t v = -7 - -9. Let m be (-10)/(-3) + v/(-6). Suppose -12 + m*k**4 + 12 = 0. Calculate k.
0
Let 4*h**5 + 46*h**3 + h**2 - 66*h**3 - h**2 + 16*h = 0. What is h?
-2, -1, 0, 1, 2
Let o(a) be the third derivative of -2*a**2 + 3/100*a**5 + 0*a - 1/60*a**4 - 1/50*a**6 + 0*a**3 + 0 + 1/210*a**7. Determine s, given that o(s) = 0.
0, 2/5, 1
Let n(v) be the first derivative of -4*v**6/9 - 4*v**5/15 + 5*v**4/6 + v**3/9 - 2*v**2/3 + v/3 + 30. Factor n(r).
-(r + 1)**2*(2*r - 1)**3/3
Let b(p) be the first derivative of -p**4/24 + p**3/6 + 2*p + 3. Let y(d) be the first derivative of b(d). Factor y(w).
-w*(w - 2)/2
Let m(u) be the second derivative of 0 - 2/7*u**2 - 1/70*u**5 + 1/21*u**3 - 5*u + 1/21*u**4. Suppose m(k) = 0. What is k?
-1, 1, 2
Let m(v) be the first derivative of -12*v**5/5 + 11*v**4/4 + 10*v**3/3 - 11*v**2/2 + 2*v + 13. Determine z, given that m(z) = 0.
-1, 1/4, 2/3, 1
Factor 6*g**2 - 50/3 + 2/3*g**3 + 10*g.
2*(g - 1)*(g + 5)**2/3
Factor 14/13*d - 2/13*d**2 - 12/13.
-2*(d - 6)*(d - 1)/13
Let b(f) be the first derivative of -1/12*f**3 - 1 + 0*f - 2*f**2 + 1/120*f**5 + 0*f**4. Let x(g) be the second derivative of b(g). Factor x(y).
(y - 1)*(y + 1)/2
Suppose 40*n - 33*n = 14. Let -w**3 + 0 + 0*w + 2/7*w**n + 5/7*w**4 = 0. What is w?
0, 2/5, 1
Let a = -681/2 - -5461/16. Let t = 341/144 - a. Find b, given that 0 + t*b**2 - 4/9*b = 0.
0, 2/7
Let g(k) = 4*k**3 + 6*k - 5. Let z(v) = -5*v**3 + v**2 - 6*v + 6. Let a(w) = 6*g(w) + 5*z(w). Let x be a(6). Factor 0 + x*u**2 - 2/7*u**3 + 2/7*u.
-2*u*(u - 1)*(u + 1)/7
Let w(u) be the third derivative of -u**8/2352 - 2*u**7/735 - u**6/280 + u**5/105 + u**4/42 - 2*u**2. Let w(g) = 0. Calculate g.
-2, -1, 0, 1
Let a(z) = -z**3 - 7*z**2 - 5*z + 4. Let f be a(-6). Let b be (-3)/(-3) + f/4. Let 0 + 0*d + 1/2*d**2 - d**3 + b*d**4 = 0. Calculate d.
0, 1
Let y = -22 + 134. Let n = y + -782/7. Factor -n*r**2 + 4/7 + 2/7*r.
-2*(r - 2)*(r + 1)/7
Let w(c) = -7*c**2 + c. Let h(p) = -11*p**2 + p. Let m(b) = 5*h(b) - 8*w(b). Factor m(x).
x*(x - 3)
Let y be ((-2)/14)/(6/(-7)). Let x(f) be the second derivative of 0 - y*f**4 + 5/12*f**3 - 1/4*f**2 - 2*f. Factor x(n).
-(n - 1)*(4*n - 1)/2
Let l(o) = 7*o**2 - 6*o - 1. Let y(n) = 5*n + 38 - 6*n**2 - 18 - 19. Suppose -4*z - 38 = 4*q + q, 0 = -3*q + 3*z - 12. Let b(g) = q*y(g) - 5*l(g). Factor b(i).
(i - 1)*(i + 1)
Factor -3/5*d**2 + 4/5 + 0*d - 1/5*d**3.
-(d - 1)*(d + 2)**2/5
Let g be (2/27)/((-9)/(-27)). Let k(w) be the first derivative of 0*w + 1 - 1/6*w**4 + 0*w**2 + g*w**3. Factor k(c).
-2*c**2*(c - 1)/3
Solve -8*n**2 - 16/5*n**3 + 23/5*n - 3/5 = 0 for n.
-3, 1/4
Factor 6 + 29*j**2 + 17*j + 4*j**3 - 8*j**2 + 12*j.
(j + 2)*(j + 3)*(4*j + 1)
Let a(y) = 7*y - 35. Let m be a(5). Let d(s) be the third derivative of 0*s**5 + m*s + 0 + s**2 + 3/32*s**4 + 1/4*s**3 - 1/160*s**6. Find n such that d(n) = 0.
-1, 2
Suppose 12 = -t + 5*t. Suppose -y + 2*d = d - 4, -t*y - 2*d = 8. Solve y + 2/3*g**2 - 2/3*g = 0.
0, 1
Let v(s) = s**2 + 5*s + 4. Let w be v(-4). Let o = 63 - 314/5. Factor w + 2/5*t**2 + 1/5*t + o*t**3.
t*(t + 1)**2/5
Let y(q) = -q**3 + q**2. Let g(f) = -7*f**3 - f**2 - 6*f. Let i(c) = c**3 - c**2 - 1. Let j(p) = 2*g(p) + 4*i(p). Let d(t) = j(t) - 6*y(t). Factor d(z).
-4*(z + 1)**3
Let i(r) be the second derivative of 5*r**7/42 + r**6/6 - 7*r**5/4 - 5*r**4/12 + 5*r**3 + 5*r. Determine p, given that i(p) = 0.
-3, -1, 0, 1, 2
Let v(t) be the second derivative of 3*t**8/560 + t**7/40 + 2*t**6/45 + t**5/30 + 2*t**3/3 + 6*t. Let x(j) be the second derivative of v(j). Factor x(r).
r*(r + 1)*(3*r + 2)**2
Let y(n) be the first derivative of -2*n**3/9 - n**2/3 + 3. Find s such that y(s) = 0.
-1, 0
Let v(l) be the first derivative of 3/16*l**4 + 9/8*l**2 + 3/4*l - 3 + 3/4*l**3. Factor v(w).
3*(w + 1)**3/4
Suppose f + 4*f = 10. Let -3*j**4 + j**f + j**3 + 2*j**3 + 5*j**2 = 0. Calculate j.
-1, 0, 2
Let v = 966 + -4828/5. Find j, given that -4/5 - v*j**2 + 6/5*j = 0.
1, 2
Let b = -37 - -197. Let x be b/88 + (-2)/(-11). What is s in 0*s + 4/7*s**x + 0 - 10/7*s**3 - 2*s**4 = 0?
-1, 0, 2/7
Suppose 4*p + 3*v - 9 = 0, -2*v + 2 = p - v. What is u in 2*u**2 - 8*u**3 - u**4 + 3*u**4 + 2*u**p + 2*u**3 = 0?
0, 1
Factor 15/2*h**3 + 9/2*h**2 - 15/2*h - 9/2.
3*(h - 1)*(h + 1)*(5*h + 3)/2
Let x(u) be the first derivative of -2*u**3/27 - 22*u**2/9 - 242*u/9 - 19. Let x(s) = 0. Calculate s.
-11
Let n be ((-4)/(-5))/(8/20). Factor -3*u**n - 9*u**4 - 9*u**3 + u**5 - 2*u**5 - 2*u**5 + 0*u**5.
-3*u**2*(u + 1)**3
Let w(f) be the first derivative of f**6/15 + 2*f**5/5 + f**4 + 4*f**3/3 + f**2 - 2*f - 2. Let u(l) be the first derivative of w(l). Factor u(r).
2*(r + 1)**4
Let c = -3 + 18. Suppose -c = -0*r - 3*r. Factor -1/2*z**r + 0 + 1/2*z**3 + 0*z**2 + 0*z**4 + 0*z.
-z**3*(z - 1)*(z + 1)/2
Suppose -5*v = -5, v = 4*j - 0*v - 23. Let w(g) be the third derivative of -3*g**2 + 0 + 0*g**3 - 1/240*g**j + 0*g**5 + 0*g + 1/48*g**4. Factor w(a).
-a*(a - 1)*(a + 1)/2
Let l(x) = -14*x**3 - 8*x**2 + 26*x + 12. Suppose i + i = 16. Let o(a) = -5*a**3 - 3*a**2 + 9*a + 4. Let q(h) = i*o(h) - 3*l(h). Solve q(y) = 0 for y.
-1, 2
Let g(y) = y - 2. Let r be g(12). Let z be (-2)/(5/(r/(-8))). Suppose -1/2*u**5 - 1/2*u**4 - 1/2*u - z + u**2 + u**3 = 0. What is u?
-1, 1
Let y(f) = 11*f**2 - 2*f + 5. Let v(t) = 10*t**2 - t + 4. Suppose 2*l = -4, 0 = 2*j - j + 2*l + 8. Let r(s) = j*y(s) + 5*v(s). Determine q so that r(q) = 0.
-1/2, 0
Let c(v) = 3*v**3 + v**2 + v + 3. Let b(j) = j + j**2 + j**3 + 1 + 0*j**2 + 0*j**3. Let k(u) = -2*b(u) + c(u). Factor k(x).
(x - 1)**2*(x + 1)
Let w(c) = -c - 3. Let m be w(-7). Suppose 0 = -5*k - 5*u + 1 + 14, 4*k = m*u + 4. Let -10/7*a + 6/7*a**k - 4/7 = 0. What is a?
-1/3, 2
Let j be (-12)/40*(-2)/3. Let q(s) be the second derivative of 0 + 0*s**2 - 3/10*s**5 - 1/6*s**4 + 3*s - 1/21*s**7 + 0*s**3 - j*s**6. Factor q(o).
-2*o**2*(o + 1)**3
Let p(n) be the third derivative of -1/2*n**3 - 1/180*n**5 + 0 + 1/72*n**4 + 3*n**2 + 1/1080*n**6 + 0*n. Let s(f) be the first derivative of p(f). Factor s(h).
(h - 1)**2/3
Let u(q) = -33*q**4 - 65*q**3 + 10*q**2 + 2*q + 2. Let k(i) = -32*i**4 - 64*i**3 + 11*i**2 + i + 3. Let x(g) = -2*k(g) + 3*u(g). Factor x(t).
-t*(t + 2)*(5*t + 1)*(7*t - 2)
Solve 3*x - 3*x**3 + 6*x**2 + 3 + 7*x**2 + 14*x**2 - 30*x**2 = 0.
-1, 1
Let a(m) = -m - 1. Let q be a(-6). Suppose 4*j + q*b = 21, 10 = 3*j - 3*b + b. Factor 1/2 + w**j + 5/4*w - 2*w**3 - 3/4*w**2.
(w - 2)*(w - 1)*(2*w + 1)**2/4
Suppose 0 = -0*z - 5*z. Let y(o) be the third derivative of 0*o - 1/300*o**6 + 0 + o**2 + 0*o**5 + 1/60*o**4 + z*o**3. Find h, given that y(h) = 0.
-1, 0, 1
Let b(p) = -p**2 + 11*p + 46. Let h be b(-3). Find x such that 2/3*x**h - 4/3*x**2 + 2/3*x**5 - 4/3*x**3 + 2/3*x + 2/3 = 0.
-1, 1
Let d(p) = 3*p**2 + 2. Let t(b) = 7*b**2 - b + 5. Let r(l) = 5*d(l) - 2*t(l). Let r(v) = 0. Calculate v.
-2, 0
Let h(b) be the second derivative of b**5/10 - b**4/3 - b**3 + 16*b. What is k in h(k) = 0?
-1, 0, 3
Suppose -5*y + 11 = 4*c, -c + 3*c + 5*y = 3. Let q(o) be the third derivative of 0*o**3 + 1/36*o**c - o**2 + 0 + 0*o + 1/180*o**5. Factor q(x).
x*(x + 2)/3
Let m(g) be the second derivative of -g**7/8820 + g**5/105 + g**4/12 - 4*g. Let s(y) be the third derivative of m(y). Determine r so that s(r) = 0.
-2, 2
Let r(c) = -c**2 - c + 16. Let d be r(0). Suppose p - d = -2*y + 4*p, -5*p = -4*y + 28. Factor -2 + m**2 + 0*m**y + m**2 + 0*m**2.
2*(m - 1)*(m + 1)
Let p(q) be the first derivative of -q**6/1440 + q**5/480 - q**3 + 3. Let o(b) be the third derivative of p(b). Factor o(j).
-j*(j - 1)/4
Let d = -2/91 + 109/819. Let a(h) be the first derivative of 0*h - 1/6*h**2 - d*h**3 + 2. Factor a(g).
-g*(g + 1)/3
Suppose 2/3*a**4 + 0 - 2/3*a**2 + 2/3*a - 2/3*a**3 = 0. Calculate a.
-1, 0, 1
Let y(a) = 22*a**5 - 26*a**4 + 10*a**3 + 2*a**2 + 2*a + 2. Let s(l) = l**5 + l**4 + l**3 + l**2 + l + 1. Let w(u) = -2*s(u) + y(u). Solve w(g) = 0.
0, 2/5, 1
Suppose 3*f = -18 - 6. Let y be (-15)/2*f/50. Factor 2/5*n**3 + 0*n**2 - y*n - 4/5.
2*(n - 2)*(n + 1)**2/5
Suppose n + 15 = 6*n. Suppose -4*f = n*w - 7, -3*w - 31 = -4*f + 2*w. Factor -f*j**2 + j - j + 14*j**3.
2*j**2*(7*j - 2)
Let o be (-1 + 1)*(-1 - 0). Suppose k + 0 - 3 = o. Factor 0 + 1/3*r**2 - 1/3*r**k + 0*r.
-r**2*(r - 1)/3
Let c(f) be the second derivative of -f**6/90 - f**