Let a = 130/423 + x. Determine b so that -4/9*b + a + 2/9*b**2 = 0.
1
Let r(o) = 3*o**2 + 13*o + 4. Suppose 0 = -j + 2 + 1. Let z(i) = 14*i**2 + 66*i + 20. Let y(t) = j*z(t) - 16*r(t). Let y(g) = 0. Calculate g.
-1, -2/3
Let z(m) be the first derivative of m**6/2 - 14*m**5/5 + 23*m**4/4 - 16*m**3/3 + 2*m**2 - 32. Factor z(v).
v*(v - 2)*(v - 1)**2*(3*v - 2)
Suppose 1 = -4*o + 9. Let f(p) be the first derivative of 0*p**2 + o + 1/16*p**4 + 0*p + 1/6*p**3. Solve f(y) = 0.
-2, 0
Let p(g) be the second derivative of 0 + 0*g**2 + 0*g**3 - 3*g + 1/12*g**4. Factor p(z).
z**2
Let h(o) be the second derivative of -o**6/225 - 2*o**5/75 - o**4/30 + 47*o. Factor h(m).
-2*m**2*(m + 1)*(m + 3)/15
Suppose 5*b - 2*z - 25 = 0, -5*b + 5*z + 30 = 2*z. Let n(w) be the first derivative of 2/3*w**3 + 4*w + 3 + b*w**2. Factor n(y).
2*(y + 1)*(y + 2)
Let g(a) be the second derivative of 0*a**4 - 1/210*a**5 + 0*a**3 - a**2 + 0 + 2*a + 1/420*a**6. Let s(l) be the first derivative of g(l). Factor s(w).
2*w**2*(w - 1)/7
Let v(i) = 88*i**4 + 177*i**3 + 105*i**2 + 10*i - 3. Let b(n) = 175*n**4 + 355*n**3 + 210*n**2 + 20*n - 5. Let q(y) = -3*b(y) + 5*v(y). Factor q(r).
-5*r*(r + 1)**2*(17*r + 2)
Let w(p) be the first derivative of -p**6/12 + p**4/4 - p**2/4 + 5. Factor w(k).
-k*(k - 1)**2*(k + 1)**2/2
Let x(o) = -3*o**4 + 7*o**3 - 2*o**2 + 3*o - 5. Let g(c) = -2*c**4 + 4*c**3 - c**2 + 2*c - 3. Let q(u) = -5*g(u) + 3*x(u). Determine v, given that q(v) = 0.
-1, 0, 1
Let s(m) = m**2 - m. Let h(q) = -q**5 + 3*q**4 + 5*q**3 + 3*q**2 - 10*q. Let d(p) = -h(p) + 6*s(p). Let d(v) = 0. Calculate v.
-1, 0, 1, 4
Let x(d) be the third derivative of d**6/180 - d**5/10 + 3*d**4/4 + d**3/2 + 5*d**2. Let l(n) be the first derivative of x(n). Find s such that l(s) = 0.
3
Let i(u) be the third derivative of 0*u**3 + 0*u**4 - 1/1512*u**8 + 0 + 0*u + 4*u**2 + 1/270*u**5 - 1/180*u**6 + 1/315*u**7. Suppose i(y) = 0. What is y?
0, 1
Let x(k) = k**5 - 3*k**4 + 2*k**3 + 6*k**2 - 7*k - 7. Let o(w) = w**5 - w**3 - w - 1. Let n(j) = -4*o(j) + x(j). Factor n(t).
-3*(t - 1)**2*(t + 1)**3
Solve 0*h**2 - 2*h - h**2 - 1 + 1 = 0 for h.
-2, 0
Let y = 93 + -145. Let t be (-2)/(-5) + y/(-20). Let -2*j**3 + 9*j**2 + 0*j**t + j**3 - 6*j - 2*j**3 = 0. What is j?
0, 1, 2
Let 1/2*i**2 + 2 + 2*i = 0. What is i?
-2
Let z(s) = -s**3 + 8*s**2 - 13*s + 6. Let b be z(6). Factor 0*p - 1/2*p**2 + b.
-p**2/2
Let f be 39/15 + 1 + (1 - 3). Solve 6/5*b**2 + 6/5*b**4 - 24/5*b + 4*b**3 - f = 0 for b.
-2, -1/3, 1
Suppose 0 = -2*u + 4*z + 324, 3*u - z - 4*z = 485. Factor u*d**3 + 7*d**4 - 22*d**4 - 21*d**2 - 47*d**2 - 49*d**4 + 8*d.
-4*d*(d - 2)*(4*d - 1)**2
Suppose -x + 3*c + 6 = 0, 4*x + 9 + 27 = -3*c. Let g be 7/(-21) + (-20)/x. What is b in 3*b**4 + g*b**2 - 3/4*b**5 - 3/4*b + 0 - 9/2*b**3 = 0?
0, 1
Let d(u) be the second derivative of 0*u**5 - 1/420*u**6 - u + 0 + 1/84*u**4 + 0*u**3 + u**2. Let z(b) be the first derivative of d(b). Factor z(v).
-2*v*(v - 1)*(v + 1)/7
Let q(u) = u**2 + 3*u - 3. Suppose -2*s + 4*s = 4. Let a(f) = 5 + f**2 - 3*f**s + f**2 - 5*f. Let i(c) = -3*a(c) - 5*q(c). Find y, given that i(y) = 0.
0
Let p be 3 + -1 - 11/(-11). Let s(n) be the first derivative of -1/6*n**2 - 1/9*n**3 + p + 0*n. Determine b, given that s(b) = 0.
-1, 0
Factor 38*v + 3*v**2 - 4*v + 6*v + 2*v**2 + 80.
5*(v + 4)**2
Let c = 33/2 + -16. Suppose 0 + 1/2*u + c*u**2 = 0. What is u?
-1, 0
Let a(d) be the first derivative of 1/6*d**3 + 0*d**4 + 0*d + 0*d**2 - 1/10*d**5 + 4. Solve a(i) = 0.
-1, 0, 1
Let z = 55 + -50. Let q = -13/8 - -25/8. Determine m, given that 0*m + 3/2*m**2 + 3/2*m**3 - q*m**z - 3/2*m**4 + 0 = 0.
-1, 0, 1
Let c be (-10)/12 + (-12)/(-9). Factor -1/4*w**4 - 5/4*w**2 + c*w + 0 + w**3.
-w*(w - 2)*(w - 1)**2/4
Let s = 7 - 5. Let k = s - 0. Find q such that -5*q**2 + q - 3*q - 4*q**2 + k*q**2 = 0.
-2/7, 0
Let p be 10/(-35)*-21 - 128/22. What is v in p*v + 4/11 - 2/11*v**2 = 0?
-1, 2
Let i be 6*(-4)/(-30) - 39/105. Solve -3/7 - i*g**4 - 3/7*g**5 - 3/7*g + 6/7*g**2 + 6/7*g**3 = 0 for g.
-1, 1
Let l(r) = -r**2 - r. Let z(i) = -3*i**2 - 2*i - 3. Let n(u) = -4*l(u) + z(u). Factor n(y).
(y - 1)*(y + 3)
Solve -2/7*n**2 - 12/7*n + 0 = 0.
-6, 0
Suppose 2*o + 12*o = 0. Factor 2/9 + o*s**3 + 0*s - 4/9*s**2 + 2/9*s**4.
2*(s - 1)**2*(s + 1)**2/9
Find v, given that 3 + 3/4*v**4 - 9/4*v**2 + 3/2*v**3 - 3*v = 0.
-2, 1
Factor -114*f**2 + 80 - 15*f**3 + 6*f + 134*f + 134*f**2.
-5*(f - 4)*(f + 2)*(3*f + 2)
Let k(i) be the second derivative of i**7/252 - i**6/90 + i**4/36 - i**3/36 + 8*i. Suppose k(r) = 0. Calculate r.
-1, 0, 1
Let h(w) = -2*w**5 - 7*w**4 + 3*w**3 + 4*w**2 - w - 3. Let i(l) = 6*l**5 + 20*l**4 - 8*l**3 - 12*l**2 + 2*l + 8. Let y(v) = -8*h(v) - 3*i(v). Solve y(x) = 0.
-1, 0, 1
Let g(i) be the first derivative of -1/7*i**2 + 1/14*i**4 + 0*i + 2/21*i**3 - 2/35*i**5 - 1. Factor g(x).
-2*x*(x - 1)**2*(x + 1)/7
Let c = 18 - 13. Let h = c + -1. Factor -3*u**4 + u**2 + 2*u**h + 0*u**4.
-u**2*(u - 1)*(u + 1)
Let j(a) be the third derivative of -1/840*a**8 + 0*a - 1/525*a**7 + 1/75*a**5 - 1/15*a**3 - 1/60*a**4 + 1/150*a**6 + 5*a**2 + 0. Factor j(r).
-2*(r - 1)**2*(r + 1)**3/5
Let n(x) be the second derivative of -x**6/180 - x**5/45 - x**4/36 - 5*x**2/2 + 7*x. Let q(u) be the first derivative of n(u). Let q(j) = 0. Calculate j.
-1, 0
Let f(d) be the second derivative of d**8/10080 + d**7/630 + d**6/90 + 2*d**5/45 - d**4/4 - 2*d. Let r(p) be the third derivative of f(p). Factor r(t).
2*(t + 2)**3/3
Let f(z) = 6 + 3 + 4*z + 6. Let x be f(-3). Determine m, given that 2*m**x + 0 + 2*m**4 + 0*m + 2/3*m**2 + 2/3*m**5 = 0.
-1, 0
Solve -2*a + a - 2 - 248*a**2 + 249*a**2 = 0.
-1, 2
Suppose -67*y = -68*y + 2. Solve -1/4*z - 1/2*z**y + 0 + 1/2*z**4 + 0*z**3 + 1/4*z**5 = 0.
-1, 0, 1
Suppose 2*b + 10 = 4*a, 3*b = -2*b + 5*a - 20. Let n be b + 11 + (2 - 0). Solve y + 3*y - n*y**2 + 13*y**2 - y = 0 for y.
-1, 0
Let u(n) be the second derivative of -1/21*n**3 - 4*n + 1/70*n**5 + 0 + 2/7*n**2 + 1/35*n**6 - 5/42*n**4. Suppose u(b) = 0. What is b?
-1, 2/3, 1
Let y(v) be the first derivative of 1/3*v**4 + 0*v - 3 - 2/3*v**3 + 0*v**2 - 2/45*v**5. Factor y(i).
-2*i**2*(i - 3)**2/9
Let w(n) be the first derivative of n**3/9 - n**2/6 + 13. Let w(f) = 0. Calculate f.
0, 1
Factor 1/4*v**2 - 1/2*v**3 + 1/4*v**4 + 0 + 0*v.
v**2*(v - 1)**2/4
Let w be (50/(-180))/(20/(-12)*1). Suppose -1/2*u - 1/3 - w*u**2 = 0. Calculate u.
-2, -1
Let u = 351547/90 + -3906. Let g(m) be the second derivative of 0 + u*m**6 + 0*m**2 - 1/9*m**3 + 1/12*m**4 - m + 1/5*m**5. Solve g(w) = 0 for w.
-1, 0, 2/7
Let h(p) be the second derivative of p**6/5 + 9*p**5/20 - p**4/4 - 3*p**3/2 - 3*p**2/2 + 4*p. Let h(b) = 0. What is b?
-1, -1/2, 1
Suppose 2 = 4*g - r - 0, 4*r + 8 = -5*g. Factor g + 4*z**2 + 142*z - 138*z - 8.
4*(z - 1)*(z + 2)
Let c = 221 - 1102/5. Let -3/5*a - c*a**2 + 0 = 0. Calculate a.
-1, 0
Let n(w) be the third derivative of -w**5/90 - w**4/18 + w**2. Solve n(i) = 0.
-2, 0
Let g(o) be the first derivative of o**7/735 - o**6/210 + o**4/42 - o**3/21 - 3*o**2/2 - 3. Let u(v) be the second derivative of g(v). Factor u(h).
2*(h - 1)**3*(h + 1)/7
Let j(w) be the third derivative of 2/525*w**7 - 1/75*w**5 + 0*w - 1/840*w**8 + 0*w**3 + 0 + 0*w**6 + 1/60*w**4 + w**2. Suppose j(a) = 0. What is a?
-1, 0, 1
Let t(s) be the second derivative of -1/2*s**4 - 1/10*s**5 - 7*s + 0 - s**3 - s**2. Factor t(u).
-2*(u + 1)**3
Let i be (7 + -7)/2 - (-16)/10. Factor -2/5*c**5 + 8/5*c**4 + 0 - 12/5*c**3 - 2/5*c + i*c**2.
-2*c*(c - 1)**4/5
Suppose 0 = -41*l + 45*l. Factor 1/2*f**2 + f**4 + 5/4*f**3 + 1/4*f**5 + 0*f + l.
f**2*(f + 1)**2*(f + 2)/4
Let l = -1552 + 1554. Find a, given that 9/4*a**l - 3/8*a**3 + 0 - 27/8*a = 0.
0, 3
Let k(z) be the third derivative of -z**7/11340 + z**6/3240 - z**4/24 + z**2. Let g(j) be the second derivative of k(j). Suppose g(m) = 0. What is m?
0, 1
Let j(z) be the third derivative of -z**5/240 - z**4/12 + 3*z**3/8 + 48*z**2. What is y in j(y) = 0?
-9, 1
Suppose 5*h - 20 = 0, 4*a - h + 4 = -0*h. Suppose 0 = -36*j + 19*j. What is d in -1/4*d**2 + j + a*d = 0?
0
Let c(x) = -4*x**3 - 2*x**2 + 6. Let d(a) = 7*a**3 + 3*a**2 - 11. Suppose -6 = -2*y + y. Let w(j) = y*d(j) + 11*c(j). Determine z so that w(z) = 0.
-2, 0
Let y(p) be the second derivative of -p - 1/10*p**5 + 1/12*p*