 -3*d. Find k, given that 3*k - 5*k**3 - 4 + k**3 + d*k**3 + 3*k = 0.
-2, 1
Let w(i) be the second derivative of i**5/100 + i**4/30 - i**3/10 + 4*i. Factor w(p).
p*(p - 1)*(p + 3)/5
Let t(i) be the first derivative of i**7/420 - i**6/90 - i**5/20 + 2*i**3 - 3. Let b(x) be the third derivative of t(x). Find q such that b(q) = 0.
-1, 0, 3
Let g(r) be the second derivative of 0*r**3 + 0 - 1/10*r**4 + 4/5*r**2 - 1/50*r**5 - 4*r. Factor g(o).
-2*(o - 1)*(o + 2)**2/5
Let k(l) be the first derivative of 2/11*l - 7 - 1/22*l**4 + 1/11*l**2 - 2/33*l**3. Solve k(y) = 0 for y.
-1, 1
Let t = -2619/4 + 657. Determine h so that -3/4*h - t*h**2 + 0 - 9/4*h**3 - 3/4*h**4 = 0.
-1, 0
Let j(z) = 5*z + 8. Let s(v) = v + 1. Let u(x) = -j(x) + 4*s(x). Let f be u(-4). Suppose 1/5*t**2 + 0 - 1/5*t**3 + f*t = 0. What is t?
0, 1
Factor -240*h - 51*h**2 + 73*h**3 - 150*h**3 - 192 + 74*h**3.
-3*(h + 1)*(h + 8)**2
Let z = 2/31 - -27/62. Let v be (15/10 + -3)*4/(-3). Find o such that z*o**3 + 5/2*o - v*o**2 - 1 = 0.
1, 2
Suppose 3*y + 5*t - 660 = 5*y, 1629 = -5*y + 2*t. Let l = 2281/7 + y. Let l*z**3 + 2/7*z - 2/7*z**4 - 6/7*z**2 + 0 = 0. Calculate z.
0, 1
Let k(b) be the first derivative of 9*b**5/5 - 11*b**4/4 + 2*b**3/3 - 16. Find d such that k(d) = 0.
0, 2/9, 1
Let v(r) be the third derivative of -r**7/84 + r**6/16 - 5*r**4/12 + 20*r**2. Let v(k) = 0. What is k?
-1, 0, 2
Suppose 12/17 + 10/17*l**2 - 26/17*l = 0. Calculate l.
3/5, 2
Suppose -4*f = -8*f. Suppose f*a = 2*a. Factor 3*d + a*d**2 - 2*d**2 - 5*d.
-2*d*(d + 1)
Suppose m + 1 = 7. Let g(f) be the third derivative of 0*f + 0*f**3 + 1/672*f**8 + 0*f**4 - f**2 + 0 - 1/210*f**7 + 0*f**5 + 1/240*f**m. Factor g(s).
s**3*(s - 1)**2/2
Let k(x) be the second derivative of x**8/12600 + x**7/3150 - x**5/450 - x**4/180 - x**3/3 + x. Let l(u) be the second derivative of k(u). Factor l(c).
2*(c - 1)*(c + 1)**3/15
Determine r so that 0 + 0*r + 3/5*r**2 = 0.
0
Let d(r) be the first derivative of -3*r**4/5 + 47*r**3/15 - 7*r**2/2 + 6*r/5 + 10. Factor d(f).
-(f - 3)*(3*f - 2)*(4*f - 1)/5
Suppose 0 = -5*w + 4*g - g + 7, w = g + 1. Suppose 3*d + y = 26, d + 3*y + 3 - 9 = 0. Factor d - 2*k**w - k**3 - 9.
-k**2*(k + 2)
Let z(w) = -2*w - 3. Let v be z(-1). Let r(h) = 7*h**2 + 6. Let y(j) = -j**2 - 1. Let o(i) = v*r(i) - 6*y(i). Factor o(q).
-q**2
Let z(h) be the first derivative of 3 + 0*h**3 - 1/4*h**4 + 1/6*h**6 + 0*h**2 + 0*h + 0*h**5. Find g, given that z(g) = 0.
-1, 0, 1
Let z(x) be the second derivative of x**4/78 + x**3/13 + 2*x**2/13 + 20*x. Factor z(s).
2*(s + 1)*(s + 2)/13
Let 0*a + 4/3*a**2 - 4/3 = 0. Calculate a.
-1, 1
Let s(r) = 2*r**2 - 5*r + 2. Let g be s(2). Determine y so that -1/4*y**5 + 0 + g*y**4 + 0*y + 1/4*y**3 + 0*y**2 = 0.
-1, 0, 1
Let h(o) be the first derivative of -4*o**6/27 + 2*o**5/5 - o**4/9 - 16*o**3/27 + 2*o**2/3 - 2*o/9 + 3. Let h(n) = 0. Calculate n.
-1, 1/4, 1
Suppose 2/7*s - 2/7 + 2/7*s**2 - 2/7*s**3 = 0. What is s?
-1, 1
Factor 0*l - 2/13*l**3 - 2/13*l**2 + 0.
-2*l**2*(l + 1)/13
Let u be (-2)/8 + 34/8. Suppose u*f + d - 8 = 0, 4*f - 6*d + 3*d = 8. Find p such that 0*p + 0 - 1/3*p**f = 0.
0
Let m(y) be the first derivative of -5*y**3/12 - 5*y**2/2 - 5*y + 22. Factor m(c).
-5*(c + 2)**2/4
Let v(m) = m**3 + 7*m**2 + 6*m + 3. Let h(l) = l**3 - l**2 - 1. Let f(t) = -t - 1. Let w be f(-2). Let c(i) = w*v(i) + h(i). What is n in c(n) = 0?
-1
Let a(g) be the first derivative of -g**4/8 - 2*g**3 - 9*g**2 + 13. Factor a(v).
-v*(v + 6)**2/2
Let h be (33/(-44))/(1/(-2)). Let 0 + h*p - 3/2*p**2 = 0. Calculate p.
0, 1
Let q(a) be the third derivative of -a**7/14 - a**6/12 + a**5/4 + 5*a**4/12 - 30*a**2. Solve q(p) = 0.
-1, -2/3, 0, 1
Let n = -36 + 60. Let f be 22/77 - n/(-14). Factor 2/3*u**3 - 2/3*u**4 - 2/3*u + 2/3*u**f + 0.
-2*u*(u - 1)**2*(u + 1)/3
Let l(o) be the first derivative of -o**4/4 - 2*o**3 - 6*o**2 - 8*o - 6. Factor l(p).
-(p + 2)**3
Suppose 6*i**4 + 2*i**2 - 5*i**3 - 7*i**5 - 3*i**3 + 2*i**3 + 5*i**5 = 0. What is i?
0, 1
Factor 2*a**2 + a**2 + 8*a**2 - 8*a - 9*a**2 + 8.
2*(a - 2)**2
Let f(o) be the third derivative of o**5/120 - o**4/16 - o**3/3 - 6*o**2. Factor f(c).
(c - 4)*(c + 1)/2
Suppose 3*f + 22 = 58. Factor 8*r**4 + f*r + 4*r - 4*r**5 - 12*r - 8*r**2.
-4*r*(r - 1)**3*(r + 1)
Let k(u) be the second derivative of -u**8/840 - u**7/210 + u**5/30 + u**4/12 - u**3/6 + u. Let m(d) be the second derivative of k(d). Factor m(j).
-2*(j - 1)*(j + 1)**3
Suppose -2*c = -5*c. Suppose c = x - 3 - 1. Suppose 1/2*y - 1/2*y**x - 3/2*y**2 + 0 + 3/2*y**3 = 0. Calculate y.
0, 1
Let b = -2 - -8. Suppose -l = -3*v - 1, -2*l + 6*v + b = 4*v. Find d, given that l*d**3 - d - d - 2*d**3 = 0.
-1, 0, 1
Let r(i) = 48*i**2 - 140*i - 168. Let p(l) = 7*l**2 - 20*l - 24. Let a(m) = 20*p(m) - 3*r(m). What is k in a(k) = 0?
-1, 6
Let h(g) be the third derivative of -g**6/840 + g**5/70 - g**4/14 + 4*g**3/21 + 2*g**2. Factor h(s).
-(s - 2)**3/7
Suppose -178 = -3*p + 62. Suppose 0 = -r + 6*r - p. Factor -10*n - 3*n**3 - 12*n**2 + n**3 - 14*n - r.
-2*(n + 2)**3
Let s(b) be the second derivative of -b**6/90 + b**4/12 + b**3/9 + 4*b. Factor s(l).
-l*(l - 2)*(l + 1)**2/3
Let p(c) be the third derivative of c**7/315 - c**6/90 - c**5/90 + c**4/18 - c**2. Factor p(s).
2*s*(s - 2)*(s - 1)*(s + 1)/3
Let a be (20/(-6))/(2/(-6)). Let f be a/15 + (-14)/(-6). Factor -2*u**4 - 4*u**3 + 5*u**3 - f*u**3.
-2*u**3*(u + 1)
Let g(k) be the second derivative of -k**7/147 + k**6/35 - 3*k**5/70 + k**4/42 + 16*k. Factor g(z).
-2*z**2*(z - 1)**3/7
Factor -231*g**2 + 28*g**2 + 7*g**2 + 112*g - 16.
-4*(7*g - 2)**2
Let t(i) be the first derivative of -11/6*i**4 + 8 - 1/6*i**6 + 13/15*i**5 + 2*i**3 + 1/3*i - 7/6*i**2. Factor t(a).
-(a - 1)**4*(3*a - 1)/3
Let d(f) be the first derivative of 0*f**3 - 1/2*f**6 - 3/2*f**2 + 0*f**5 + 0*f - 1 + 3/2*f**4. Factor d(u).
-3*u*(u - 1)**2*(u + 1)**2
Let q(p) = -2*p**2 - 8*p - 6. Let z be q(-3). Let j(u) be the third derivative of 1/60*u**6 + 0*u**3 + 0 + 2*u**2 + 1/30*u**5 + z*u + 0*u**4. Factor j(v).
2*v**2*(v + 1)
Let u = 720 - 5030/7. Factor -u*o - 4/7 - 8/7*o**2 - 2/7*o**3.
-2*(o + 1)**2*(o + 2)/7
Let c(s) = -5*s**3 - 9*s**2 - 3*s + 5. Let i(x) = 4*x**3 + 8*x**2 + 2*x - 4. Let a(w) = 5*c(w) + 6*i(w). Factor a(p).
-(p - 1)**3
Let c(d) be the second derivative of -d**8/168 + 4*d**7/105 - d**6/10 + 2*d**5/15 - d**4/12 + d**2 + 7*d. Let v(f) be the first derivative of c(f). Factor v(w).
-2*w*(w - 1)**4
Let r(m) = m**2 - m. Let w(y) = -16*y**2 + 10*y. Let x(j) = -1. Let h(c) = -w(c) - 2*x(c). Let b(i) = -2*h(i) + 28*r(i). Determine l so that b(l) = 0.
-1
Let h = -54 - -56. Let -1/3*m**4 + 0 - 1/3*m**5 + 1/3*m**3 + 1/3*m**h + 0*m = 0. Calculate m.
-1, 0, 1
Let a = 11 + -8. Let r(d) be the first derivative of -1/8*d**4 - 1/12*d**a + 0*d + 0*d**2 + 2 - 1/20*d**5. Factor r(l).
-l**2*(l + 1)**2/4
Let z(j) = j**5 - 3*j**4 + 3*j**3 + 5*j**2 - 2*j. Let w(n) = 5*n**5 - 12*n**4 + 13*n**3 + 21*n**2 - 9*n. Let s(t) = -2*w(t) + 9*z(t). Let s(a) = 0. What is a?
-3, -1, 0, 1
Let -128/5 - 2/5*r**2 - 32/5*r = 0. What is r?
-8
Suppose 0 = 20*s + 34*s - 108. Factor 28/3*m**3 - 64/3*m**s - 68/3*m + 8.
4*(m - 3)*(m + 1)*(7*m - 2)/3
Let k(w) be the first derivative of 0*w**2 - 5/9*w**6 + 16/15*w**5 + 0*w**3 + 4 + 0*w + 2/3*w**4. Determine n, given that k(n) = 0.
-2/5, 0, 2
Factor 74*w - 154*w + 72*w + 2*w**2 + 8.
2*(w - 2)**2
Let -18*t**2 + 4*t + 7*t**3 - 12*t**3 + 19*t**3 = 0. Calculate t.
0, 2/7, 1
Let r(t) be the second derivative of -t**6/60 + 3*t**5/40 - t. Factor r(b).
-b**3*(b - 3)/2
Let s(q) be the first derivative of -q**3/18 + 7*q**2/12 - q - 9. Factor s(u).
-(u - 6)*(u - 1)/6
Let z(s) be the first derivative of 2/27*s**3 + 2 - 2/9*s**2 + 2/9*s. Factor z(u).
2*(u - 1)**2/9
Let q = 1/39 - -49/117. Factor 0 + 14/9*x**2 + q*x.
2*x*(7*x + 2)/9
Suppose -3*q + q + 16 = 0. Determine s so that -q*s**2 + 17*s**2 - s - 8*s**2 = 0.
0, 1
Determine o, given that -7*o**2 - 2*o**2 + 4*o**4 + 0*o**2 + o**4 - 3*o**3 - o**5 = 0.
-1, 0, 3
Let j(h) be the third derivative of -1/60*h**6 + 0 - 1/6*h**3 + 1/210*h**7 + 4*h**2 + 0*h + 0*h**5 + 1/12*h**4. Factor j(p).
(p - 1)**3*(p + 1)
Let g(y) = 19*y - 4 - y**3 - 16*y + 7*y**2 - y**2. Let m(n) = -3*n**3 + 24*n**2 + 12*n - 15. Let a(s) = 15*g(s) - 4*m(s). Factor a(l).
-3*l*(l + 1)**2
Let b(i) = i**3 