 g**5 - 5*g**4 + 4*g**3 + 2*g. Let q(c) = -5*c**5 + 26*c**4 - 21*c**3 - 11*c. Let y(w) = 11*p(w) + 2*q(w). Suppose y(t) = 0. What is t?
0, 1, 2
Let b be 36/50*80/(-84). Let p = -2/5 - b. Factor 2/7*k**3 + 0*k**2 - p*k + 0.
2*k*(k - 1)*(k + 1)/7
Let j(b) = 23*b**2 + 23*b + 17. Let m(r) = 3*r - 3. Let q be m(3). Let u(f) = 6*f + 2*f + 2*f**2 + 6 + 6*f**2. Let y(v) = q*j(v) - 17*u(v). Factor y(p).
2*p*(p + 1)
Let j(o) be the second derivative of -o**7/42 - o**6/15 + o**4/6 + o**3/6 + 2*o + 31. Find g such that j(g) = 0.
-1, 0, 1
Let n be 4/8 + (-9)/(-6). Determine g, given that 68 + 2*g**n - 68 - 2*g**4 = 0.
-1, 0, 1
Let c be 10 - -1 - 0/(-6). Let m = -31/3 + c. Let 0 - 2/3*x - m*x**2 = 0. What is x?
-1, 0
Let f = 4354/57171 + -6/1003. Let r = 34/57 + f. Let 0 + 2/3*s**3 - 2/3*s**2 + r*s**4 - 2/3*s = 0. Calculate s.
-1, 0, 1
Let h(r) be the second derivative of r + 1/24*r**4 + 0 + 0*r**3 + 1/40*r**5 + 0*r**2. Factor h(z).
z**2*(z + 1)/2
Solve -2*n**3 - 5*n + 8*n**3 + 4*n**3 - 5*n**5 = 0.
-1, 0, 1
Let j(t) be the first derivative of -1/3*t**2 - 3 + 0*t - 1/12*t**4 - 1/3*t**3. Factor j(a).
-a*(a + 1)*(a + 2)/3
Let n = 74/3 - 24. Find d, given that -1/3*d**4 + 1/3*d**5 + 1/3*d + n*d**2 - 2/3*d**3 - 1/3 = 0.
-1, 1
Factor -6/7*f**2 - 3/7 + 9/7*f.
-3*(f - 1)*(2*f - 1)/7
Let t be ((-7)/2)/1 - -4. Suppose -1/4*n**4 - 1/4*n**2 + 0*n + 0 + t*n**3 = 0. What is n?
0, 1
Let o = 0 - -4. Factor y**o + y + y**4 - 2*y + 3*y - 2*y**2 - 2*y**3.
2*y*(y - 1)**2*(y + 1)
Suppose 4 - 4 + 2*n**5 + 2*n**3 + 3*n**4 - 7*n**4 = 0. Calculate n.
0, 1
Suppose -6*o = -3*o - 36. Factor -7*l**2 + l**3 - o + 24*l - 2*l**2 - 6*l**2 + 2*l**3.
3*(l - 2)**2*(l - 1)
Let l(i) be the third derivative of 1/6*i**3 - 2*i**2 + 1/420*i**7 - 1/240*i**6 - 1/40*i**5 + 1/48*i**4 + 0 + 0*i. Find g such that l(g) = 0.
-1, 1, 2
Let c(p) = -192*p**5 + 48*p**4 + 6*p**3 + 3*p**2. Let n(h) = -384*h**5 + 96*h**4 + 11*h**3 + 7*h**2. Let a(j) = -13*c(j) + 6*n(j). Determine y so that a(y) = 0.
-1/4, 0, 1/4
Let -4/5*z**4 + 8/5*z**2 + 2/5*z + 2/5*z**5 - 4/5*z**3 - 4/5 = 0. Calculate z.
-1, 1, 2
Let a(v) = -5*v**4 - 5*v**3 + 7*v**2 + 9*v + 6. Let n(w) = 11*w**4 + 11*w**3 - 15*w**2 - 19*w - 13. Let b(z) = -9*a(z) - 4*n(z). Factor b(i).
(i - 2)*(i + 1)**3
Let m(o) be the second derivative of o**6/75 - o**5/50 - o**4/30 + o**3/15 - o. Find q, given that m(q) = 0.
-1, 0, 1
Factor 0 + 1/3*d + 1/3*d**3 - 2/3*d**2.
d*(d - 1)**2/3
Let x = -122 + 76. Let j be (-17)/(-5) + x/115. Suppose 0 - 3/4*f + 3/4*f**j + 3/4*f**2 - 3/4*f**4 = 0. What is f?
-1, 0, 1
Let w be (-4 + 6 - -2) + -4. Find x, given that w - 10/9*x**2 - 4/9*x - 2/9*x**4 - 8/9*x**3 = 0.
-2, -1, 0
Let n be (-4*(-1)/6)/((-4)/(-30)). Let o(y) be the first derivative of -1/2*y**4 - 1/3*y**3 + y**2 + 3/10*y**n - 3 - 1/2*y. Find k, given that o(k) = 0.
-1, 1/3, 1
Suppose 3 + 7 = 5*f. Factor 5 - 1 - 5*c + 6*c**2 - f - 3*c.
2*(c - 1)*(3*c - 1)
Find p, given that 2/5 + 2/15*p**2 + 8/15*p = 0.
-3, -1
Let x(b) = b**2 + 5*b - 5. Let f be x(-5). Let o be f*(4/(-10) + 0). Suppose -2*i + 0*i + i**o + i**2 = 0. Calculate i.
0, 1
Let n be 12/(-54) + 2/9. Suppose 2/7*o**2 - 4/7*o + n = 0. Calculate o.
0, 2
Let w(n) = -2 + 1 - n + 4. Let b be w(0). Determine m so that -b*m**2 + 1 + 5*m**2 - 8*m**3 + 4*m**5 - 2 - m**4 + 4*m = 0.
-1, 1/4, 1
Let i(v) be the first derivative of -v**4/4 - 2*v**3/3 - v**2/2 + 14. Factor i(r).
-r*(r + 1)**2
Let j(c) be the first derivative of -c**7/70 + c**6/20 + c**2 + 3. Let q(h) be the second derivative of j(h). Factor q(p).
-3*p**3*(p - 2)
Let v(a) be the first derivative of 2*a**5/45 - a**4/18 - 2*a**3/9 + a**2/9 + 4*a/9 - 3. Determine k, given that v(k) = 0.
-1, 1, 2
Solve 0*w + 3/5*w**4 + 0 + 0*w**2 - 6/5*w**3 = 0.
0, 2
Solve -b - 12 + 10 + b**2 + 0*b = 0 for b.
-1, 2
Let m(o) be the first derivative of 1/15*o**3 - 1/5*o - 3/20*o**4 + 5 + 3/10*o**2. What is i in m(i) = 0?
-1, 1/3, 1
Let b be (40/70)/(2/21). Let p(z) be the third derivative of 1/24*z**4 + 0 + 0*z + z**2 - 1/360*z**b + 1/9*z**3 + 0*z**5. Suppose p(f) = 0. What is f?
-1, 2
Let o = 7 - 5. Factor -2*k**2 - 3*k**o - 9*k + 3*k**3 - k**2.
3*k*(k - 3)*(k + 1)
Let q be 4 + 504/(-48)*2/6. Factor 1/4*n + q - 1/4*n**2.
-(n - 2)*(n + 1)/4
Let o(m) be the second derivative of -m**5/330 + m**2/2 + 2*m. Let c(j) be the first derivative of o(j). Factor c(p).
-2*p**2/11
Let b be 6*((-57)/15 - -4). Factor -3/5*v**3 - 3/5*v + 0 - b*v**2.
-3*v*(v + 1)**2/5
Factor 0*j + 0*j**3 - 2/7*j**2 + 2/7*j**4 + 0.
2*j**2*(j - 1)*(j + 1)/7
Let z(l) be the third derivative of -1/15*l**4 + 1/150*l**6 - 1/50*l**5 + 0*l + 1/525*l**7 + 0 - l**2 + 4/15*l**3. Factor z(c).
2*(c - 1)**2*(c + 2)**2/5
Let q be (1 - -1)*(-3)/2. Let g = -1 - q. Factor -2*m**3 + 2*m**3 + g*m**3 - 2*m**5.
-2*m**3*(m - 1)*(m + 1)
Let r be 9/4*(-8)/3. Let v = 6 + r. Determine f, given that 72*f**5 + 32/7*f**3 + 354/7*f**4 - 22/7*f**2 - 4/7*f + v = 0.
-1/3, -2/7, 0, 1/4
Let a(f) = f**3 - 2*f**2 + 1. Let p(o) = -o**3 + 7*o**2 + 3*o - 1. Let x(n) = -2*a(n) - p(n). Factor x(l).
-(l + 1)**3
Suppose 4*r + 6*r = 3*r. Let d(x) be the first derivative of 2/3*x**3 - 2/5*x**5 + r*x + 2 + 2*x**2 - x**4. Factor d(u).
-2*u*(u - 1)*(u + 1)*(u + 2)
Determine s, given that -1/3*s**2 - 2/3*s - 1/3 = 0.
-1
Let j(m) be the first derivative of -m**5/2 + 17*m**4/8 - 7*m**3/2 + 11*m**2/4 - m + 5. Factor j(p).
-(p - 1)**3*(5*p - 2)/2
Suppose 4*d**4 - 3*d**4 + d - 3*d**4 + 2*d**2 - d**5 = 0. Calculate d.
-1, 0, 1
Let y be 1*(-7 + 4 - -3). Suppose -k = 4*l - 55, k - 70 = l - 6*l. Determine p, given that -21*p - l*p**3 + 3*p**4 + 3 + 27*p**2 + 3 + y = 0.
1, 2
Let h = 2 - 1. Suppose 2*q + 3*b + 3 = 0, -5*q - 3*b = 3 - 0. Factor 3*l + h - l**3 - l**2 + q*l**2 - 2*l.
-(l - 1)*(l + 1)**2
Let d(f) be the first derivative of -f**3 - 3*f**2 - 3*f - 6. Solve d(u) = 0.
-1
Let m(x) = -3*x - 8*x**2 + 3 + 3*x**2 - 7. Let q(t) = -9*t**2 - 5*t - 7. Let d(h) = -7*m(h) + 4*q(h). Let d(o) = 0. What is o?
0, 1
Let b(h) be the first derivative of -3/2*h**2 + 0*h - 7 - h**3. Let b(k) = 0. Calculate k.
-1, 0
Let m be (-12)/6 - (-1 + -4). Suppose -m*n + 0 = -6. Factor -5*x**4 + x**4 + x**3 - 3*x**5 + 2*x**n + 0*x**2.
-x**2*(x + 1)**2*(3*x - 2)
Let f = -11 + 6. Let u be (-2)/4 - (f - -4). What is m in 0 - 2*m**2 + 0*m**3 + 0*m + 3/2*m**4 - u*m**5 = 0?
-1, 0, 2
Suppose -3*p = -0*u - 3*u + 21, -p = -3*u + 17. Let o be (12/(-35))/(p/5). Factor 4/7 + o*k**2 + 2*k.
2*(k + 2)*(3*k + 1)/7
Let f(g) be the first derivative of g**4/20 - g**3/5 + 4*g/5 + 7. Let f(d) = 0. What is d?
-1, 2
Let p be (-2)/(-13) + 150/39. Factor 4*d**2 + d - 2*d**2 - p*d**2 + d**2.
-d*(d - 1)
Let n be (3/(-6))/(4/(-40)). What is b in 3*b**4 + 2*b**n - 7*b**3 - 2*b - 4*b**2 + b**4 + 7*b**3 = 0?
-1, 0, 1
Let y(c) = -5*c**2 + 2*c + 3. Let q(r) = r - 1. Let p(o) = -2*q(o) + y(o). Determine f so that p(f) = 0.
-1, 1
Factor -10/7*j + 8/7 + 2/7*j**2.
2*(j - 4)*(j - 1)/7
Let k(y) be the second derivative of y**8/560 - y**7/140 - y**6/120 + y**5/20 - 5*y**3/6 - 5*y. Let b(z) be the second derivative of k(z). Factor b(q).
3*q*(q - 2)*(q - 1)*(q + 1)
Suppose k - 6 = -k. What is x in -16*x**2 - 2 + x**3 - 14*x**3 - 11*x + 6*x**k = 0?
-1, -2/7
Let p(w) be the third derivative of -w**5/420 + w**4/84 - w**3/42 - 11*w**2. Factor p(o).
-(o - 1)**2/7
Let d(p) = 5*p**4 - 10*p**3 - 10*p - 25. Let o(g) = -g**3 - 1. Let c(z) = -d(z) + 20*o(z). Factor c(h).
-5*(h - 1)*(h + 1)**3
Suppose -2*f - b + 2 = 0, 0*b + 5*b = 4*f + 10. Factor f + 2/3*p**3 + 0*p**2 - 2/3*p.
2*p*(p - 1)*(p + 1)/3
Suppose -w = -5*s - 25 + 3, 5*w - 30 = 5*s. Suppose 0 = a + w*a. Let -6*f**5 + 2/3*f**2 + 10/3*f**3 + 0*f + a + 2*f**4 = 0. What is f?
-1/3, 0, 1
Let c(m) be the second derivative of -m**5/30 + m**4/6 - 2*m. Factor c(a).
-2*a**2*(a - 3)/3
Let o(z) be the first derivative of 0*z + 0*z**2 - 3 + 2/21*z**3. Factor o(t).
2*t**2/7
Let f be 8/3*(-45)/(-75). Factor -26/5*w**2 + 24/5*w**3 - f*w**4 + 12/5*w - 2/5.
-2*(w - 1)**2*(2*w - 1)**2/5
Suppose -3*o + 19 = 10. Let p(d) be the second derivative of 8/9*d**2 + 0 + 25/18*d**5 + 20/9*d**o + 25/9*d**4 + d. Factor p(h).
2*(5*h + 2)**3/9
Suppose 4 = s - g, -8*s = -5*s + 2*g - 2. Let 1/2*f**2 - 2*f + s = 0. What is f?
2
Let g(u) be the second derivative of 0 - 1/3*u**3 + 0*u**2 - 3/10*u**5 - 1/2*u**4 - 1/15*u**6 + 3*u. Factor