d(w).
3*w**2*(w + 1)**2*(4*w - 1)/4
Find a such that 24*a - a**3 - 2*a**3 - 4*a**3 + 28*a**2 + 11*a**3 = 0.
-6, -1, 0
Suppose -6 + 2 = -2*l. Let t be 0/(3 - 1 - 1). Factor -2*u + 0*u**2 + 1 + u**l + t*u**2.
(u - 1)**2
Let x(y) be the first derivative of 4*y**5/5 - 4*y**4 - 20*y**3/3 + 44. Determine f,