5/5 - 5*z**4/3 + 16*z**3/3 - 8*z**2 + 9*z. Find n such that w(n) = 0.
1, 2
Let s(h) = 4*h**3 + 13*h**2 - 10*h + 7. Let z(c) = c**3 + 4*c**2 - 3*c + 2. Let t(d) = 4*s(d) - 14*z(d). Determine p, given that t(p) = 0.
0, 1
Suppose -3*s**2 + 12*s + 1/4*s**3 - 16 = 0. What is s?
4
Suppose -4*c + 78 = -26. Let k = c - 76/3. Solve 2/3*z**2 + 0 + k*z = 0 for z.
-1, 0
Factor 0 + 18/11*h**2 - 6/11*h**5 - 30/11*h**3 - 4/11*h + 2*h**4.
-2*h*(h - 1)**3*(3*h - 2)/11
Factor -2/5*q**2 + 8/5*q - 6/5.
-2*(q - 3)*(q - 1)/5
Let j(y) = y**3 - 5*y**2 + 5*y. Let b(f) = -f**3 + 4*f**2 - 4*f. Let m = -2 - -8. Suppose -m*p = -2*p - 20. Let k(o) = p*b(o) + 4*j(o). What is s in k(s) = 0?
0
Let b(t) = -t**3 + 11*t**2 - 11*t + 16. Let m be b(10). Suppose -4*o + 5*w = -25, -5*w - 19 = o + m. Factor -2/9*s + o - 2/9*s**2.
-2*s*(s + 1)/9
Let m = -308 - -1544/5. Suppose -5*v + 1 = 4*t - 7, 3*t = -2*v + 6. Factor 2/5*q + 0 + v*q**3 + 4/5*q**4 - 2/5*q**5 - m*q**2.
-2*q*(q - 1)**3*(q + 1)/5
Let a(y) be the first derivative of y**6/30 + 3*y**5/20 + y**4/12 - y**3/2 - y**2 + 6*y + 6. Let h(n) be the first derivative of a(n). Factor h(b).
(b - 1)*(b + 1)**2*(b + 2)
Let c(b) = -4*b**4 + 16*b**3 - 12*b + 20. Let a(p) = -p**2 + p - 1. Let y(i) = 20*a(i) + c(i). Suppose y(k) = 0. What is k?
0, 1, 2
Let u(s) be the first derivative of -2/3*s**3 - 4*s**2 - 8*s - 5. Suppose u(v) = 0. What is v?
-2
Let a(j) be the third derivative of j**6/60 - j**5/15 - 23*j**2. Factor a(g).
2*g**2*(g - 2)
Let r(y) = y**2 - 1. Let o = 7 + -11. Let a(x) = -x**2 + 1. Suppose -11*m - 6 = -9*m. Let g(j) = m*a(j) + o*r(j). Determine t so that g(t) = 0.
-1, 1
Let u(q) = 2*q**2 - 36*q + 40. Let x be u(17). Let h(l) be the third derivative of 0 - 3/10*l**5 + 1/3*l**3 + 1/4*l**4 - 4*l**2 + 0*l + 1/12*l**x. Factor h(c).
2*(c - 1)**2*(5*c + 1)
Let v be (3/(-6))/((-21)/108). Let x = -65/28 + v. Factor 1/4*t**3 + 1/4*t**4 - x*t - 1/4*t**2 + 0.
t*(t - 1)*(t + 1)**2/4
Solve 1/2*q**3 - 1/2*q + 0 - 1/2*q**2 + 1/2*q**4 = 0.
-1, 0, 1
Let i = 11 - 8. Find a, given that 4*a**2 - a**2 + 2*a**4 - 6*a**i + a**4 = 0.
0, 1
Let v = 198 + -198. Factor v*o + 2/3*o**5 + 4/3*o**4 + 0*o**2 + 0 + 2/3*o**3.
2*o**3*(o + 1)**2/3
Factor -49*c**2 - 7*c**3 - 3*c**3 + 14*c**3 + 57*c**2.
4*c**2*(c + 2)
Let u(x) be the second derivative of 0*x**3 - 6*x - 4/3*x**2 + 1/30*x**5 + 1/6*x**4 + 0. Factor u(k).
2*(k - 1)*(k + 2)**2/3
Let m(y) = -y**5 + y**3 - y**2. Let d(b) = -3*b**5 + 16*b**4 - 15*b**3 + 6*b**2. Let k(u) = d(u) + 4*m(u). Solve k(f) = 0 for f.
0, 2/7, 1
Let c = 7/5 - 58/45. Let x(s) be the first derivative of 0*s**2 + 2 - c*s**3 + 0*s. What is y in x(y) = 0?
0
Let s(c) be the second derivative of -c**4/102 - c**3/51 + 2*c**2/17 + 6*c. Suppose s(w) = 0. Calculate w.
-2, 1
Let u = -19 - -58/3. Solve u*g**2 - 2/3*g + 1/3 = 0 for g.
1
Suppose v + 3*k = 18, -v - 3*v - k + 17 = 0. Factor 6*h**4 - h - 2 - 6*h**3 - 5*h**5 + 7*h - 4*h**2 + v*h**5 + 2*h**3.
-2*(h - 1)**4*(h + 1)
Let l be (-40 + 4)*26/(-429). What is m in -8/11*m**2 - l*m**3 + 2/11*m**4 + 0*m + 0 + 30/11*m**5 = 0?
-2/3, -2/5, 0, 1
Let x = 41 - 39. Let z(u) be the first derivative of 1/6*u**6 + 0*u**2 + 0*u - 3/5*u**5 - 1/3*u**3 + 3/4*u**4 - x. Factor z(o).
o**2*(o - 1)**3
Let x(s) be the first derivative of -s**6/120 + s**5/48 - s**4/96 - s**2 + 2. Let o(m) be the second derivative of x(m). Factor o(u).
-u*(u - 1)*(4*u - 1)/4
Let v(f) be the third derivative of -f**5/480 - f**4/192 - 5*f**2. Determine w so that v(w) = 0.
-1, 0
Let i(v) = -v**2 + 6*v + 5. Let d be i(5). Let b = d + -6. Factor 3*o**5 - 4*o**b + 3*o**4 - 2*o**5.
o**4*(o - 1)
Let p(b) be the second derivative of 5*b**4/12 - 5*b**3/6 - 40*b. Factor p(z).
5*z*(z - 1)
Let w be ((-115)/(-20))/((-15)/14). Let c = 37/6 + w. Factor 2/5 - c*d + 2/5*d**2.
2*(d - 1)**2/5
Let h be -2 + 11 + (0 - 7). Determine u so that -4/7*u**3 + 0*u + 0 - 1/7*u**h - 3/7*u**4 = 0.
-1, -1/3, 0
Suppose 5*y = -x, 0 = -4*x - 3*y + 5*y. Factor -2/7*o**5 + 2/7*o + x - 4/7*o**2 + 4/7*o**4 + 0*o**3.
-2*o*(o - 1)**3*(o + 1)/7
Factor 0 - 4/5*n**2 + 2/5*n**3 + 0*n.
2*n**2*(n - 2)/5
Suppose 3*d + 0*d = 0. Let l = -10 - -12. Factor -10/7*f**4 + d + 0*f - 4/7*f**3 + 0*f**l.
-2*f**3*(5*f + 2)/7
Suppose -3*l + 10 = 4*x, l + 0 = -3*x + 5. Factor 18*f - 6*f - f**5 - l*f**2 + 8 - 33*f**3 - 6*f**4 + 22*f**3.
-(f - 1)*(f + 1)*(f + 2)**3
Suppose -2*u + 8 = 2*u. Solve -4/3*j + 0 - 2/3*j**u = 0.
-2, 0
Let j(g) be the third derivative of -g**4/24 - g**3/6 - 7*g**2. Let x be j(-3). Factor -4/5 + 6/5*q + x*q**2.
2*(q + 1)*(5*q - 2)/5
Let g be (4 - 2)*(13 + -6). Let m be (-6)/g - (-87)/105. Suppose 0*f + 2/5*f**4 + m*f**2 + 0 + 4/5*f**3 = 0. What is f?
-1, 0
Let f(l) = 45*l**5 - 15*l**4 - 80*l**3 + 15*l**2 + 85*l. Let p(x) = 11*x**5 - 4*x**4 - 20*x**3 + 4*x**2 + 21*x. Let y(c) = -6*f(c) + 25*p(c). Factor y(v).
5*v*(v - 3)*(v - 1)*(v + 1)**2
Let o(r) = -r + 15. Let i be o(15). Let q(b) be the third derivative of i*b**3 + 0*b**5 - 1/60*b**6 + 0*b**4 + 0*b - 4*b**2 - 1/105*b**7 + 0. Factor q(w).
-2*w**3*(w + 1)
Let l(o) = o. Let u(q) = q**3 - q**2 - 3*q. Let z(c) = -3*l(c) - u(c). Find n, given that z(n) = 0.
0, 1
Let z(p) be the third derivative of 4*p**7/1365 - 23*p**6/780 + p**5/15 + 2*p**4/39 + 60*p**2. Find x, given that z(x) = 0.
-1/4, 0, 2, 4
Suppose -3*i + 4*a + 10 = 0, 4*a + 10 = 4*i + 2*a. Suppose 4*o - 6 = 3*v, v + 5 = 5*o - 8. Find h such that -2*h**4 + i*h**3 - 2*h**o + 0*h**4 + 2*h**3 = 0.
0, 1
Suppose -a - 30 = a. Let b be (-5)/a + 32/3. Suppose 2*s - b*s**2 + 7 + 9*s**3 - 7 = 0. Calculate s.
0, 2/9, 1
Let b(n) be the third derivative of -1/105*n**7 + 0*n**3 + 1/6*n**4 - 6*n**2 + 0*n - 1/20*n**6 + 0 + 1/168*n**8 + 1/30*n**5. Factor b(p).
2*p*(p - 2)*(p - 1)*(p + 1)**2
Suppose 2*h + 23*v - 19*v = 6, -3 = -5*h + 2*v. Let h + 17/2*z + 18*z**2 = 0. Calculate z.
-1/4, -2/9
Let y = -5 - -9. What is l in 3*l**4 - 2*l**5 - 4*l**3 - 9*l**y - 2*l**3 - 2*l**2 = 0?
-1, 0
Let d(j) be the first derivative of -2 + 5/4*j**4 + 5/4*j**2 + 1/12*j**6 + 1/2*j**5 + 5/3*j**3 + 1/2*j. Suppose d(p) = 0. What is p?
-1
Let o(x) be the third derivative of 4*x**2 + 1/8*x**4 + 0 + 0*x - 1/20*x**5 + 0*x**3. Suppose o(s) = 0. Calculate s.
0, 1
Suppose -18 + 6*k - 1/2*k**2 = 0. What is k?
6
Let u(v) be the second derivative of -38*v**6/15 + 8*v**5 - 23*v**4/3 + 4*v**3/3 + 9*v. Find g such that u(g) = 0.
0, 2/19, 1
Let m = 1 - -1. Let t be (5/(-2))/((-1)/m). What is y in y**4 + 3*y**3 - 2*y**4 - t*y**3 - y**2 = 0?
-1, 0
Factor -5*v**2 + v**4 + 3*v**4 + 10*v - 10*v**3 + v**4.
5*v*(v - 2)*(v - 1)*(v + 1)
Let x = -595/2 + 301. Let a be -1 + 2 + (2 - 0). Solve -x*y**2 + 3/2*y + 4*y**a + 1/2*y**5 - 9/4*y**4 - 1/4 = 0 for y.
1/2, 1
Let 6/7*c**2 + 0 + 2/7*c**3 + 0*c = 0. Calculate c.
-3, 0
Let y(c) = -c**3 + c**2. Let p be (-3 - (-39)/(-9))*-3. Let a(u) = u**4 - 13*u**3 + 12*u**2. Let r(v) = p*y(v) - 2*a(v). Factor r(o).
-2*o**2*(o - 1)**2
Factor 0 - 6/5*t - 3/5*t**2.
-3*t*(t + 2)/5
Find f such that 5 + f**3 - 10*f + 3*f**3 + 5*f**3 + f**3 - 5*f**4 = 0.
-1, 1
Let b = 6 - -6. Let r(p) = p**2 + 3*p - 2. Let s be r(-4). Factor -2*u**3 + 3*u**3 + 15*u - b*u**s - 6 + 2*u**3 + 0*u**3.
3*(u - 2)*(u - 1)**2
Let v(u) = 12*u - 8. Let p be v(1). Let j(z) be the third derivative of -1/360*z**6 + 0*z**4 + 0 - 1/630*z**7 - p*z**2 + 0*z + 0*z**3 + 1/90*z**5. Factor j(i).
-i**2*(i - 1)*(i + 2)/3
Let z(r) be the third derivative of -r**9/1008 - r**8/280 + r**6/60 + r**5/40 + r**3/2 - 2*r**2. Let g(i) be the first derivative of z(i). Solve g(c) = 0 for c.
-1, 0, 1
Let r(q) be the first derivative of 4 + 9/2*q**2 - 3/2*q**4 - 1/2*q**6 - 2*q**3 + 9/5*q**5 - 3*q. Solve r(v) = 0 for v.
-1, 1
Let b = 2 + -2. Let a(p) be the third derivative of 0*p**3 + 0 - 2/105*p**7 + b*p - 1/336*p**8 + 3*p**2 - 1/24*p**4 - 1/15*p**5 - 1/20*p**6. Factor a(x).
-x*(x + 1)**4
Let p be 326/(-15) + 6/15. Let q = -21 - p. Factor 2/3*o - 1/3*o**3 - q*o**2 + 0.
-o*(o - 1)*(o + 2)/3
Let u = -8 - -5. Let w = u - -7. Factor n**w + 0*n**2 + 0*n**4 + 2*n**2 - n**2 - 2*n**3.
n**2*(n - 1)**2
Let l be 1/(-2)*(-1 + -5). Suppose 4*t - 4*k - 36 = 0, t - l*k - 7 = 3*t. Determine u so that -u**5 + t*u**2 - 4*u**4 + 11*u**5 - 12*u**3 + 2*u**3 = 0.
-1, 0, 2/5, 1
Let z(b) be the second derivative of b**7/105 + b**6/25 - b**5/50 - b**4/10 - 6*b. What is u in z(u