*x = 0. Calculate x.
-1
Let o(t) = 2*t**5 + 2*t**4 + 5*t**3 - 3*t**2 - 3*t + 3. Let a(h) = h**5 + h**4 + 4*h**3 - 2*h**2 - 2*h + 2. Let k(s) = 3*a(s) - 2*o(s). Let k(j) = 0. What is j?
-2, 0, 1
Let g(d) be the third derivative of -d**11/55440 - d**10/9450 - d**9/5040 + d**7/2520 - d**5/30 + 2*d**2. Let x(k) be the third derivative of g(k). Factor x(h).
-2*h*(h + 1)**3*(3*h - 1)
Let h = -2/3 + 1. Let m(g) be the first derivative of -g**4 + g**2 + 2*g + 2/5*g**5 + h*g**6 - 4/3*g**3 - 3. Factor m(a).
2*(a - 1)**2*(a + 1)**3
Let l = 4/11 - 1/33. Factor -l + 7/6*u - 5/6*u**2.
-(u - 1)*(5*u - 2)/6
Let m = 80 + -475/6. Let i(f) be the first derivative of 14/27*f**3 + 4/27*f**6 + m*f**4 + 1/9*f**2 - 3 + 0*f + 26/45*f**5. Factor i(g).
2*g*(g + 1)**3*(4*g + 1)/9
Let n(q) = 12*q**4 + 75*q**3 + 108*q**2 - 3*q - 42. Let l(u) = -u**4 + u**3 + 1. Let h(a) = 6*l(a) + n(a). Suppose h(d) = 0. What is d?
-12, -1, 1/2
Suppose -8401*y - 2*y**2 + 8401*y + 2 = 0. Calculate y.
-1, 1
Let b(f) = -2*f**2 + 18*f - 7. Let a be b(9). Let p be (-2)/(-3) - (-7 - a). Factor p*d + 0 + 2/3*d**2.
2*d*(d + 1)/3
Factor -25*i + 161*i**3 - 10 - 7*i**2 - 13*i**2 - 166*i**3.
-5*(i + 1)**2*(i + 2)
Let x(u) be the first derivative of -2*u**5/65 - u**4/13 + 2*u**2/13 + 2*u/13 - 13. Solve x(g) = 0 for g.
-1, 1
Let j(c) be the second derivative of -c**6/60 + c**4/24 + 8*c. Factor j(y).
-y**2*(y - 1)*(y + 1)/2
Let t(k) = -2*k**4 - 7*k**3 + k**2 + 10*k - 1. Let d(l) = -l**4 - 3*l**3 + l**2 + 5*l. Let z(h) = -5*d(h) + 2*t(h). Solve z(r) = 0.
-1, 2
Let h(y) be the third derivative of 0*y - 3*y**2 + 0*y**3 + 1/40*y**4 + 0 + 1/100*y**5. Factor h(u).
3*u*(u + 1)/5
Let f(h) = 2*h**2 + 2*h + 5. Let l(c) = -3*c**2 - 3*c - 6. Let n(x) = 6*f(x) + 5*l(x). Factor n(q).
-3*q*(q + 1)
Let q(x) = -x**3 - x**2 - 1. Let v(f) = -f**4 + 3*f**3 - 20*f**2 - 8*f + 11. Let b(l) = 5*q(l) - v(l). Let b(p) = 0. Calculate p.
-1, 1, 4
Let i(z) be the first derivative of -z**8/112 + z**7/35 - 9*z**2/2 - 1. Let x(v) be the second derivative of i(v). Factor x(q).
-3*q**4*(q - 2)
Let r(c) be the first derivative of -1/12*c**3 + 2 + 0*c + 0*c**2 + 1/8*c**4 + 3/20*c**5. Factor r(w).
w**2*(w + 1)*(3*w - 1)/4
Let p = 5993/7 - 856. Find b such that -p*b**3 - 1/7*b + 0 + 2/7*b**2 = 0.
0, 1
Let s(r) = -1 - 19*r**3 - 4 - r**2 + 4*r**2 + 23*r - 2*r**2. Let c(i) = -6*i**3 + 8*i - 2. Let v(f) = 8*c(f) - 3*s(f). Solve v(d) = 0.
-1/3, 1
Let h be -1*(1 + 0 - -16). Let z = -13 - h. Factor 2/7*s**z + 2/7*s**2 - 6/7*s + 6/7*s**3 - 4/7.
2*(s - 1)*(s + 1)**2*(s + 2)/7
Suppose -2*s = -5*k - 342, 3*k = 4*s + 5*k - 684. Let v be 6/21 + s/63. Determine h so that 0*h**2 + 0 - 1/3*h**4 + 0*h + 1/3*h**v = 0.
0, 1
Suppose 0 = 4*j + j - 25. Let w = -3 + j. Solve a**3 - 3*a**4 - 15*a - 2*a**2 + 6 + 2*a**3 + 11*a**w = 0.
-2, 1
Let l(g) = -g**3 - 12*g**2 - 11*g + 4. Let m be l(-11). Let w be 2/m*2 + -1. Let w*r + 0 - 1/4*r**3 + 0*r**2 = 0. Calculate r.
0
Suppose 3*h - 6 = h. Factor -1 + 0*o**2 + h - 4*o + 2*o**2.
2*(o - 1)**2
Let k = 13 + -16. Let s be 35/21 - k/9. Factor 0 - s*z**2 + 1/2*z.
-z*(4*z - 1)/2
Let s(q) = q**2 - 3*q - 7. Let g(k) = -k**2 - k - 1. Let h(o) = -3*g(o) + s(o). Factor h(l).
4*(l - 1)*(l + 1)
Let o(p) be the second derivative of p**5/100 + p**4/30 + p**3/30 - 5*p. Find j, given that o(j) = 0.
-1, 0
Let b = -53/2 - -27. Let i(v) be the second derivative of -v - 1/20*v**5 - b*v**3 + 1/4*v**4 + 0 + 1/2*v**2. Factor i(d).
-(d - 1)**3
Suppose 2*b = -b. Let k(u) be the second derivative of 0 + 1/3*u**3 + b*u**2 - 1/6*u**4 + u. Find z such that k(z) = 0.
0, 1
Let g(t) be the first derivative of 1/10*t**5 - 1/4*t**2 - 3 + 0*t + 1/8*t**4 - 1/6*t**3. Suppose g(x) = 0. What is x?
-1, 0, 1
Let m(i) be the third derivative of -i**7/210 - i**6/120 + i**5/60 + i**4/24 + 5*i**2. Factor m(y).
-y*(y - 1)*(y + 1)**2
Let q be 722/180 - 2 - 2. Let i(v) be the second derivative of -1/135*v**6 + 2/9*v**2 + q*v**5 + v + 1/18*v**4 + 0 - 5/27*v**3. Find z such that i(z) = 0.
-2, 1
Solve 12*y + 3205 - y**2 - 3205 = 0 for y.
0, 12
Let o(b) = -b**2 - 9*b - 9. Let d be o(-7). Suppose 0 = 3*f - 3*z + 3, -3*f + 5 = -d*z + 18. Factor -7*u**4 + 6*u**2 - 2*u**f + 2*u**3 - 2*u + 3*u**4.
-2*u*(u - 1)*(u + 1)*(3*u - 1)
Let i(d) = d**3 - d**2 + d - 8. Let t be i(0). Let a = 11 + t. Factor -2*m**4 + m**3 + 0*m**4 - a*m**3.
-2*m**3*(m + 1)
Let h(x) = 2*x**3 - x**2 - 2*x - 4. Let r(b) = -b**3 + b + 2. Let n(s) = 2*h(s) + 5*r(s). Factor n(m).
-(m - 1)*(m + 1)*(m + 2)
Let y be 3/(-1*3) + 4. Factor 2*i**2 - i**y + i**4 - 3*i**2 - 3*i**5 + 4*i**5.
i**2*(i - 1)*(i + 1)**2
What is o in 2/7*o - 4/7*o**2 + 4/7*o**4 + 0*o**3 + 0 - 2/7*o**5 = 0?
-1, 0, 1
Let u(c) = 1 - 10*c**2 - 2*c - c + 1. Let i(n) be the first derivative of n**3/3 + n**2/2 - 1. Let j(o) = -2*i(o) + u(o). Find a, given that j(a) = 0.
-2/3, 1/4
Let s = 2 + -2. Suppose 0 = -m - 5*w - 7 + 31, 3*w - 12 = s. Factor 0*v**2 + m*v**3 + 4*v**2 + 14*v**5 + 2*v**3 - 24*v**4.
2*v**2*(v - 1)**2*(7*v + 2)
Let d be 30/(-12) + 10/4. Let u(l) be the first derivative of 0*l**4 + 0*l + 0*l**5 - 1/36*l**6 + 0*l**3 + d*l**2 - 2. Determine m so that u(m) = 0.
0
Let 1/2*b**4 - 1/4*b**5 - 1/4*b**3 + 0*b**2 + 0 + 0*b = 0. Calculate b.
0, 1
Let o(i) be the second derivative of 2*i**3 + 0 - 5/6*i**4 - i**2 + 2*i. Find t such that o(t) = 0.
1/5, 1
Let o = 5 - 3. Let s(k) be the second derivative of 0 - 1/7*k**o - k - 3/70*k**5 + 1/42*k**4 + 1/7*k**3. Solve s(w) = 0 for w.
-1, 1/3, 1
Suppose l + 2*l = 0. Suppose 0*m = 3*m - 6. Find g, given that 1/4*g**3 + 0 - 1/4*g + l*g**m = 0.
-1, 0, 1
Factor -6*c**2 + 0 + 9/2*c + 3/2*c**3.
3*c*(c - 3)*(c - 1)/2
Let t(f) be the third derivative of -f**9/90720 - f**8/60480 - f**5/20 + f**2. Let h(q) be the third derivative of t(q). Factor h(o).
-o**2*(2*o + 1)/3
Let l(u) be the second derivative of -25*u**7/42 + 7*u**6/6 + 13*u**5/4 - 55*u**4/12 - 20*u**3/3 + 10*u**2 + 13*u. Suppose l(a) = 0. What is a?
-1, 2/5, 1, 2
Let t = 13 + -9. Let a(c) = 2*c - 12. Let m be a(6). Factor -8/7*l**2 - 162/7*l**t + 0*l + m - 72/7*l**3.
-2*l**2*(9*l + 2)**2/7
Suppose -1/4*y**2 - 5/4*y - 1 = 0. Calculate y.
-4, -1
Let p(v) be the first derivative of 2*v**3/3 - 2*v**2 + 38. Suppose p(m) = 0. Calculate m.
0, 2
Let v be -1 - (-2 - 16)/3. Suppose -v*t + 4*s = -20, 2*s = -8 - 2. Find a such that 0*a**5 + 2*a + 2*a**5 + 0*a - 4*a**3 + t*a = 0.
-1, 0, 1
Let 69/7*l**2 - 48/7 + 3/7*l**5 + 3*l**3 - 3*l**4 - 24/7*l = 0. Calculate l.
-1, 1, 4
Let q = 6 - 2. Let d(s) = -s + 1. Let h be d(-1). Factor -4 - 57*w**h - 3*w**q - w**3 + w**5 + 0*w**4 + 64*w**2.
(w - 2)**2*(w - 1)*(w + 1)**2
Suppose 5*h = 11 + 4. Factor -z - z**3 + h*z**3 - z.
2*z*(z - 1)*(z + 1)
Factor 18*t**2 + 6*t + 9*t**4 + 3/2*t**5 + 0 + 39/2*t**3.
3*t*(t + 1)**2*(t + 2)**2/2
Let a(r) be the second derivative of 4*r**5/5 - 2*r**3 + 2*r**2 + 3*r. Suppose a(o) = 0. Calculate o.
-1, 1/2
Let q(p) be the second derivative of -p**6/90 - p**5/15 - p**4/6 - 5*p**3/6 + 5*p. Let v(w) be the second derivative of q(w). Factor v(h).
-4*(h + 1)**2
Let d(t) = 5*t**3 - 14*t**2 - 16*t. Let c(b) = 4*b**3 - 13*b**2 - 16*b. Let m(l) = 6*c(l) - 5*d(l). Find o, given that m(o) = 0.
-4, 0
Let r(o) = o**3 + 2*o**2 + 5*o - 8. Let k be r(1). Determine w so that k + 0*w**2 + 8/9*w - 14/9*w**3 + 2/3*w**4 = 0.
-2/3, 0, 1, 2
Let p(t) be the first derivative of -2 + 0*t**2 + 4/3*t**3 + 2/5*t**5 + 0*t - 3/2*t**4. Factor p(g).
2*g**2*(g - 2)*(g - 1)
Suppose r = -2*r + 12. Factor 3*h**3 + h - h**r - h**2 + h**2 + 2*h**4 + 3*h**2.
h*(h + 1)**3
Find a, given that 4 + 4*a + 6 - 10 - 6*a**2 + 2*a**4 = 0.
-2, 0, 1
Suppose 0 = k + l - 2, -4*l - 5 = l. Let 1/2*p**k + 1/4 - 3/4*p**2 + 0*p = 0. What is p?
-1/2, 1
Let g(m) = 10*m**2 - 6*m - 10. Let w(h) = 21*h**2 - 11*h - 19. Let i(l) = -13*g(l) + 6*w(l). Determine a, given that i(a) = 0.
-1, 4
Suppose a = 4*a - 4*h - 4, h + 1 = -2*a. Let f(c) be the third derivative of 0*c - 1/12*c**3 + a - c**2 - 1/120*c**5 + 1/24*c**4. Factor f(u).
-(u - 1)**2/2
Let l(g) be the second derivative of g**6/360 + g**5/60 + g**4/24 + g**3/6 + 2*g. Let h(t) be the second derivative of l(t). Let h(n) = 0. What is n?
-1
Let x(d) be the second derivative of 0 - 2*d + 1/12*d**3 + 1/8*d**2 + 1/48*d**4. Factor x(g).
(g + 1)**2/4
Let t(q) be the first derivative of -27*q**5/10 - 27*q**4/