) = -65*a(x) - 6*c(x). Determine k so that b(k) = 0.
-1, 0
Let x(b) be the second derivative of 0 + 1/6*b**4 - b**2 + 0*b**3 + 3*b. Factor x(c).
2*(c - 1)*(c + 1)
Suppose 18/7 + 2/7*i**2 + 20/7*i = 0. What is i?
-9, -1
Let x(v) = -4*v**2 + v - 4. Suppose 0*u + u = -2. Let n(f) be the first derivative of f**3/3 + f - 2. Let y(d) = u*x(d) - 9*n(d). Factor y(a).
-(a + 1)**2
Let x(y) be the second derivative of -y**6/15 + 6*y**5/5 - 15*y**4/2 + 50*y**3/3 + 57*y. What is b in x(b) = 0?
0, 2, 5
Let l(f) = 5*f**3 - 3*f**2 + 6*f - 5. Let p(n) = -4*n**3 + 4*n**2 - 6*n + 4. Let u(i) = 2*l(i) + 3*p(i). Find o such that u(o) = 0.
1
Let n(y) = -3*y**3 + 6*y**2 - 21*y + 18. Let a(v) = -v + 1. Let m = -4 + 22. Let d(w) = m*a(w) - n(w). Suppose d(i) = 0. Calculate i.
0, 1
Factor 4/5*g**3 + 0*g**2 - 4/5*g - 2/5 + 2/5*g**4.
2*(g - 1)*(g + 1)**3/5
Let w(r) be the second derivative of r**6/45 - r**5/60 - r**4/18 + r**3/18 + 3*r. Let w(c) = 0. What is c?
-1, 0, 1/2, 1
Let p(v) be the third derivative of v**6/720 + v**5/60 + v**4/12 + v**3/3 + 3*v**2. Let q(a) be the first derivative of p(a). Factor q(n).
(n + 2)**2/2
Let h(f) be the first derivative of -8 - 1/10*f**5 + 0*f**2 - 1/4*f**4 + 0*f - 1/6*f**3. Solve h(g) = 0.
-1, 0
Solve 4/17 - 2/17*b**3 - 10/17*b + 8/17*b**2 = 0 for b.
1, 2
Let -1/9*q**3 + 5/9*q - 1/9*q**2 - 1/3 = 0. What is q?
-3, 1
Let l(p) be the third derivative of p**6/80 - p**5/20 + p**4/16 + 11*p**2. Suppose l(x) = 0. Calculate x.
0, 1
Let z = 21 + -12. Let x be z/6*24/9. Factor -3*s**2 - x - s**4 - 3*s**3 - s + 4.
-s*(s + 1)**3
Let d be 208/160 - (-16)/(-20). Factor d*v + 1/2*v**4 + 1/2 - v**2 + 1/2*v**5 - v**3.
(v - 1)**2*(v + 1)**3/2
Let a(n) = -21*n**4 + 36*n**3 + 216*n**2 + 132*n + 27. Let i(m) = 3*m**4 - 5*m**3 - 31*m**2 - 19*m - 4. Let t(d) = -4*a(d) - 27*i(d). Factor t(b).
3*b*(b - 5)*(b + 1)**2
Let q(i) be the first derivative of -3/8*i**2 + 4 - 1/2*i - 1/12*i**3. Determine c, given that q(c) = 0.
-2, -1
Let g be 1/(-4)*(-220)/25. Factor 0 + 21/5*j**3 - 17/5*j**4 - g*j**2 + j**5 + 2/5*j.
j*(j - 1)**3*(5*j - 2)/5
Let j be -4 - 0*(1 + 0). Let z be 2 + -2*2/j. Let -3*k**3 - 3*k**3 - 2 + 5*k**z + 3*k = 0. What is k?
-2, 1
Let t(r) = 2*r**2 - 3*r + 1. Let z be ((-33)/(-44))/(6/16). Let i be t(z). Factor 0 + 1/5*u**i - 1/5*u + 0*u**2.
u*(u - 1)*(u + 1)/5
Let c(n) be the second derivative of n**8/672 - n**6/240 - n**2/2 - 2*n. Let i(d) be the first derivative of c(d). Factor i(f).
f**3*(f - 1)*(f + 1)/2
Let x be -51 + 46 + (-62)/(-6). Factor -4*q**2 - 2/3*q**3 - x - 8*q.
-2*(q + 2)**3/3
Let d be (7 - 4)*((-1)/(-1) - 0). Factor 2/7*s**2 + 0*s**d + 0*s - 2/7*s**4 + 0.
-2*s**2*(s - 1)*(s + 1)/7
Let v be 3/3*(-4 + 6). Solve 2/3*h**5 + v*h + 14/3*h**2 + 3*h**4 + 16/3*h**3 + 1/3 = 0 for h.
-1, -1/2
Let j(u) = u. Let m be j(3). Suppose -5*x + m*l - 15 = -0*x, 2*l - 10 = x. Factor 0 - 2/9*q**2 + x*q.
-2*q**2/9
Let l(f) = -f**3 + 4*f**2 + 5*f + 4. Let a be l(5). What is d in 8*d**2 + a*d**3 - 2*d**3 - 3*d**2 - 1 + 2 + 4*d = 0?
-1, -1/2
Suppose 0 = 3*w - 5*w. Suppose w = q, -3*q + 16 = 4*l - 2*q. Factor -2*s**3 + 4*s**2 + 8*s**3 + 2*s**l + 0*s**3.
2*s**2*(s + 1)*(s + 2)
Find i such that -i + 0 + 1/2*i**3 + 1/2*i**2 = 0.
-2, 0, 1
Let -1/2*b + 0 - 3/4*b**2 - 1/4*b**3 = 0. Calculate b.
-2, -1, 0
Let z(x) be the second derivative of -x**4/24 + 3*x**3/4 - 2*x**2 - 9*x - 1. Solve z(s) = 0 for s.
1, 8
Let v(x) = -x**2. Let g(b) = b**2 + 5. Let q(u) = 2*u**2 - u + 14. Let i(f) = 8*g(f) - 3*q(f). Let k(h) = -i(h) - 3*v(h). Factor k(p).
(p - 2)*(p - 1)
Let d(h) be the third derivative of -h**8/1512 - h**7/135 - h**6/30 - 11*h**5/135 - 13*h**4/108 - h**3/9 - 8*h**2. Factor d(s).
-2*(s + 1)**4*(s + 3)/9
Suppose 3*i + 3 + 0 = 0. Let z be (0/(-2))/(2 + i). Factor 10/7*w**2 + 2*w**3 + z - 4/7*w.
2*w*(w + 1)*(7*w - 2)/7
Suppose 0*g + 0 + 0*g**3 + 2/3*g**5 + 4/3*g**4 + 0*g**2 = 0. Calculate g.
-2, 0
Let m be 5/((-15)/(-18)) + 0. Let n be (m/(-15))/(1/(-5)). Find u such that -2/5 + 0*u + 2/5*u**n = 0.
-1, 1
Let j(g) be the third derivative of 1/120*g**5 + 1/24*g**4 + 0*g + 0 + 0*g**3 + 5*g**2 - 1/240*g**6. Find o such that j(o) = 0.
-1, 0, 2
Let m(l) be the first derivative of -4*l**3 - 6*l**2 + 9/4*l**4 + 0*l + 7. Suppose m(v) = 0. Calculate v.
-2/3, 0, 2
Let c = 3 - 5/2. Find w, given that -1/4*w**3 + 0*w + 0 + 1/4*w**2 - c*w**4 = 0.
-1, 0, 1/2
Let k(l) be the first derivative of l**6/45 - l**4/18 + 4*l + 4. Let c(u) be the first derivative of k(u). Suppose c(r) = 0. What is r?
-1, 0, 1
Let j be (-30)/36*(4 + 24/(-5)). Solve 0 + 0*k - 4/9*k**3 - 2/9*k**5 - j*k**4 + 0*k**2 = 0.
-2, -1, 0
Suppose -5 + 3 = -l. Suppose 5*h + 5 = l*n, -h + 7 = 2*n - 4*h. Factor 0*i + 2/7*i**4 - 2/7*i**2 + 2/7*i**n - 2/7*i**3 + 0.
2*i**2*(i - 1)*(i + 1)**2/7
Let p = 10 + 0. Suppose p*a - 10*a**3 - 4 - a**2 - 2*a**4 - a**2 + 6*a**4 + 2*a**4 = 0. What is a?
-1, 2/3, 1
Factor 32 - 69*v**3 + 4*v + 18*v**2 + 44*v + 71*v**3.
2*(v + 1)*(v + 4)**2
Let v(l) be the third derivative of -l**8/1008 + l**6/90 - l**5/90 - l**4/24 + l**3/9 + 16*l**2. Let v(m) = 0. Calculate m.
-2, -1, 1
Let m = 5524/21 + -263. Let s(u) be the first derivative of m*u**6 - 4/21*u**3 + 0*u + 0*u**4 - 1/7*u**2 - 4 + 4/35*u**5. Factor s(a).
2*a*(a - 1)*(a + 1)**3/7
Let z = 35 - 30. Let m(y) be the second derivative of 1/12*y**4 + 1/9*y**3 + 0 + 0*y**2 - 1/12*y**z - 3*y. Factor m(j).
-j*(j - 1)*(5*j + 2)/3
Determine b so that 10*b**2 - 6*b**2 + 17*b**2 - 2*b - 4*b - 6*b**3 - 9*b**4 = 0.
-2, 0, 1/3, 1
Let s = 730 + -728. Let -4/3*q**3 - 28/3*q + 20/3*q**s + 4 = 0. What is q?
1, 3
Suppose 9*r**3 - 20*r - 12*r**4 + 8*r**3 + 4*r**2 + 8 + 3*r**3 = 0. Calculate r.
-1, 2/3, 1
Let b(j) be the third derivative of 0*j**6 + 0 - 7*j**2 + 0*j**5 + 0*j**3 + 0*j**4 + 0*j + 2/105*j**7. Factor b(h).
4*h**4
Let x(b) be the third derivative of -b**7/630 + b**6/120 + b**5/30 + 5*b**4/24 + 6*b**2. Let c(g) be the second derivative of x(g). Factor c(t).
-2*(t - 2)*(2*t + 1)
Suppose p - 1 = 1. Factor -3*l**p + 0*l**3 + 2*l**3 + 0*l**2 + l**2.
2*l**2*(l - 1)
Let u(t) be the second derivative of t**5/40 + t**4/18 - 5*t**3/36 - t**2/6 - 4*t. Suppose u(l) = 0. What is l?
-2, -1/3, 1
Suppose 0 = -2*g + g + 2*z - 8, -3*z + 25 = 5*g. Let m(k) be the first derivative of 3 - 1/8*k**4 + 0*k - 1/3*k**3 - 1/4*k**g. Factor m(q).
-q*(q + 1)**2/2
Let m(s) be the first derivative of -6 + 1/3*s**3 + 2*s**2 + 4*s. Factor m(a).
(a + 2)**2
Let f = 39 + -37. Let n(z) be the first derivative of 2/3*z - 5/6*z**f - 3 + 1/3*z**3. Factor n(a).
(a - 1)*(3*a - 2)/3
Let x = 58 + -55. Suppose 5*o + 5*w + 20 = 0, -4*w - 16 = o - 0. Solve -3/2*g**x + o*g - g**2 + 0 = 0 for g.
-2/3, 0
Factor 8*j**2 + 4*j**5 + 4*j**3 - 4*j - 4*j**3 - 8*j**4.
4*j*(j - 1)**3*(j + 1)
Suppose 5*h = 3*h + 36. Let s be (14/h - 1)*-1. Find c such that 4/9*c + s + 2/9*c**2 = 0.
-1
Let n(j) be the first derivative of -j**7/1260 + j**5/360 + j**2/2 + 2. Let l(d) be the second derivative of n(d). Factor l(f).
-f**2*(f - 1)*(f + 1)/6
Let i = -79/22 - -14/33. Let q = -3 - i. Factor -q*p**2 - 2/3*p - 2/3.
-(p + 2)**2/6
Let p be -4 - 16/11 - 18/(-3). Factor p*q**4 - 2/11*q**2 - 4/11*q + 0 + 8/11*q**3.
2*q*(q + 1)**2*(3*q - 2)/11
Suppose 16 = 5*t + 3*x, 13*x = -4*t + 11*x + 12. Factor 0 - 1/2*w**3 + 1/2*w + 1/2*w**t - 1/2*w**4.
-w*(w - 1)*(w + 1)**2/2
Let y(i) be the third derivative of i**8/40320 - i**7/5040 + i**6/1440 - i**5/60 - i**2. Let d(p) be the third derivative of y(p). What is l in d(l) = 0?
1
Let o(u) be the second derivative of -u**6/40 - u**5/5 - 5*u**4/8 - u**3 - u**2 + 5*u. Let t(l) be the first derivative of o(l). Factor t(q).
-3*(q + 1)**2*(q + 2)
Factor 8*i + 5*i + 5*i**2 + 2*i - 20.
5*(i - 1)*(i + 4)
Let s(u) = -1. Let c(i) = 5*i**5 + 5*i**4 - 15*i**3 - 25*i**2 - 10*i + 3. Let r(w) = c(w) + 3*s(w). Determine z so that r(z) = 0.
-1, 0, 2
Let w(q) = -q**3 + 2*q**2 + 5*q - 2. Let z be w(3). Suppose c = -2*t + 2 + z, -2*t - 6 = 4*c. Factor 1/2*x - x**2 + 0*x**3 - 1/2*x**t + 0 + x**4.
-x*(x - 1)**3*(x + 1)/2
Factor 2/5*j - 4/5*j**2 + 0*j**3 + 4/5*j**4 - 2/5*j**5 + 0.
-2*j*(j - 1)**3*(j + 1)/5
Solve -4/7*d**2 + 4/7*d**4 + 0 + 4/7*d - 4/7*d**3 = 0 for d.
-1, 0, 1
Let u = 1516 + -12113/8. Solve 3/2*f**3 + 0*f**2 + 0 - 3*f**4 - u*f**5 + 0*f = 0 for f.
-2, 0, 2/5
Factor -2/3*p**2 + 2/3 + 0*p.
-2*(p - 1)