 k such that v(k) = 0.
-1, 1
Let k(z) be the third derivative of z**7/6720 + z**6/2880 + z**3/3 - 5*z**2. Let f(u) be the first derivative of k(u). Factor f(c).
c**2*(c + 1)/8
Let o(f) = 14*f**3 - 11*f**2 - 9*f + 17. Let x(r) = 5*r**3 - 4*r**2 - 3*r + 6. Let j(h) = -4*o(h) + 11*x(h). Factor j(y).
-(y - 1)**2*(y + 2)
Factor 0*c**2 - 10*c**2 + 8*c - 3*c**3 + 5*c**3 + 0*c**3.
2*c*(c - 4)*(c - 1)
Factor 2/3*s + 0 + 2/3*s**4 + 2*s**2 + 2*s**3.
2*s*(s + 1)**3/3
Let p(u) be the second derivative of -u**4/4 - 3*u**3/2 - 3*u**2 + 8*u. Let p(y) = 0. Calculate y.
-2, -1
Let m be 12/21*(-49)/(-14). What is o in 2/13*o**m + 0 + 2/13*o**3 - 2/13*o**4 + 0*o - 2/13*o**5 = 0?
-1, 0, 1
Let i(o) be the third derivative of o**8/4200 + o**7/2100 - o**3/2 - 2*o**2. Let c(g) be the first derivative of i(g). Factor c(t).
2*t**3*(t + 1)/5
Let s(v) be the third derivative of v**2 + 1/3*v**3 + 0*v + 0 - 1/2*v**4 - 5/48*v**6 + 3/8*v**5. Determine b, given that s(b) = 0.
2/5, 1
Let y(b) be the third derivative of b**5/330 - b**4/33 + 4*b**3/33 + 3*b**2. Solve y(h) = 0.
2
Let x(h) = -h**3 - 15*h**2 + h + 17. Let o be x(-15). Suppose 6*w**3 - 11*w + o*w**2 - 6*w**2 - 2*w**4 + 11*w = 0. What is w?
0, 1, 2
Factor p**2 + 3*p**4 - 2*p + 2*p**3 + 8*p**2 + 5*p + 7*p**3.
3*p*(p + 1)**3
Let t(h) = 3*h**3 + 7*h**2 - 5*h + 5. Let p(r) = -4*r**3 - 6*r**2 + 4*r - 6. Let x(v) = 5*p(v) + 6*t(v). Factor x(d).
-2*d*(d - 5)*(d - 1)
Let v(l) be the third derivative of -8*l**7/105 + 7*l**6/30 - 2*l**5/15 - l**4/6 - 14*l**2. Solve v(u) = 0 for u.
-1/4, 0, 1
Let n(a) be the first derivative of 2/21*a**3 + 3 + 2/7*a + 2/7*a**2. Factor n(d).
2*(d + 1)**2/7
Let j(u) = -2*u - 5. Let f be j(-3). Let o(a) be the first derivative of 8/3*a**3 + 0*a - 3*a**4 - f - 1/3*a**6 + 8/5*a**5 - a**2. Factor o(w).
-2*w*(w - 1)**4
Let f(w) be the third derivative of -2*w**2 + 1/6*w**3 + 0*w + 0 - 1/120*w**6 - 1/40*w**5 + 1/4*w**4. Let z(c) be the first derivative of f(c). Factor z(t).
-3*(t - 1)*(t + 2)
Let p(o) be the third derivative of o**7/210 - o**6/60 - o**5/20 + o**4/6 + 2*o**3/3 + 28*o**2. Factor p(f).
(f - 2)**2*(f + 1)**2
Let y = -20/33 + 364/165. Let r(n) be the first derivative of 1/15*n**6 + 13/10*n**4 - 2 + 4/5*n**2 + 12/25*n**5 + y*n**3 + 0*n. What is l in r(l) = 0?
-2, -1, 0
Let a(p) be the first derivative of p**5/15 - p**4/12 - 4*p**3/9 + 2*p**2/3 - 9. Factor a(f).
f*(f - 2)*(f - 1)*(f + 2)/3
Let p(s) be the second derivative of s**7/21 - 3*s**5/10 - s**4/3 - 6*s. Suppose p(l) = 0. Calculate l.
-1, 0, 2
Let a(n) be the third derivative of n**6/420 + n**5/210 - n**4/84 - n**3/21 + 7*n**2. Determine h, given that a(h) = 0.
-1, 1
Let b(p) = 10*p**4 + 6*p**3 + 2*p**2 - 6*p + 6. Let h(y) = -y**4 - y**3 - y**2 + y - 1. Let s(d) = -b(d) - 6*h(d). Solve s(c) = 0 for c.
-1, 0, 1
Let i = -14 - -26. Factor a**2 - 5*a**2 + i*a**2 - 10*a**4 - 8*a + 2*a**5 + 6*a**3 + 2*a**4.
2*a*(a - 2)**2*(a - 1)*(a + 1)
Let d(q) be the first derivative of 14*q**3/3 + 12*q**2 - 8*q - 6. Factor d(x).
2*(x + 2)*(7*x - 2)
Factor 6*z**2 - 9*z**2 - z - 5*z + 3*z.
-3*z*(z + 1)
Find s, given that -6/19*s**5 + 8/19*s**2 - 14/19*s**4 + 0*s**3 + 0*s + 0 = 0.
-2, -1, 0, 2/3
Let b(a) be the third derivative of -a**5/210 + a**3/21 - 25*a**2. Factor b(w).
-2*(w - 1)*(w + 1)/7
Let u = -16 - -21. Let b = 13 - 9. Determine i, given that 2/3*i**2 - 1/3*i**b - 1/3 - 1/3*i**u + 2/3*i**3 - 1/3*i = 0.
-1, 1
Suppose 0 = 5*a + 3*f - 45, a + 2*a + 2*f = 26. Let t = a + -8. Find d, given that -3*d**3 - 2*d**2 - 2*d + d**t + 7*d**3 + 4 - 3 - 2*d**5 = 0.
-1, 1/2, 1
Let s(o) = o**2 - 12*o + 38. Let u be s(7). Solve 1/2*l**u + 0*l + 0*l**2 + 0 = 0.
0
Let h(a) be the first derivative of 3*a - 9/2*a**2 + 4 + 9/4*a**3. Factor h(t).
3*(3*t - 2)**2/4
Let u(i) be the second derivative of i**5/50 + i**4/10 + 2*i**3/15 - 38*i. Solve u(k) = 0 for k.
-2, -1, 0
Let r(h) be the second derivative of -h**5/10 - 2*h**4/3 + 5*h**3/3 - 19*h. Solve r(z) = 0 for z.
-5, 0, 1
Solve 0 - 2/3*k**3 - 2/3*k**2 + 4/3*k = 0.
-2, 0, 1
Determine z so that -4/7*z + 6/7*z**2 - 2/7 = 0.
-1/3, 1
Suppose -40 = -y - 9*y. Let x(q) be the third derivative of 0*q**5 + 1/480*q**6 + 0*q**y + 4*q**2 + 0*q**3 + 0*q + 0. Factor x(f).
f**3/4
Let j be -6*2*(-15)/20. Factor 0*z**2 + 3 + j*z**2 - 15*z + 0 + 3*z.
3*(z - 1)*(3*z - 1)
Let l = -418/3 + 140. Suppose -2*k + 2*k**2 + 2/3 - l*k**3 = 0. What is k?
1
Suppose 0 = -2*z + 4. Suppose 0 = 6*f - z*f - 12. Factor 4/3 - 4/3*i**2 + 2*i + 2/3*i**5 - 8/3*i**f + 0*i**4.
2*(i - 2)*(i - 1)*(i + 1)**3/3
Let w(h) = -h**2 + 6*h - 5. Let k be w(4). Suppose 0 = 2*s + 25 - 29. Let -s*d**k + 33*d - 33*d = 0. What is d?
0
Let k(t) be the first derivative of -4 + 32/3*t - 10/3*t**4 + 80/9*t**3 - 1/18*t**6 + 2/3*t**5 - 40/3*t**2. Factor k(o).
-(o - 2)**5/3
Let k(h) be the second derivative of 35*h**4/12 - 19*h**3/6 + 5*h**2/2 + h. Let y(v) = -174*v**2 + 94*v - 24. Let o(j) = 14*k(j) + 3*y(j). Factor o(u).
-2*(4*u - 1)**2
Let d = 459 - 22031/48. Let m(c) be the third derivative of 1/240*c**5 + d*c**4 + 0*c**3 + c**2 + 0*c + 0 - 1/480*c**6. Factor m(s).
-s*(s - 2)*(s + 1)/4
Let v(x) be the third derivative of -x**5/135 - 5*x**4/54 + 2*x**2 + 10*x. Factor v(k).
-4*k*(k + 5)/9
Solve -1/2*i**2 + 5*i - 25/2 = 0 for i.
5
Let y(i) = i**4 + 1. Suppose 0*b + 4*k = 5*b + 22, 0 = -5*b + 5*k - 25. Let v(r) = -3*r**4 - r**3 - 2. Let z(t) = b*y(t) - v(t). Let z(m) = 0. Calculate m.
-1, 0
Let c = -11 + 9. Let r be 3/9 + 0/c. Factor -r*u**3 + 0*u - u**2 + 4/3.
-(u - 1)*(u + 2)**2/3
Let b(o) be the third derivative of -2*o**7/105 - o**6/15 + 4*o**5/15 + o**4/3 - 2*o**3 + 12*o**2. Factor b(z).
-4*(z - 1)**2*(z + 1)*(z + 3)
Suppose 7 = -3*a - 2. Let g be 10 - 14 - a*2. Factor 0 - 2/7*u - 2/7*u**3 - 4/7*u**g.
-2*u*(u + 1)**2/7
Let j(r) be the first derivative of r**6/15 + 12*r**5/25 + 11*r**4/10 + 4*r**3/15 - 12*r**2/5 - 16*r/5 + 18. Determine b so that j(b) = 0.
-2, -1, 1
Let r(u) be the first derivative of -u**5/5 + u**4/2 + 5*u**3 + 2*u**2 - 20*u + 48. Suppose r(v) = 0. What is v?
-2, 1, 5
Let w(j) = -j**3 - j**2 + j - 1. Let d(i) = 6*i**3 - 5*i**2 - 43*i + 7. Let y(g) = -3*d(g) - 21*w(g). Factor y(t).
3*t*(t + 6)**2
Let k(l) be the second derivative of 1/3*l**4 + 8*l**2 - 2/15*l**6 + 2/21*l**7 + 0 + 5*l - l**5 + 16/3*l**3. Factor k(i).
4*(i - 2)**2*(i + 1)**3
Let l(s) be the first derivative of 2*s**6/9 + 4*s**5/15 + 4. Factor l(h).
4*h**4*(h + 1)/3
Let q = 69 + -37. Let s be 0 - (q/(-28))/4. Factor 0*o - 2/7*o**2 + s.
-2*(o - 1)*(o + 1)/7
Suppose 2*r = -r. Factor t + 6*t**2 - 7*t**2 + r*t + 5 - 3.
-(t - 2)*(t + 1)
Factor -5/3*t**4 - 10*t**2 - 5/3 - 20/3*t - 20/3*t**3.
-5*(t + 1)**4/3
Let i(d) = d**3 - d**2 - 2*d + 3. Let o be i(2). Suppose -o*j = -j. Factor -w + j*w - w + 2*w**3.
2*w*(w - 1)*(w + 1)
Let x(w) = w**2 + 21*w - 6. Let t(z) = -5*z**2 - 85*z + 25. Let d(g) = -6*t(g) - 25*x(g). Factor d(s).
5*s*(s - 3)
Let z(q) be the first derivative of 3*q**4/4 + q**3 - 15*q**2/2 + 9*q - 14. Factor z(d).
3*(d - 1)**2*(d + 3)
Let g = 16 + -16. Let d(i) be the first derivative of -1 + i**2 + g*i - 2/3*i**3. Factor d(k).
-2*k*(k - 1)
Let t(g) be the second derivative of -g**7/28 + 3*g**5/10 + g**4/4 - 3*g**3/4 - 3*g**2/2 + 14*g. Determine i, given that t(i) = 0.
-1, 1, 2
Solve 2*c**2 + c**5 - 2*c**4 - 59*c**3 - c + 59*c**3 = 0.
-1, 0, 1
Let w(z) = -16*z**5 - 11*z**4 + 7*z**3 + 18*z**2 + 16*z + 7. Let h(b) = -5*b**5 - 4*b**4 + 2*b**3 + 6*b**2 + 5*b + 2. Let x(r) = -7*h(r) + 2*w(r). Factor x(y).
3*y*(y - 1)*(y + 1)**3
Let t be 6/(-4) + 3/2. Let j(d) be the first derivative of -2/3*d**3 + 2*d - 1 + t*d**2. What is z in j(z) = 0?
-1, 1
Solve 2/15*w**3 + 0*w + 0*w**2 + 0 + 2/15*w**4 = 0 for w.
-1, 0
Let s(y) be the first derivative of y**5/150 + y**4/30 + y**3/15 - 3*y**2/2 - 2. Let n(c) be the second derivative of s(c). What is p in n(p) = 0?
-1
Let s be 30/(-1 - 5) - -8. Let z(y) be the first derivative of -3/2*y**2 + 3 + 2*y + 1/3*y**s. Factor z(w).
(w - 2)*(w - 1)
Suppose 5/4*j**3 + 0 - 1/2*j - 3/4*j**2 = 0. What is j?
-2/5, 0, 1
Suppose -5*w + m + 5 = -4*w, -5*m = -w + 25. Find v such that 0*v**3 + 0 + w*v**2 + 0*v + 1/3*v**4 = 0.
0
Suppose 0*c - 2*c - 10 = 0. Let p = 7 + c. Solve 8/3*x**3 - 2/3*x**4 + 4/3*x + 0 - 10/3*x**p = 0 for x.
0, 1, 2
Let k = 43/10 + -119/30. Solve 1/2*b**3 + 0*b