**2 + 28*r - 4. Let y(g) = 20*g**3 - 40*g**2 + 29*g - 4. Let z(t) = -5*j(t) + 4*y(t). Suppose z(h) = 0. What is h?
2/5, 1
Let c(k) be the second derivative of -k**6/40 + k**5/10 - k**4/8 - 2*k**2 + 2*k. Let s(v) be the first derivative of c(v). Factor s(i).
-3*i*(i - 1)**2
Let b be 1/5*((-8)/(-12) + 1). Determine u so that 0 - 1/6*u**3 - 1/6*u**2 + b*u = 0.
-2, 0, 1
Let y(o) = 2*o**2 - 2*o - 7. Let x be y(3). Suppose -2/3*u**x + 0*u - 2*u**3 - 2/3*u**2 + 0 - 2*u**4 = 0. Calculate u.
-1, 0
Let b be 225/(-81) - (5 - 8). Find c such that 8/9*c + 8/9*c**2 + 0 + b*c**3 = 0.
-2, 0
Let q = -77 - -77. Let 0*v**2 + 0*v + 12/5*v**4 - 3/5*v**5 + q - 12/5*v**3 = 0. What is v?
0, 2
Let n(p) = 65*p**2 + 65*p - 45. Let m(l) = 3*l**2 + 3*l - 2. Let u(z) = 45*m(z) - 2*n(z). Factor u(b).
5*b*(b + 1)
Let b be 18/27*(-30)/(-4). Let u(w) be the second derivative of -1/30*w**b + 1/90*w**6 + 0*w**3 + 2*w + 0*w**2 + 0 + 1/36*w**4. Find a, given that u(a) = 0.
0, 1
Suppose 2*o + 15 = -o. Let n = -3 - o. Find h such that -4/11*h**3 + 0*h**n - 2/11 + 4/11*h + 2/11*h**4 = 0.
-1, 1
Let y(o) = o**2 - 11*o + 2. Let t be y(11). Factor -1/2*p**3 - 1/4*p**5 - 1/2*p**t + 3/4*p + 3/4*p**4 - 1/4.
-(p - 1)**4*(p + 1)/4
Let y(f) = 6*f**4 + 3*f**3 - 4*f**2. Let j(k) = k**3 + 0*k**2 + 5*k**4 - k**2 - 4*k**4. Let o(t) = -10*j(t) + 2*y(t). Let o(n) = 0. What is n?
0, 1
Let n(c) = -c - 11. Let s be n(-11). Let b(d) be the third derivative of 0*d**3 - 1/150*d**6 + s + 0*d + 0*d**4 + d**2 + 0*d**5 + 1/75*d**7. Factor b(g).
2*g**3*(7*g - 2)/5
Let z be ((-2)/8)/(1/4). Let s = 3 - z. Factor 0 + 2/3*p**3 + 2/3*p**s - 2/3*p**2 - 2/3*p.
2*p*(p - 1)*(p + 1)**2/3
Let c = -1052/5 - -127282/605. Let t = c - -129/484. Find j such that -t*j + 0*j**2 + 1/4*j**3 + 0 = 0.
-1, 0, 1
Let b = 47 + -47. Factor 6/5*f**3 - 2/5*f**5 - 4/5*f**4 + b - 8/5*f + 8/5*f**2.
-2*f*(f - 1)**2*(f + 2)**2/5
Let g(p) = p**2 + 5*p + 3. Let y be g(-5). Factor -2*j**2 - 2*j**2 + j - j**y - 5*j.
-j*(j + 2)**2
Suppose -3*u = 5*b + 6, -b - u = -0 + 2. Let r(l) be the third derivative of 0*l + 0*l**3 + 0*l**4 + 2*l**2 - 1/60*l**5 + b. Factor r(x).
-x**2
Suppose -1 + 9*n + 0*n**2 + 2*n**2 - 5 - 5*n**2 = 0. Calculate n.
1, 2
Factor -2/7*c**2 - 1/7*c + 1/7*c**3 + 2/7.
(c - 2)*(c - 1)*(c + 1)/7
Let r be (7/(21/(-2766)))/3. Let o = r - -312. Factor o*c**2 - 4/3 + 10/3*c.
2*(c + 1)*(7*c - 2)/3
Let f(s) be the third derivative of -1/60*s**6 - 1/3*s**3 + 0*s + 1/30*s**5 + s**2 + 0 + 1/12*s**4. Find k such that f(k) = 0.
-1, 1
Let y(r) = -5*r**2 - 4*r - 1. Let t(w) = 3*w**2 - 39*w**2 - 6 - 17*w - 11*w + w. Let m(p) = -2*t(p) + 15*y(p). Factor m(a).
-3*(a + 1)**2
Suppose -2*m = -7*m + 10. What is h in -6*h + 4*h**m + 10*h - 5 - 3 = 0?
-2, 1
Let w(p) be the second derivative of -p**4/12 - p**3/6 - 6*p. Factor w(v).
-v*(v + 1)
Let k(v) be the first derivative of v**4/4 + v**3/2 - v - 1. Let o(y) be the first derivative of k(y). Factor o(g).
3*g*(g + 1)
Let k(z) = -z**3 - 8*z**2 + 11*z - 2. Let p be k(-10). Let x = p - 262/3. Factor x*l**3 - 2/3*l + 0 + 0*l**2.
2*l*(l - 1)*(l + 1)/3
Let u(g) be the second derivative of -g**7/273 + 4*g**6/195 - 3*g**5/130 - 2*g**4/39 + 4*g**3/39 - 4*g. Suppose u(z) = 0. What is z?
-1, 0, 1, 2
Let h(z) be the third derivative of 2/35*z**7 + 0 - 2*z**2 + 0*z + 0*z**3 + 3/20*z**6 + 1/8*z**4 + 1/112*z**8 + 1/5*z**5. What is n in h(n) = 0?
-1, 0
Let m(a) be the first derivative of -2*a**3/27 - 4*a**2/3 - 8*a + 28. Factor m(f).
-2*(f + 6)**2/9
Let f = 22 + -16. Let 6 + y**2 - f + 2*y = 0. Calculate y.
-2, 0
Let v(g) be the second derivative of 27*g**4/4 - 32*g**3 + 96*g**2 + 4*g. Let r(b) = 5*b**2 - 12*b + 12. Let h(t) = -33*r(t) + 2*v(t). Let h(l) = 0. What is l?
2
Let n(j) = j**2 - 5*j - 20. Let c be n(8). Factor -21/4*y**3 - 3/4 - 15/4*y - 3/2*y**c - 27/4*y**2.
-3*(y + 1)**3*(2*y + 1)/4
Suppose 3*o - 32 = -5*x - 14, -4*o + 16 = 4*x. Determine v, given that 2/7*v**x - 4/7*v**2 - 2/7*v**5 + 0*v + 4/7*v**4 + 0 = 0.
-1, 0, 1, 2
Let g be 2 - -1 - 5 - -3. Let s(h) be the first derivative of -2/21*h**3 - 2/7*h - 2/7*h**2 + g. Factor s(a).
-2*(a + 1)**2/7
Let c(z) = -3*z**2 - 38*z + 16. Let m be c(-13). Let j(g) be the first derivative of 0*g**2 - 4 - 2/3*g**m + 2*g. Determine y so that j(y) = 0.
-1, 1
Let m be (-93)/(-9) + (-1)/3. Let l be (-64)/m*(-2)/8. What is f in l*f - 2/5*f**2 - 8/5 = 0?
2
Let y be (7/((-7)/6))/(-1). Suppose y*d = 17 + 1. Factor 1/5 - 4/5*r - 4/5*r**d + 1/5*r**4 + 6/5*r**2.
(r - 1)**4/5
Let o = 1186081/480 - 2471. Let v(d) be the third derivative of 1/96*d**4 + d**2 - o*d**6 + 1/210*d**7 + 0*d + 0*d**3 - 1/60*d**5 + 0. Factor v(f).
f*(f - 1)*(f + 1)*(4*f - 1)/4
Let t be (2 - -9)/(1/2). Let -29*w**2 - t*w - 2*w**2 - 3*w**2 - 5 + 1 - 12*w**3 = 0. What is w?
-2, -1/2, -1/3
Let q(y) = -y**2 - y + 44. Let c be q(6). Factor 15/4*s**3 + 3/4*s**4 + 0 + 6*s**c + 3*s.
3*s*(s + 1)*(s + 2)**2/4
Let q(i) be the second derivative of 1/12*i**4 + 0*i**2 + 1/30*i**6 - 3*i + 0*i**3 + 1/10*i**5 + 0. Let q(g) = 0. What is g?
-1, 0
Let d(o) be the third derivative of -o**8/560 - o**7/70 - 7*o**6/200 + o**5/100 + o**4/5 + 2*o**3/5 + 4*o**2. What is n in d(n) = 0?
-2, -1, 1
Let b(k) be the first derivative of -k**4/24 + k**3/12 + k**2/2 + 4*k - 5. Let i(n) be the first derivative of b(n). Factor i(l).
-(l - 2)*(l + 1)/2
Let a(n) = 10*n**3 - 32*n**2 + 8*n + 2. Let b(i) = -51*i**3 + 159*i**2 - 40*i - 11. Let m(l) = -22*a(l) - 4*b(l). Solve m(u) = 0.
0, 1/4, 4
Let m = -7 + 11. Determine i so that 4*i + 0*i**3 - m - 2*i**3 + i**4 + 3*i**2 - 2*i**3 = 0.
-1, 1, 2
Let w(g) = 5*g**4 - 9*g**3 - 4*g**2 + 24*g - 13. Let n(q) = -9*q**4 + 17*q**3 + 8*q**2 - 48*q + 27. Let v(s) = 3*n(s) + 5*w(s). Factor v(d).
-2*(d - 2)**2*(d - 1)*(d + 2)
Factor 3*r - 3*r**5 + 0*r**5 - 5*r**2 + 6*r**4 - r**2.
-3*r*(r - 1)**3*(r + 1)
Factor -216/5*i**2 - 162/5 + 12*i**3 + 324/5*i - 6/5*i**4.
-6*(i - 3)**3*(i - 1)/5
Suppose 5*p = 3*l - 7*l + 25, 10 = 3*l + 2*p. Let s be -6*(-3)/6 - l. Find n, given that 3/2*n**s + 0 + 1/4*n + 1/4*n**5 - n**2 - n**4 = 0.
0, 1
Let q(u) be the third derivative of u**8/288 - u**7/252 - u**6/45 - u**5/90 - 21*u**2. What is x in q(x) = 0?
-1, -2/7, 0, 2
Suppose 3*v - 92 = -83. Let s(f) be the first derivative of 1/24*f**6 + 0*f + 0*f**v + 0*f**5 + 0*f**2 - 1/16*f**4 + 4. Factor s(t).
t**3*(t - 1)*(t + 1)/4
Let g(t) = -8*t. Let m be g(-1). Let p**4 - 8*p + m*p + p**5 = 0. What is p?
-1, 0
Suppose -3*q - 5*o = -17, 5*o - 25 = -5*q - 0*o. Let y(h) be the second derivative of -3/2*h**2 + 0 - 3/4*h**q - 3/2*h**3 - 3/20*h**5 - 4*h. Solve y(z) = 0.
-1
Let i(b) be the second derivative of -3/14*b**4 - 1/14*b**5 + b + 0 - 1/3*b**3 - 1/105*b**6 - 2/7*b**2. Factor i(u).
-2*(u + 1)**3*(u + 2)/7
Let z(w) = 3*w**2 + 7*w + 2. Let t(v) = 5*v**2 + 13*v + 3. Let n(p) = -4*t(p) + 7*z(p). Factor n(g).
(g - 2)*(g - 1)
Suppose 2*d - 4*d + 3*m + 21 = 0, d = -m + 3. Let n(x) = x**2 - 5*x + 1. Let h be n(d). Factor 8*j - 2 + 6*j - h*j + 11*j**3 + 20*j**2.
(j + 1)**2*(11*j - 2)
Let a(o) = 0 + 1 + o**2 - 2 + 0*o**2. Let j(s) = 3*s**2 - s - 2. Let w(z) = 5*a(z) - 2*j(z). Suppose w(q) = 0. Calculate q.
1
Suppose -2*j + 5*w + 20 = 3*j, 0 = -2*j + w + 7. Suppose -2*k + k = 3*q - 2, 2*q + 3*k = 6. Solve 2/3*n**5 + 2*n**j + 2/3*n**2 + q + 2*n**4 + 0*n = 0 for n.
-1, 0
Let n(y) = -y + 1. Let m(j) = 0*j - 5*j + 4*j**2 - 5*j**2 + 2. Suppose -5 + 3 = 2*x. Let b(a) = x*m(a) + 3*n(a). Factor b(u).
(u + 1)**2
Let w(h) = h**2 - 5*h. Let j be w(5). Suppose -5*s + 15 = -5. Suppose -16/3*t**s - 2/3*t**2 + 0*t - 7/3*t**5 - 11/3*t**3 + j = 0. What is t?
-1, -2/7, 0
Factor -110 + 110 - x**5 - 3*x**3 + 3*x**4 + x**2.
-x**2*(x - 1)**3
Let d = 5/3 - 3/2. Let y(t) be the third derivative of 1/12*t**6 - d*t**4 - 1/10*t**5 + 0*t + 0*t**3 + 0 - t**2. Let y(n) = 0. What is n?
-2/5, 0, 1
Let j(r) be the third derivative of -r**7/1260 + r**6/480 + r**5/240 + r**4/12 - r**2. Let m(f) be the second derivative of j(f). Factor m(l).
-(l - 1)*(4*l + 1)/2
Let w(x) be the second derivative of -x**5/30 - x**4/18 + 2*x**3/9 + 5*x. Factor w(z).
-2*z*(z - 1)*(z + 2)/3
Let w be (-4 + 5)/(4/12). Factor 4*r**2 - 16*r**3 + 6*r**2 + 13*r**w - 3*r - 4*r**2.
-3*r*(r - 1)**2
Suppose 13 = 5*m + 3. Find z, given that z - z**2 - 1 - z - m*z = 0.
-1
Let r(l) be the first derivative of 4*l**5/5 - 3*l