*2 + 7*g - 1. Let n(z) = p*y(z) + 3*j(z). Let n(o) = 0. What is o?
-1
Suppose 3*k + 4 = 2*k - 3*f, -3*k + 10 = -2*f. Let -6/5*j + 4/5*j**k + 2/5*j**3 + 0 = 0. What is j?
-3, 0, 1
Let 0*z**3 - 5*z**4 - 10*z**3 - 56*z**2 + 51*z**2 = 0. Calculate z.
-1, 0
Let z(a) be the first derivative of 1/2*a**4 + 4/3*a**3 + 0*a**2 - 5 + 0*a. Factor z(j).
2*j**2*(j + 2)
Let s be 5/(-25) + 2/10. Let b(q) be the second derivative of -1/30*q**4 + 0*q**5 + 0 + 1/75*q**6 - q + 0*q**3 + s*q**2. Factor b(j).
2*j**2*(j - 1)*(j + 1)/5
Let m = 80 - 12792/161. Let j = m + -6/23. Factor 8/7*a**2 + 0 - 12/7*a**3 + 8/7*a**4 - 2/7*a**5 - j*a.
-2*a*(a - 1)**4/7
Let c = -11 + 14. Let o(r) be the first derivative of 4 - 2*r + 0*r**2 + 2/3*r**c. Factor o(k).
2*(k - 1)*(k + 1)
Let d(t) be the first derivative of -t**4/14 + 6*t**3/7 - 24*t**2/7 + 32*t/7 + 19. Determine p, given that d(p) = 0.
1, 4
Let d(q) = 3*q**3 - 50*q**2 - 80*q - 53. Let m(v) = -v**3 + 25*v**2 + 40*v + 26. Let t(u) = 6*d(u) + 13*m(u). Factor t(f).
5*(f + 1)*(f + 2)**2
Suppose 0 = -s - 5*l + 13, 0*l = 5*s - 2*l - 11. Let -8*f**2 - f**s + 2*f**2 + 4*f**2 - f**3 = 0. Calculate f.
-1, 0
What is d in 0*d**3 + 6*d**3 + 41*d**4 - 50*d**4 + 3*d**5 = 0?
0, 1, 2
Suppose -5*h = -222 - 158. Let -6*z**3 + 74*z - h*z + 4*z**3 - 4*z**2 = 0. What is z?
-1, 0
Let u(d) = -d**2 + 1. Let h(b) = 9*b**3 + 15*b**2 - 6*b - 12. Let g(m) = -h(m) - 12*u(m). Factor g(z).
-3*z*(z + 1)*(3*z - 2)
Let l(i) = -5*i**2 - 3. Let r(n) be the first derivative of -11*n**3/3 - 7*n + 1. Let f(h) = 9*l(h) - 4*r(h). Factor f(g).
-(g - 1)*(g + 1)
Let n = 2 - -3. Factor n*x - 2*x - x**2 - 2 - 3*x + 3*x.
-(x - 2)*(x - 1)
Suppose -2/9*w + 0*w**2 + 0*w**4 - 2/9*w**5 + 0 + 4/9*w**3 = 0. What is w?
-1, 0, 1
Let m(g) be the second derivative of -g**5/30 + g**4/18 + 2*g**3/9 + 21*g. Factor m(j).
-2*j*(j - 2)*(j + 1)/3
Let n(o) be the second derivative of 0 - 2/3*o**3 + 3*o + 0*o**2 + 11/6*o**4. Let n(h) = 0. What is h?
0, 2/11
Factor 4/13*j**2 - 2/13*j**3 - 2/13*j + 0.
-2*j*(j - 1)**2/13
Let f(j) be the first derivative of 35*j**4/4 - 50*j**3 + 90*j**2 - 40*j - 17. Determine w so that f(w) = 0.
2/7, 2
Factor -1/5*i**2 - 4/5*i + 12/5.
-(i - 2)*(i + 6)/5
Let n be (-2 - 11/(-4))*20. Suppose q - n = -2*q. Find a such that 0*a + a + 14*a**3 - q*a + 10*a**2 = 0.
-1, 0, 2/7
Let x(b) be the first derivative of 9*b**5/25 + 6*b**4/5 + 4*b**3/5 + 14. Find t such that x(t) = 0.
-2, -2/3, 0
Let t be -6*1/3*-1. Factor 4 + 2*y - 2*y**2 + t - 6.
-2*y*(y - 1)
Let u be 12/(-66) + (-36)/(-77). Determine b, given that u*b**3 + 0 + 0*b**2 - 2/7*b = 0.
-1, 0, 1
Let a(r) be the third derivative of -r**6/180 + r**5/60 - r**3/6 + 2*r**2. Let n(f) be the first derivative of a(f). Factor n(g).
-2*g*(g - 1)
Suppose 3*s - 3*u = -9, 7*u = 3*s + 2*u + 15. Let v(q) be the second derivative of -1/30*q**5 + 1/90*q**6 + 0 + s*q**4 + q + 0*q**2 + 0*q**3. Solve v(j) = 0.
0, 2
Let d(n) be the third derivative of -2/3*n**3 - 1/30*n**5 + n**2 - 1/4*n**4 + 0 + 0*n. Solve d(j) = 0 for j.
-2, -1
Let m = 2 - 2. Let g be 2 + m - 0/(-1). Solve 3*a + g*a**2 - 3*a + 2*a - 4 = 0.
-2, 1
Let h(r) be the first derivative of -2 + 1/7*r**4 - 8/7*r - 2/35*r**5 - 4/7*r**2 + 2/7*r**3. Solve h(m) = 0 for m.
-1, 2
Let d(g) be the second derivative of g**5/210 - g**4/84 + g**2/2 + 2*g. Let h(w) be the first derivative of d(w). Solve h(q) = 0 for q.
0, 1
Let n(r) = r**3 + 9*r**2 + 6*r - 9. Let g be n(-8). Let w = g - 3. Solve 0*p - 4/3*p**3 - 2/3*p**w - 2/3*p**2 + 0 = 0.
-1, 0
Let k(c) be the third derivative of -1/66*c**4 - 2*c**2 + 1/330*c**5 + 0*c**3 + 0 + 0*c. Determine r so that k(r) = 0.
0, 2
Let q(k) be the first derivative of -k**6/30 + 2*k**5/15 - k**4/6 + k**2 - 9. Let f(h) be the second derivative of q(h). Solve f(l) = 0 for l.
0, 1
Let s(y) = 2*y**2 + 73*y - 118. Let i(d) = -d**2 - 24*d + 39. Let v(l) = -17*i(l) - 6*s(l). Determine w, given that v(w) = 0.
3
Let n(x) = x. Let i be n(0). Let b = i - -2. What is d in -3*d**3 + 7*d**4 + d**2 + 3*d - 6*d**4 + b - 4 = 0?
-1, 1, 2
Factor -c**3 - 1/2*c - 7/4*c**2 + 1/4.
-(c + 1)**2*(4*c - 1)/4
Suppose -10*b + 8*b = 0. Let a(u) be the first derivative of -1/3*u**6 + 0*u**5 + b*u - 1 + 1/2*u**4 + 0*u**2 + 0*u**3. Let a(v) = 0. What is v?
-1, 0, 1
Let c(t) be the second derivative of 0*t**2 + 0 + 1/60*t**4 + 5*t - 1/15*t**3. Factor c(u).
u*(u - 2)/5
Let p(a) = 4*a + 1. Let n be p(1). Suppose -n*q + 3*q = 0. Factor -2/5*i**5 + 0*i + q*i**2 + 2/5*i**3 + 0 + 0*i**4.
-2*i**3*(i - 1)*(i + 1)/5
Let m(w) be the first derivative of 245*w**6/6 + 70*w**5 - 505*w**4/4 - 310*w**3/3 + 130*w**2 - 40*w + 2. Suppose m(n) = 0. Calculate n.
-2, -1, 2/7, 1
Let u(y) be the first derivative of 2*y**5/95 + 2*y**4/19 + 2*y**3/19 - 7. Factor u(w).
2*w**2*(w + 1)*(w + 3)/19
Let y(d) be the second derivative of -d**6/30 - d**5/20 - 6*d. Determine r, given that y(r) = 0.
-1, 0
Let u(a) be the first derivative of -a**4/7 + 4*a**3/21 + 4*a**2/7 - 29. Let u(o) = 0. What is o?
-1, 0, 2
Factor -2/3 + 1/3*l**4 + l**3 - l + 1/3*l**2.
(l - 1)*(l + 1)**2*(l + 2)/3
Let x be -2 + 118/68 + (-7)/(-14). Solve -2/17*u**5 + 4/17*u**4 - x*u**2 + 0*u**3 + 2/17*u + 0 = 0 for u.
-1, 0, 1
What is v in 4/11*v**2 + 10/11*v + 4/11 = 0?
-2, -1/2
Let d = -201 + 201. Factor -1/5 + 0*o + d*o**3 - 1/5*o**4 + 2/5*o**2.
-(o - 1)**2*(o + 1)**2/5
Let y(l) = l**3 - 2*l**2 - 5*l. Let o(x) = 4*x**3 - 9*x**2 - 21*x - 1. Let r be ((-6)/4)/((-3)/4). Let s(m) = r*o(m) - 9*y(m). Let s(z) = 0. Calculate z.
-2, 1
Let v be (-40)/64 - (-2 + 0). Let c(x) be the first derivative of -3 + 0*x**2 + 0*x - 8/5*x**5 + v*x**4 + 7/12*x**6 - 1/3*x**3. Determine u so that c(u) = 0.
0, 2/7, 1
Let x = 113 + -113. Solve 2/3*z**4 + x*z - 2/3*z**2 + 0 + 2/3*z**3 - 2/3*z**5 = 0.
-1, 0, 1
Let f(d) be the second derivative of -d**6/30 - 3*d**5/20 + d**4/12 + d**3/2 + 7*d**2/2 + d. Let v(i) = i**3 - i - 3. Let z(x) = 3*f(x) + 7*v(x). Factor z(b).
-b*(b - 1)*(b + 1)*(3*b + 2)
Let h(i) = -i**3 - i**2 + 3. Let x be h(0). Solve -2/5*t + 16/5*t**4 + 4/5 - 4*t**2 - 8/5*t**x + 2*t**5 = 0 for t.
-1, 2/5, 1
Factor -3/5*i + 6/5*i**2 + 0 - 3/5*i**3.
-3*i*(i - 1)**2/5
Let x(g) be the third derivative of 2*g**5/15 + g**4/2 - 10*g**3/3 + 13*g**2. What is a in x(a) = 0?
-5/2, 1
Let f(k) be the third derivative of k**7/42 - 13*k**6/180 - k**5/15 + k**4/9 + 27*k**2. Let f(h) = 0. Calculate h.
-2/3, 0, 2/5, 2
Let v(z) = -19*z - 5*z - 4 - 8*z**2 + 7 + 7*z. Let k(f) = -3*f**2 - 6*f + 1. Let h(j) = -11*k(j) + 4*v(j). Let h(c) = 0. What is c?
1
Let o(v) be the first derivative of 2*v**3/21 - 3*v**2/7 + 28. Factor o(p).
2*p*(p - 3)/7
Let p(k) = -3*k**2 + 6*k + 12. Let b(g) = 1. Suppose -3*n + 34 = -5*w, 5*w = 4*n - 24 - 13. Let s(m) = n*b(m) - p(m). Factor s(a).
3*(a - 3)*(a + 1)
Let s be 16/6*9/(-4). Let k(a) = -a**2 + 4*a + 5. Let n(f) be the first derivative of -f**3/3 + 5*f**2/2 + 6*f + 2. Let l(g) = s*n(g) + 7*k(g). Factor l(v).
-(v + 1)**2
Let y(f) = -2*f - 3. Let u be y(-4). Suppose -2*t = n + t + 8, 0 = 4*n + t - 12. Factor 0*p**4 + p**3 + 0*p**2 - 4*p**n - p**5 + u*p**4 - p**2.
-p**2*(p - 1)**2*(p + 1)
Let x(h) = h**4 + h**3 + h**2. Let m(u) = -26*u**4 - 4*u**3 - 8*u**2. Let l(q) = -m(q) - 8*x(q). Solve l(t) = 0.
0, 2/9
Let c(y) be the second derivative of 0 + 0*y**2 + 0*y**3 - 1/30*y**4 + y. Solve c(w) = 0.
0
Factor 2/9*g**3 - 10/9*g - 2/3 - 2/9*g**2.
2*(g - 3)*(g + 1)**2/9
Let o be (-8)/10*(-50)/20. Solve 0*z**3 + 0 + 2/7*z**o - 2/7*z**4 + 0*z = 0.
-1, 0, 1
Let j(r) = -2*r - 4. Let i be j(-4). Let m be (-2)/(-12) - 2/(-6). Factor 3/4*f + m*f**2 + 1/4 - 1/2*f**3 - 3/4*f**i - 1/4*f**5.
-(f - 1)*(f + 1)**4/4
Determine t, given that 40*t**3 + 31*t**2 + 4*t - 4*t**4 - 47*t**2 - 14*t**4 - 10*t**2 = 0.
0, 2/9, 1
Let o(p) be the first derivative of -p**4/2 + 5*p**3 - 12*p**2 - 16*p - 30. Factor o(l).
-(l - 4)**2*(2*l + 1)
Let y = -837 - -837. Find n, given that y*n**2 + 2/13*n - 2/13*n**3 + 0 = 0.
-1, 0, 1
Let q(z) be the first derivative of 20*z**6/3 - 6*z**5 - 35*z**4/4 + 10*z**3 - 5*z**2/2 + 1. Let q(u) = 0. Calculate u.
-1, 0, 1/4, 1/2, 1
Let z be 2/(-3) + (-51)/(-9). Find a such that 0*a**2 + 0*a + a**2 - 3*a - z + 7 = 0.
1, 2
Let f(g) be the second derivative of 49*g**7/3 - 392*g**6/15 + 84*g**5/5 - 16*g**4/3 + 16*g**3/21 - 4*g. Factor f(u).
2*u*(7*u - 2)**4/7
Let k(q)