, -4*r - 2*q + 10 = -0*q. Factor 3/2*l**r + 1/2*l**2 + 0*l + 3/2*l**4 + 1/2*l**5 + 0.
l**2*(l + 1)**3/2
Factor 0 + 1/3*r**5 + 0*r**2 + 0*r + r**3 - 4/3*r**4.
r**3*(r - 3)*(r - 1)/3
Suppose -3*t - 13 = o + t, o = 4*t + 3. Let n be -1*o*(-2)/(-2). Determine m so that m**5 + 0*m**n - 3*m**4 + 4*m**4 = 0.
-1, 0
Factor 6*q - 2*q**2 - 2*q**3 + 5*q**2 + 4 - 2*q - q**4 + 4*q.
-(q - 2)*(q + 1)**2*(q + 2)
Let v(f) = 3*f**3 + 3*f**2 + f + 1. Let z(j) = 3*j**3 + 3*j**2. Let q(i) = 3*v(i) - 4*z(i). Factor q(m).
-3*(m - 1)*(m + 1)**2
Let p be (-6)/9 + (-34)/(-6). Suppose 2*v + 0 = p*c + 4, 2*v + c = 4. Factor 0*s - 2/3*s**v + 2/3.
-2*(s - 1)*(s + 1)/3
Factor -1/4 + 1/2*y - 1/4*y**2.
-(y - 1)**2/4
What is z in 3 + 5*z**3 + 18*z**2 + 3*z**3 + 12*z + 3*z**3 + z**3 + 3*z**4 = 0?
-1
Let u be 3/6 - (-18)/12. Let y(l) be the first derivative of 3 - 3/2*l**u + 0*l + l**3. Factor y(q).
3*q*(q - 1)
Let w(r) be the first derivative of -4/7*r**2 + 2/7*r - 2 - 2/7*r**4 + 2/35*r**5 + 4/7*r**3. Factor w(o).
2*(o - 1)**4/7
Let m(h) be the second derivative of -h**7/10080 + h**5/480 - 5*h**4/12 - 2*h. Let x(a) be the third derivative of m(a). Factor x(i).
-(i - 1)*(i + 1)/4
Let r(v) be the third derivative of -v**8/168 - 4*v**7/315 + 13*v**6/180 + v**5/5 - v**4/9 - 8*v**3/9 + 13*v**2. Determine w so that r(w) = 0.
-2, -1, 2/3, 2
Let t(b) be the third derivative of b**8/504 - b**7/126 + b**6/120 + b**5/180 - b**4/72 + 12*b**2. Suppose t(c) = 0. What is c?
-1/2, 0, 1
Factor -44*s**3 + 45*s**3 - s**2 + s**4 - 2*s**5 + s**5.
-s**2*(s - 1)**2*(s + 1)
Let f = -2169/13 + 167. Factor -4/13*x**2 - 2/13*x - f*x**3 + 0.
-2*x*(x + 1)**2/13
Factor 3*c**2 - 13*c**2 - 5*c**3 + 3*c**3 - 6*c + 18.
-2*(c - 1)*(c + 3)**2
Let m(f) be the second derivative of 2*f**6/15 + 2*f**5/5 + f**4/3 + 6*f. Factor m(n).
4*n**2*(n + 1)**2
Let x = -3 - -8. Suppose 6*c**4 + 2*c**x - 5*c**2 - 3*c**2 + 0*c**5 = 0. What is c?
-2, 0, 1
Let y(f) be the first derivative of 2*f**3/27 - 2*f**2/3 + 10*f/9 - 62. Solve y(c) = 0.
1, 5
Let l be ((-38)/(-24) - -1) + 1/(-4). Let k be (2/(-15))/(1/(-5)). Factor r**3 + l*r - k - 8/3*r**2.
(r - 1)**2*(3*r - 2)/3
Let q(m) = m**3 + 9*m**2 + 8*m - 2. Let d be q(-8). Let p be -1 + 1 + d - -6. Factor -3*b**2 + 2*b**3 - 3*b**2 - 2*b + 4*b**2 + 2*b**p.
2*b*(b - 1)*(b + 1)**2
Let o(k) = 3*k**5 + 5*k**3 + 8. Let i be 3 - (0 + -1 + 1). Let n(y) = y**5 + 2 + 3*y**3 - y**3 + 1. Let b(h) = i*o(h) - 8*n(h). Factor b(r).
r**3*(r - 1)*(r + 1)
Let b(u) = u**2 - 8*u + 7. Let w be b(7). Suppose 2*g**2 + 4 + 4*g - 4 + w = 0. What is g?
-2, 0
Let q(b) be the second derivative of b**7/8820 - b**6/1260 + b**5/420 + b**4/6 - 3*b. Let h(j) be the third derivative of q(j). Solve h(i) = 0.
1
Let p(l) = 16*l**4 + 28*l**3 - 13*l**2 - 11*l + 2. Let b(x) = -63*x**4 - 111*x**3 + 51*x**2 + 45*x - 9. Let o(h) = -4*b(h) - 15*p(h). Solve o(d) = 0 for d.
-2, -1, 1/2
Let q be (-62)/(-63) + (-36)/(-81). Determine f, given that 2/7*f**4 + 4/7 - q*f**3 - 2*f + 18/7*f**2 = 0.
1, 2
Suppose -8 - 12 = -g - 5*h, -16 = 5*g - 4*h. Let l(i) be the third derivative of -1/210*i**5 + 1/84*i**4 + 0*i**3 - 2*i**2 + 0*i + g. Factor l(x).
-2*x*(x - 1)/7
Suppose -186 = 4*s - s - 3*k, 0 = 5*s - 2*k + 319. Let q = s + 197/3. Factor 2/9*x**2 + 4/9*x - q.
2*(x - 1)*(x + 3)/9
Let o(g) be the first derivative of g**4/12 - 5*g**3/9 - 13*g**2/6 - 7*g/3 + 55. Factor o(p).
(p - 7)*(p + 1)**2/3
Let h be (2/3)/((-4)/(-12)). Let f(b) be the third derivative of 0 + 0*b + 1/48*b**4 - h*b**2 - 1/240*b**5 + 0*b**3. Factor f(d).
-d*(d - 2)/4
Let v(g) be the first derivative of g**6/33 - 6*g**5/55 + 8*g**3/33 + 20. Find m, given that v(m) = 0.
-1, 0, 2
Let f(u) be the second derivative of 0 - 1/12*u**4 - u + 0*u**2 - 1/6*u**3. Factor f(q).
-q*(q + 1)
Let p(u) be the third derivative of u**8/336 - u**7/35 + 7*u**6/60 - 4*u**5/15 + 3*u**4/8 - u**3/3 - 11*u**2. Factor p(g).
(g - 2)*(g - 1)**4
What is y in -1/4*y**4 + 0 + 0*y**2 + 0*y + 1/4*y**3 = 0?
0, 1
Factor 0*u - 1/2*u**2 + 0 + 1/4*u**4 - 1/4*u**3.
u**2*(u - 2)*(u + 1)/4
Let k be (-4)/10 - 57/(-5). Suppose 3*z + 2 - k = 0. Suppose h**2 + 0 - 1/3*h**4 + 2/3*h + 0*h**z = 0. What is h?
-1, 0, 2
Suppose x - 8 + 2 = 0. Let m(l) = 3*l**4 + 5*l**3 + 7*l**2 + 7*l. Let f(r) = r**4 - r**2 - 1. Let n(y) = x*f(y) - 3*m(y). Factor n(d).
-3*(d + 1)**3*(d + 2)
Let m(f) be the second derivative of f**6/80 - 3*f**5/160 - f**4/16 - f - 3. Let m(z) = 0. Calculate z.
-1, 0, 2
Let r(m) = -m**4 - m**3 - 8. Let j(z) = -1. Let p(q) = 40*j(q) - 5*r(q). Determine i, given that p(i) = 0.
-1, 0
Suppose -2*k - 5*s = k + 16, -4 = 2*s. Let p be 25/10 + k/4. Factor 0*a + 7*a**3 + 2*a + 6*a**p - a**3 + 2*a**4.
2*a*(a + 1)**3
Let 2/3*k**2 - 1/3*k**4 - 1/3 + 0*k + 0*k**3 = 0. Calculate k.
-1, 1
Let k(r) = -r**2 + 5*r - 6. Let t be k(3). Factor t + 3/4*w**2 - 3/4*w.
3*w*(w - 1)/4
Factor 1/5*l**2 - 2/5 + 1/5*l.
(l - 1)*(l + 2)/5
Let r(c) be the second derivative of 0*c**5 + 3*c + 2/135*c**6 + 0*c**2 - 1/189*c**7 - 1/27*c**4 + 0 + 1/27*c**3. Factor r(l).
-2*l*(l - 1)**3*(l + 1)/9
Let m = 82/519 - -3/346. Determine g so that m*g**4 + 0*g + 0 - 1/6*g**3 + 0*g**2 = 0.
0, 1
Let v = 12 + -8. Let d be (60/(-50))/(v/(-10)). Factor 0 + 2/3*o**d - 2/3*o**5 - 2/3*o**2 + 2/3*o**4 + 0*o.
-2*o**2*(o - 1)**2*(o + 1)/3
Let p be (3*(-2)/3)/(-1). Let t be p/2 - 11/22. Factor 5/2*k**3 + 0*k + t*k**5 + k**2 + 2*k**4 + 0.
k**2*(k + 1)**2*(k + 2)/2
Factor -2/3*f**4 + 2*f**2 - 8/3 + 4/3*f**3 - 8/3*f.
-2*(f - 2)**2*(f + 1)**2/3
Suppose 4*l = 41 + 35. Let i = 59/3 - l. Solve 0 - 1/3*x**3 + x**2 - i*x = 0.
0, 1, 2
Let u(s) be the first derivative of s**3 + 2*s**2 + s - 1. Factor u(c).
(c + 1)*(3*c + 1)
Let w(z) = z - 8. Let u be w(11). Factor 2*p**4 - 2 + p**u - 4*p + 3*p**3 + 0*p**4.
2*(p - 1)*(p + 1)**3
Let y(w) be the first derivative of -w**6/12 + 3*w**4/8 - w**3/3 + 7. Let y(d) = 0. Calculate d.
-2, 0, 1
Let n(u) be the third derivative of 5*u**7/14 - u**6/4 + u**5/20 + u**2. Factor n(d).
3*d**2*(5*d - 1)**2
Let k(d) be the second derivative of d**6/75 + 3*d**5/50 + d**4/30 - d**3/5 - 2*d**2/5 - d. Factor k(s).
2*(s - 1)*(s + 1)**2*(s + 2)/5
Let r(q) be the first derivative of q**5/5 - q**4/4 - q**3/3 + q**2/2 - 7. Suppose r(h) = 0. Calculate h.
-1, 0, 1
What is w in 5*w**3 + 6*w**2 + 4*w - 16*w**3 + 9*w**3 - 2*w**5 - 6*w**4 = 0?
-2, -1, 0, 1
Let b be (2/(-20))/(1*-6). Let i(u) be the third derivative of -1/120*u**6 + b*u**5 + 0*u - 1/6*u**3 + 0 + 1/24*u**4 + u**2. Factor i(t).
-(t - 1)**2*(t + 1)
Let w(z) = 3*z**2 + 3*z - 3. Let d(u) be the second derivative of u**4/2 + 7*u**3/6 - 7*u**2/2 + 6*u. Let f(s) = 3*d(s) - 7*w(s). Determine q so that f(q) = 0.
0
Let n(y) be the first derivative of 2*y**3/15 - 3*y**2/5 + 4*y/5 - 1. Factor n(u).
2*(u - 2)*(u - 1)/5
Let g(o) = -3*o**2 - o + 4. Let i(h) = h**2 + h - 2. Let k(l) = 6*g(l) + 14*i(l). Determine m so that k(m) = 0.
1
Let m be (13 - 549/45)*(-15)/(-18). Suppose -3*c = -2*c. Find r, given that -16/15*r**3 + c + m*r**4 + 4/15*r + 2/15*r**2 = 0.
-2/5, 0, 1
Let d = -6 + 8. Suppose -4*l = -d*l - 10. Suppose -7/2*u**2 - 1/2*u**3 + 0*u + 3/2*u**4 + 1/2*u**l + 2 = 0. Calculate u.
-2, -1, 1
Let o(s) = -2*s**5 + 7*s**4 + s**3 + 3*s. Let c(z) = 8*z**5 - 27*z**4 - 3*z**3 - 11*z. Let v(m) = 6*c(m) + 22*o(m). Factor v(q).
4*q**3*(q - 1)**2
Let x = 21 - 11. Let h = x - 7. Let -2*w**3 + 20*w**3 + 11*w**2 - 2*w**h + 7*w**4 + 2*w = 0. What is w?
-1, -2/7, 0
Suppose 5*r - 2*r = 48. Let d = 33/2 - r. Find f such that 0*f**3 + d*f**5 + f**4 - 1/2*f + 0 - f**2 = 0.
-1, 0, 1
Let m(w) = -2*w**5 + w**4 + 3*w**3 + 2*w**2 + 2*w - 3. Let l(d) = -d**5 + d**4 + d**3 + d - 1. Let t(b) = 6*l(b) - 2*m(b). Factor t(r).
-2*r*(r - 1)**3*(r + 1)
Let u(f) = -f**2 + 8*f + 5. Let m(s) = -s**2 + 4*s + 3. Suppose k = -0 + 2. Suppose x - 3 = k*x. Let n(b) = x*u(b) + 5*m(b). Factor n(a).
-2*a*(a + 2)
Let x = -33 + 37. Factor 9*q**x - 8/3 - 28/3*q + 9*q**3 - 6*q**2.
(q - 1)*(3*q + 2)**3/3
Let b = 497 - 495. Let 6/7*v + 3/7 + 3/7*v**b = 0. Calculate v.
-1
Let t be ((-10)/(-6))/(15/45). Let j(k) be the second derivative of 0 - k - 1/4*k**4 + 1/6*k**3 + 3/20*k**t + 0*k**2 - 1/30*k**6. Factor j(z).
-z*(z - 1)**3
Factor 2/3*a**2 + 0 - 2/3*a**4 - 4/3*a + 4/3*a**3.
-2*a*(a - 2)*(a - 1)*(a + 1)/3
Let r(t) be the first derivative of 0*t**2 - 1 - t + 1/42