ermine k, given that r(k) = 0.
1, 2
Let q(r) be the third derivative of -2*r**2 - 1/60*r**5 + 1/180*r**6 - 1/3*r**3 + 0*r**4 + 0 + 0*r. Let m(o) be the first derivative of q(o). Factor m(h).
2*h*(h - 1)
Suppose -4 = 4*v + b, -6 = -3*v - 0*b - 3*b. Let t = v + 8/3. Factor t*s**2 - 2/3*s + 0.
2*s*(s - 1)/3
Let i(v) be the third derivative of v**6/24 + v**5/4 - 5*v**4/24 - 5*v**3/2 + 13*v**2. Factor i(z).
5*(z - 1)*(z + 1)*(z + 3)
Let a(y) be the first derivative of -y**4/16 + y**3/4 - 3*y**2/8 + y/4 - 19. Solve a(m) = 0.
1
Let q(g) = -g**2 + 16*g + 36. Let f be q(18). Find o, given that -1/4*o**3 + f*o + 1/4*o**4 + 0*o**2 + 0 = 0.
0, 1
Factor 5*m**4 + 5*m**3 + 10*m**4 + 12*m**4 - 12*m**4.
5*m**3*(3*m + 1)
Let o(r) be the third derivative of r**7/700 - r**6/300 + r**5/600 - 36*r**2. Let o(m) = 0. Calculate m.
0, 1/3, 1
Let o(k) be the second derivative of 0 + 1/3*k**3 + 1/15*k**6 + 2*k + 0*k**2 + 3/10*k**5 + 1/2*k**4. What is g in o(g) = 0?
-1, 0
Let w(u) be the third derivative of 1/420*u**6 + 0*u**5 - 3*u**2 + 0 + 0*u + 1/588*u**8 + 0*u**4 + 1/245*u**7 + 0*u**3. Determine g, given that w(g) = 0.
-1, -1/2, 0
Suppose 12 = -5*p - 3, -3*y = 2*p + 21. Let d = -5 - y. Let 14/11*l**3 + 0*l + d + 4/11*l**2 = 0. Calculate l.
-2/7, 0
Let k(w) be the first derivative of w**4 - 4*w**3/3 - 2*w**2 + 4*w + 1. What is l in k(l) = 0?
-1, 1
Let -2/11*b**2 + 2/11*b**3 + 0 + 0*b = 0. What is b?
0, 1
Let n(w) = -w**2 - 11*w + 16. Let t be n(-12). Solve -9*s**2 - t*s + 5*s**2 - 4*s = 0 for s.
-2, 0
Let u(w) be the third derivative of w**5/30 + w**4/2 - 29*w**2. Let u(d) = 0. Calculate d.
-6, 0
Suppose -3*s = -4*c - 10, 0 = 3*c + 2 + 1. Solve -i**4 + 0*i**3 + s*i**3 - i**2 + 0*i**3 = 0 for i.
0, 1
Let n(s) = s**2 - 1. Let y = 4 + -3. Let p be 1 - (y - 1 - 4). Let l(w) = -w**3 + 7*w**2 - w - 5. Let b(a) = p*n(a) - l(a). Suppose b(z) = 0. What is z?
0, 1
Factor j**2 - 20 - 60*j**3 + 7*j**2 + 20.
-4*j**2*(15*j - 2)
Suppose -1 = 4*c - 5. Let y = c - -5. Factor 4*m**2 - m + 2*m - 2*m**5 + 4*m**4 + y*m**3 + 3*m**5.
m*(m + 1)**4
Solve 95*b**4 + 7*b + 120*b**4 - 80*b**3 + 20 - 27*b - 707*b**2 + 100*b**5 + 472*b**2 = 0 for b.
-2, -1, -2/5, 1/4, 1
Let t(z) = -z. Let f be t(-2). Determine h, given that 19*h**2 - h**4 + 4*h**3 - 4*h**5 - 2*h - h**5 + 3*h**5 - 17*h**f - 1 = 0.
-1, -1/2, 1
Let j(h) = -10*h**4 - 24*h**3 - 4*h**2 + 6*h + 14. Let r(p) = p**3 + p**2 - 1. Let x(a) = 2*j(a) + 36*r(a). Find s such that x(s) = 0.
-1, 2/5, 1
Let c be 935/(-2400) + 4/10. Let u(o) be the third derivative of 0*o**5 + 0*o**3 + 1/480*o**6 + 2*o**2 - c*o**4 + 0 + 0*o. Determine h so that u(h) = 0.
-1, 0, 1
Let x(r) = 7*r**5 - 10*r**4 - 18*r**3 + 64*r**2 - 57*r + 22. Let v(c) = c**5 - c**4 + c**2 + 1. Let b(t) = 4*v(t) - x(t). Suppose b(w) = 0. What is w?
-3, 1, 2
Suppose 0 = m + 1, 4*g + 3*m = -m + 16. Let t(c) = -c**3 + 5*c**2 + 2. Let v be t(g). Factor -9*b**v + 8*b**2 - 4*b + 3*b.
-b*(b + 1)
Factor -2*o - 4*o + 4*o**2 + 3*o + 4*o**3 - o - 4*o**4.
-4*o*(o - 1)**2*(o + 1)
Suppose 6 - 2 = 2*r. Let b = 5 - r. Solve 2/5*m**5 - 2/5*m - 4/5*m**4 + 0*m**b + 4/5*m**2 + 0 = 0.
-1, 0, 1
Suppose -2*u = -7*u + 20. Factor 299*p**4 - 299*p**u - 2*p**5.
-2*p**5
Let b(c) be the first derivative of -3*c**4/4 - 4*c**3 - 6*c**2 + 6. Solve b(o) = 0.
-2, 0
Factor -3*a + 33*a**2 + 2*a**3 - 2 + 24*a + 5 + 13*a**3.
3*(a + 1)**2*(5*a + 1)
Let p(q) be the first derivative of q**4/3 - 8*q**2 - 7*q + 4. Let j(t) be the first derivative of p(t). Factor j(a).
4*(a - 2)*(a + 2)
Let f(a) be the first derivative of -a**6/216 - a**5/60 - a**4/72 + a**3 + 2. Let y(r) be the third derivative of f(r). What is b in y(b) = 0?
-1, -1/5
Determine p, given that -6*p**2 + 8 - 3*p**3 - 2*p - 9 + 5*p + 7 = 0.
-2, -1, 1
Let s(o) = -9*o + 4. Let a be s(-4). Let l = a - 38. Factor 0 - 2/9*i**l + 0*i - 2/9*i**3.
-2*i**2*(i + 1)/9
Suppose 0 = 2*v + 2*h - 24 - 10, -2*h = -10. Factor 3*l**2 - 8*l**2 - v*l - 3*l**4 - 4 + 1 - 12*l**3 - 13*l**2.
-3*(l + 1)**4
Factor -10*h - 12*h + 12*h**3 + 10*h + 4*h**4 - 4*h**2.
4*h*(h - 1)*(h + 1)*(h + 3)
Find i such that 4*i**2 + 3*i + 6*i**2 + 9*i + 2*i**2 + 3 = 0.
-1/2
Let d = 462 - 462. Factor 0 + d*t + 2/9*t**4 + 4/9*t**2 - 2/3*t**3.
2*t**2*(t - 2)*(t - 1)/9
Let t(h) be the first derivative of -2*h**5/75 + 4*h**3/45 - 2*h/15 - 1. Solve t(s) = 0.
-1, 1
Let o = 95 - 853/9. Let t(m) = m**2 + m. Let d be t(0). What is n in d - 2/9*n**4 + 2/9*n**2 - 2/9*n**3 + o*n = 0?
-1, 0, 1
Let p(g) = g**2 - 11*g + 2. Let s be p(11). Let w(v) be the first derivative of -1 - 10/3*v**3 + 12*v**s - 8*v. Suppose w(z) = 0. What is z?
2/5, 2
Let g = -244/3 + 82. Find q, given that -2/3*q**3 - g*q**2 + 0 + 0*q = 0.
-1, 0
Let k be (-1 - -2)/((-6)/(-30)). Solve 3*f**k - f**5 - 2*f**4 + 2*f**4 - 2*f**4 = 0.
0, 1
Let m(z) = 3*z**4 + 19*z**3 - 31*z**2 + 45*z - 16. Let n(t) = 5*t**4 + 29*t**3 - 46*t**2 + 68*t - 24. Let d(y) = -8*m(y) + 5*n(y). Factor d(v).
(v - 2)**3*(v - 1)
Let h(q) be the second derivative of 0 + 0*q**2 - 2*q + 1/24*q**3 - 1/48*q**4. Let h(j) = 0. Calculate j.
0, 1
Let p(h) be the second derivative of -h**7/42 - 17*h**6/120 - 7*h**5/20 - 11*h**4/24 - h**3/3 - h**2/8 + 2*h. What is f in p(f) = 0?
-1, -1/4
Let k(z) be the first derivative of z**4/6 - z**2/3 + 3. Factor k(i).
2*i*(i - 1)*(i + 1)/3
Let y(n) be the third derivative of n**8/16800 + n**7/3150 - n**6/1800 - n**5/150 - n**4/6 - 3*n**2. Let l(x) be the second derivative of y(x). Factor l(c).
2*(c - 1)*(c + 1)*(c + 2)/5
Solve -8*y - y**2 + 2*y + 7*y = 0 for y.
0, 1
Let f be 2*2/30*3. Factor f + 18/5*o**3 + 6/5*o**2 - 2*o.
2*(o + 1)*(3*o - 1)**2/5
Solve -2*n**5 - 120*n**2 + n**3 + n**5 + 118*n**2 + 2*n**4 = 0 for n.
-1, 0, 1, 2
Factor 2*y**5 - y**5 - y - 70 - 2*y**2 + 70 + 2*y**4.
y*(y - 1)*(y + 1)**3
Suppose 4*k - 8 = 3*t, -3*t + 2*k - 2 = -t. Let l(c) be the second derivative of 0 - 1/48*c**t + 1/12*c**3 - 2*c - 1/8*c**2. Factor l(q).
-(q - 1)**2/4
Let x(b) be the third derivative of -2*b**7/105 - b**6/15 + b**4/3 + 2*b**3/3 - 5*b**2. Factor x(n).
-4*(n - 1)*(n + 1)**3
Find p, given that 13*p**2 - 3*p**3 - 8*p**3 + 6*p**3 + 2*p**2 = 0.
0, 3
Let c(i) be the second derivative of i**7/126 - i**5/20 - i**4/18 + 13*i. Factor c(s).
s**2*(s - 2)*(s + 1)**2/3
Factor 0 + 4/5*j + 4/5*j**3 + 2*j**2.
2*j*(j + 2)*(2*j + 1)/5
Let v(y) = -y**2 - y + 2. Let d be v(0). Suppose d*p = -2*p + 12. Factor 0*w**4 + 2*w**2 - 2*w**5 + 5*w**3 - 2*w**4 - p*w**3.
-2*w**2*(w - 1)*(w + 1)**2
Suppose 3*t = -t. Let j(k) be the first derivative of 0*k + 2 + 0*k**2 + 0*k**3 - 1/5*k**5 + t*k**4. Suppose j(o) = 0. What is o?
0
Let s(m) be the first derivative of m**4/6 + 2*m**3/9 - 6. Factor s(v).
2*v**2*(v + 1)/3
Let c(m) = 3*m**2 + 2*m - 8. Let a(w) = -2*w. Let f be a(-7). Let z(t) = 1. Let q(i) = f*z(i) + 2*c(i). Factor q(r).
2*(r + 1)*(3*r - 1)
Let 8*r**2 + 14 + 5*r**3 - 11*r**5 - 18 - r**3 - 4*r**4 + 9*r**5 - 2*r = 0. What is r?
-2, -1, 1
Let z be (-45 + 44)*8/(-9). Factor 4/9 - 2/9*d**3 + z*d**2 - 10/9*d.
-2*(d - 2)*(d - 1)**2/9
Let d(o) = 3*o**2 - o + 2. Let j be d(0). Suppose j*a = 3*a. Find r such that 1/3*r**2 + a*r - 1/3*r**3 + 0 = 0.
0, 1
Let r(d) be the third derivative of -d**6/210 + d**5/105 - 6*d**2. Suppose r(s) = 0. Calculate s.
0, 1
Let n(i) be the third derivative of i**5/12 + 65*i**4/24 - 35*i**3/3 + 35*i**2. Factor n(m).
5*(m - 1)*(m + 14)
Let w(j) be the second derivative of -3*j + 5/36*j**3 - 1/9*j**4 - 7/60*j**5 + 1/6*j**2 + 0 + 1/30*j**6 + 1/28*j**7. Find o, given that w(o) = 0.
-1, -1/3, 2/3, 1
Suppose 60 = -37*w + 67*w. Factor -2/3*s - 1/3*s**w + 1.
-(s - 1)*(s + 3)/3
Factor 5*f**3 + 4*f**2 + 4*f**3 + 5*f**3 + 2*f**2 + 10*f**4 + 2*f**5.
2*f**2*(f + 1)**2*(f + 3)
Let z be 2*2 + -1 + (-104)/39. Factor z*b**2 + 4/3*b + 4/3.
(b + 2)**2/3
Suppose 3*k - 5 = -2*k. Let z be 9/6 - k/(-2). Find i, given that 2/3 + 2/3*i - 2/3*i**3 - 2/3*i**z = 0.
-1, 1
Let a be 590/40 + 1/4. Suppose a = 2*s + 9. Find r, given that 2*r**s + 5/3*r**4 + 1/3*r**2 + 0*r + 0 = 0.
-1, -1/5, 0
Let l(r) be the first derivative of 1/6*r**3 + 1/2*r**2 - 4 + 0*r. Find i such that l(i) = 0.
-2, 0
Find v such that -v**5 - 39*v**3 + v**4 + 2*v**4 + 37*v**3 = 0.
0, 1, 2
Let n(y) be the first derivative of y**9/10584 + y**8/2940 - y**6/630 - y**5/420 + 5*y**3/3 + 2. Let i(x) be the third derivative of n(x).