0)/((-2)/10). Let t(l) be the first derivative of d + 1/8*l**2 - 1/2*l + 1/12*l**3. Find v, given that t(v) = 0.
-2, 1
Suppose -1/3*j**3 - 1/3*j**4 + 0 + 0*j + 1/3*j**2 + 1/3*j**5 = 0. Calculate j.
-1, 0, 1
Let v(k) = -23*k**3 - 31*k**2 + 37*k + 17. Let q(a) = 4*a**3 + 5*a**2 - 6*a - 3. Let m(x) = -34*q(x) - 6*v(x). Factor m(p).
2*p*(p - 1)*(p + 9)
Let b(x) be the first derivative of -x**5/10 - x**4/3 + x**3/3 + 2*x**2 + 3*x + 1. Let m(s) be the first derivative of b(s). Factor m(y).
-2*(y - 1)*(y + 1)*(y + 2)
Let d = 611/2 - 305. Factor 3/4*a**4 + 0 + 9/4*a**2 + d*a + 5/2*a**3.
a*(a + 1)*(a + 2)*(3*a + 1)/4
Let a(f) be the third derivative of f**5/75 - 2*f**4/15 + 8*f**3/15 + 17*f**2. What is i in a(i) = 0?
2
Let i(h) be the third derivative of -h**7/140 + h**6/80 + 3*h**5/40 - h**4/16 - h**3/2 + 10*h**2. Let i(k) = 0. Calculate k.
-1, 1, 2
Let k(l) be the third derivative of l**7/1680 - l**6/480 - l**5/480 + l**4/96 - 8*l**2. Factor k(p).
p*(p - 2)*(p - 1)*(p + 1)/8
Let d be (2/12)/((-2)/(-4)). Factor 0*n + 1/3*n**3 - d*n**2 + 0.
n**2*(n - 1)/3
Let h(u) be the third derivative of -u**6/1620 - u**5/540 + u**3/2 - 3*u**2. Let f(l) be the first derivative of h(l). Factor f(d).
-2*d*(d + 1)/9
Factor -6/5*b + 1 + 1/5*b**2.
(b - 5)*(b - 1)/5
Let l(t) = -11*t**4 + 19*t**3 - 15*t**2 + 2*t - 5. Let k(n) = -34*n**4 + 58*n**3 - 46*n**2 + 6*n - 16. Let a(r) = -5*k(r) + 16*l(r). Factor a(w).
-2*w*(w - 1)**2*(3*w - 1)
Factor -12*g**2 + 7*g + 4*g**3 + 5*g**3 - 19*g.
3*g*(g - 2)*(3*g + 2)
Suppose -4*l - 11 = -5*x, 3*x - 12 = 7*l - 4*l. Let f be ((-7)/(-42))/((-6)/l). Factor f*i**2 + 0*i - 1/4.
(i - 1)*(i + 1)/4
Let f(x) = -x**5 + x**4 + x**2 - x - 1. Let p(o) = 8*o**5 - 4*o**4 - 12*o**3 - 12*o**2 + 4*o + 4. Let i(n) = 4*f(n) + p(n). Factor i(u).
4*u**2*(u - 2)*(u + 1)**2
Find q, given that 1/5*q**2 - 2*q + 5 = 0.
5
Suppose 25 = 5*n - 0*n. Let g(l) be the second derivative of l + 1/10*l**4 + 1/50*l**n + 0*l**3 - 4/5*l**2 + 0. Factor g(d).
2*(d - 1)*(d + 2)**2/5
Let w(s) be the second derivative of 0*s**3 + 0*s**2 - 3*s + 0 - 2/75*s**6 - 1/105*s**7 + 0*s**4 - 1/50*s**5. Factor w(x).
-2*x**3*(x + 1)**2/5
Factor 16/7 + 12/7*i**2 - 24/7*i - 2/7*i**3.
-2*(i - 2)**3/7
Let w(y) be the third derivative of 0*y + 10*y**2 - 1/30*y**6 + 0*y**5 + 0 + 1/168*y**8 + 0*y**7 + 1/12*y**4 + 0*y**3. Factor w(p).
2*p*(p - 1)**2*(p + 1)**2
Let p be 2/8 + 205/(-20). Let u = p - -10. Find o, given that -1/4*o**3 + u + 0*o**2 + 1/4*o = 0.
-1, 0, 1
Let c(s) be the first derivative of 1/8*s**4 + 2 - 1/6*s**3 + 1/2*s - 1/4*s**2. Suppose c(q) = 0. What is q?
-1, 1
Let j(x) be the second derivative of -x**6/15 - x**5/10 + x**4/2 + x**3/3 - 2*x**2 + 14*x. Determine l so that j(l) = 0.
-2, -1, 1
Factor -4/3*o**3 + 36 + 12*o**2 - 36*o.
-4*(o - 3)**3/3
Solve 0*r - 2/11*r**4 + 0 + 0*r**2 + 0*r**3 = 0.
0
Let s(g) be the first derivative of -4*g + 0*g**2 + 1/3*g**3 - 4 - 1/12*g**4. Let b(o) be the first derivative of s(o). Let b(p) = 0. Calculate p.
0, 2
Let c = -1300 - -1300. Factor -2/11*q**2 + c*q + 8/11.
-2*(q - 2)*(q + 2)/11
Let f be 5/6*36/20. Factor -3*g + f + 3/2*g**2.
3*(g - 1)**2/2
Suppose -3 = -n - 3*c + 7*c, 3*n - 2*c - 9 = 0. Solve -7/4*m**5 + 7/4*m**n + 1/2*m**4 + 0*m - 1/2*m**2 + 0 = 0.
-1, 0, 2/7, 1
Let t(n) be the second derivative of -2*n**6/15 + 9*n**5/5 - 14*n**4/3 + 16*n. Solve t(m) = 0.
0, 2, 7
Let r = 18 + -14. Let n(t) = t**2 - 6*t + 1. Let c(a) = -6*a**2 + 30*a - 6. Let o(z) = r*c(z) + 21*n(z). Determine j so that o(j) = 0.
-1
Suppose -j**2 + 2*j**2 - 5*j + j**2 - 4 - 3*j**2 = 0. Calculate j.
-4, -1
Let b be (-1)/2*8/(-10). Suppose v - 2*i + 2 = 0, -2*v + 4*i - 2 = i. Suppose 2/5*r**v + b*r - 4/5 = 0. What is r?
-2, 1
Find k such that 8/9*k**3 - 14/9*k**2 + 4/9*k + 2/9 = 0.
-1/4, 1
Let z be 36/90 - (-18)/5. Let q(t) be the first derivative of -3 + 0*t + 1/2*t**z - 2/3*t**3 + 0*t**2 - 1/3*t**6 + 2/5*t**5. Factor q(i).
-2*i**2*(i - 1)**2*(i + 1)
Let a = 14/29 - -18/203. Let u be (0 + 0)/(-3 + 1). Find h such that 2/7*h**5 + 4/7*h**4 - a*h**2 + u*h**3 + 0 - 2/7*h = 0.
-1, 0, 1
Suppose -4*t = 20 - 44. Let 1 - 1 - t*j**4 + 4*j**4 - j**5 = 0. What is j?
-2, 0
Let h(s) be the third derivative of -s**8/84 + s**6/30 - s**5/10 - s**4/4 + 3*s**2. Let g(p) = p**5 - p**3 + p**2 + p. Let f(v) = 6*g(v) + h(v). Factor f(d).
2*d**3*(d - 1)*(d + 1)
Let b be (3 - (-6)/8) + 0 + -3. Find m, given that -1/4 + b*m - 3/4*m**2 + 1/4*m**3 = 0.
1
Suppose 0 = -2*a - 3 - 1. Let s be 8/2 + 0/a. Suppose -1/3*c**s + 0*c + 1/3*c**2 + 0 + 0*c**3 = 0. What is c?
-1, 0, 1
Factor 5*i**2 + 3*i**4 + 35*i**2 - 25*i**3 - 20*i + 2*i**4.
5*i*(i - 2)**2*(i - 1)
Let d be 1/(-2) - 13/(-18). Suppose -4 = 3*v - 5*i, -5*i = 2*v - 3*i - 8. Factor -d*n**v + 0 + 2/9*n.
-2*n*(n - 1)/9
Let h(k) be the third derivative of k**5/30 + k**4/3 + k**3 - 15*k**2. Determine l so that h(l) = 0.
-3, -1
Suppose 16 = -u + 5*u. Factor -u*z**5 - 1/4 + 5/4*z**2 - 10*z**4 + 5/4*z - 25/4*z**3.
-(z + 1)**3*(4*z - 1)**2/4
Factor 0*d - 14/9*d**3 + 0 + 2/3*d**4 + 4/9*d**2.
2*d**2*(d - 2)*(3*d - 1)/9
Let u(g) = 9*g**3 - 13*g**2 - 9*g. Suppose -3*a = -4*a + 2. Let t(i) = 3*i**a - 2*i - 2*i**3 + 6*i - 2*i. Let z(k) = -26*t(k) - 6*u(k). Factor z(o).
-2*o*(o - 1)*(o + 1)
Let x(l) be the first derivative of l**4/9 - 2*l**3/9 - l**2/3 + 4*l/9 - 34. Suppose x(d) = 0. What is d?
-1, 1/2, 2
Let p(y) = -y**2 - y - 1. Suppose u - 2 = 4*i - 3, -2*i + 2*u + 8 = 0. Let n(b) = 2*b**3 - 2*b**2 - 8*b - 4. Let j(a) = i*n(a) + 4*p(a). What is l in j(l) = 0?
-2, 0, 1
Let f = 23 - 22. Let n be 42/(-15) + 4*f. Factor -n - 27/5*q**2 - 33/5*q.
-3*(q + 1)*(9*q + 2)/5
Let z(a) be the second derivative of -a**7/42 - a**6/30 + a**5/20 + a**4/12 - 5*a. Factor z(m).
-m**2*(m - 1)*(m + 1)**2
Let q(g) be the second derivative of -g**5/50 - g**4/15 - g**3/15 - 8*g. Factor q(a).
-2*a*(a + 1)**2/5
Factor 5*h**2 - 3*h**2 + 2*h + 0*h.
2*h*(h + 1)
Let o be (-10)/28*(-22)/(-1). Let m = 57/7 + o. Solve 0 + m*b**2 - 2/7*b = 0.
0, 1
Factor -4/19*o**3 + 2/19*o**4 + 2/19*o**5 - 4/19*o**2 + 2/19*o + 2/19.
2*(o - 1)**2*(o + 1)**3/19
Let v(b) be the first derivative of b**4/26 - 4*b**3/39 - b**2/13 + 4*b/13 + 3. Factor v(d).
2*(d - 2)*(d - 1)*(d + 1)/13
Let q(t) be the second derivative of 3*t**5/20 + t**4/4 - 5*t**2/2 + 7*t. Let d(y) be the first derivative of q(y). Factor d(f).
3*f*(3*f + 2)
Let -1/3*m**4 + 1/3*m**3 + m**2 - 5/3*m + 2/3 = 0. Calculate m.
-2, 1
Let n(r) = 11 - 7*r**2 + 6*r**2 + 2*r - 3*r. Let h = -7 + 5. Let o(a) = -1. Let z(v) = h*n(v) - 22*o(v). Factor z(q).
2*q*(q + 1)
Let i(v) be the second derivative of -1/6*v**4 + 0 + 2*v**2 - 1/3*v**3 - 3*v. Factor i(f).
-2*(f - 1)*(f + 2)
Let i(p) be the second derivative of -25*p**4/12 + 35*p**3/3 - 49*p**2/2 - p. Factor i(j).
-(5*j - 7)**2
Factor -2*w - 2*w + 2 + 4*w**2 + 9*w + w**3.
(w + 1)**2*(w + 2)
Let d(q) be the second derivative of -5*q**4/48 + 5*q**2/8 + 10*q. Factor d(z).
-5*(z - 1)*(z + 1)/4
Let d = 139/3 + -46. Let x(l) be the first derivative of -d*l**3 + 0*l**2 - 2 + l. Factor x(c).
-(c - 1)*(c + 1)
What is y in 4/3*y**5 + 0 - 8/3*y**3 + 4/3*y**4 + 0*y**2 + 0*y = 0?
-2, 0, 1
Factor -4*b**2 + 4*b + 0*b**2 + 16*b.
-4*b*(b - 5)
Suppose -3*d - 23 + 5 = 0. Let c(a) = a**3 + 6*a**2 + a + 8. Let g be c(d). What is u in 3*u**g + 1 - 3*u + 2*u**3 + 6*u - u**3 = 0?
-1
Let z(i) be the first derivative of -i**4/28 - i**3/21 + i**2/7 + 17. Determine x, given that z(x) = 0.
-2, 0, 1
Let n be 6/21 + (-2 - 150/(-63)). Solve 3*a - 3*a**3 - n + 7/3*a**4 - 5/3*a**2 = 0.
-1, 2/7, 1
Suppose 4*v - 21 + 1 = 0. Let z be 1/2 - (-3)/2. Solve -2/3*f + 44/3*f**3 - 28/3*f**4 + z*f**v + 4/3 - 8*f**2 = 0.
-1/3, 1, 2
Let i(u) be the first derivative of -4*u**3/15 + 14*u**2/5 + 1. Factor i(a).
-4*a*(a - 7)/5
Determine u, given that 0 - 1/3*u - 1/3*u**2 = 0.
-1, 0
Let j(v) be the third derivative of v**7/840 + v**6/120 + v**5/48 + v**4/48 + v**2 - 6*v. Let j(u) = 0. Calculate u.
-2, -1, 0
Let d(z) = -2*z**2 - 6*z - 5. Let l be d(-4). Let k = -11 - l. Factor 2/5 + 16/5*s**2 + k*s + 8/5*s**3.
2*(s + 1)*(2*s + 1)**2/5
Let d(l) be the second derivative of -l**6/30 + l**5/20 + l**4/12 - l**3/6 - l. Factor d(o).
-o*(o - 1)**2*(o + 1)
Let h be (10/(-30))/(0 + (-2)/18). Solve 9/2*s**2 + 7/4*s**h + 2 + 5*s + 1/4*s**4 = 0 for s.
-2, -1
Suppose m = v + 3*v +