4 + 8*i**3/27 + 16*i**2/9 - 11*i. Let r(b) = 0. Calculate b.
-4
Let x(l) be the first derivative of -2/3*l**3 + 3 + 0*l**2 + 2*l. Factor x(t).
-2*(t - 1)*(t + 1)
Suppose 5*u + 6 - 21 = 0. Factor 2/3*a**4 + 0*a**u - 2/3*a**2 + 0 - 1/3*a + 1/3*a**5.
a*(a - 1)*(a + 1)**3/3
Let o(r) be the third derivative of 0*r**3 + 0*r - 1/30*r**5 + 0 - 1/4*r**4 - 5*r**2. Suppose o(m) = 0. What is m?
-3, 0
Let l(y) = 11*y**3 - 12*y**2 + 20*y + 8. Let j(p) = 4*p**3 - 4*p**2 + 7*p + 3. Let i(s) = 8*j(s) - 3*l(s). Let i(w) = 0. What is w?
0, 2
Let y(n) be the first derivative of -2/5*n**5 - 1/2*n**4 + 0*n + 0*n**2 + 2/3*n**3 + 8 + 1/3*n**6. Find f such that y(f) = 0.
-1, 0, 1
Let b = 2/405 - -133/405. Let t(h) = -h + 5. Let y be t(5). Factor -b*a**2 + 2/3*a + y.
-a*(a - 2)/3
Suppose 5*w = 183 - 168. Determine j, given that 1/2*j + 3/4*j**w + 1/4*j**4 - 5/4*j**2 + 0 - 1/4*j**5 = 0.
-2, 0, 1
Let x(v) be the first derivative of -v**4/16 + v**3/4 - v - 17. Factor x(p).
-(p - 2)**2*(p + 1)/4
Let g be 2 - (0 - 186/(-96)). Let x(q) be the first derivative of -3 + 0*q - 1/20*q**5 + 1/12*q**3 + g*q**4 - 1/8*q**2. Factor x(z).
-z*(z - 1)**2*(z + 1)/4
Suppose 0 = h + 3*h - 108. Let j be (1 - 4) + 117/h. Factor -j - 2/3*u**2 - 2*u.
-2*(u + 1)*(u + 2)/3
Suppose -b + 4 = b. Let a(n) = n**3 - 3*n**2 + 3*n. Let d be a(b). Solve 0 - 2/7*x**3 - 2/7*x**d + 2/7*x + 2/7*x**4 = 0 for x.
-1, 0, 1
Suppose -3*i - 3*s = 0, i + s - 3*s - 3 = 0. Let p be i/(-6)*-3 + 0. Let 0 + p*o**2 - 1/4*o + o**3 - 1/2*o**4 - 3/4*o**5 = 0. What is o?
-1, 0, 1/3, 1
Factor 7 - 4*q**2 + 2*q**4 - 14 + 9.
2*(q - 1)**2*(q + 1)**2
Let p be (12/126)/((-2)/(-6)). Let c(w) be the second derivative of 5/21*w**3 - 2*w + 0 - p*w**2 - 1/14*w**4. Factor c(y).
-2*(y - 1)*(3*y - 2)/7
Let y(g) be the first derivative of -1/3*g**6 + 2*g + 3*g**2 - 6/5*g**5 - g**4 + 3 + 4/3*g**3. Determine j so that y(j) = 0.
-1, 1
Let j(i) be the third derivative of -1/105*i**7 + 0 - 1/12*i**4 - i**2 + 1/504*i**8 + 1/90*i**6 + 1/9*i**3 + 0*i + 1/45*i**5. Factor j(h).
2*(h - 1)**4*(h + 1)/3
Let d(p) = -4*p**2 - 2*p. Let c(z) = -z**3 + 3*z**2 - 3*z. Let s be c(2). Let o(v) = -3*v**2 - v. Let a(u) = s*d(u) + 3*o(u). Determine n so that a(n) = 0.
0, 1
Let b(r) be the second derivative of -55/12*r**3 - 7*r + 0 - 5/2*r**2 - 15/8*r**4. Factor b(y).
-5*(y + 1)*(9*y + 2)/2
Factor 9*g**4 - 24*g**2 - 102*g - 12*g**3 + 86*g - 11*g**4.
-2*g*(g + 2)**3
Let p(r) be the first derivative of -9*r**5/10 + 15*r**4/4 - 37*r**3/6 + 5*r**2 - 2*r - 12. Factor p(l).
-(l - 1)**2*(3*l - 2)**2/2
Let l(j) be the first derivative of 3*j**5/20 - j**4/6 - j**3/6 - 4*j - 2. Let n(q) be the first derivative of l(q). Factor n(k).
k*(k - 1)*(3*k + 1)
Suppose c + t = 4, -5*c - 3*t + 1 = -17. Let w(j) be the second derivative of 0 + 7/27*j**c - 1/18*j**4 - 2/9*j**2 + 3*j. Determine h, given that w(h) = 0.
1/3, 2
Let r be 1*(4 + -3 + 2). Let s(b) be the second derivative of 0*b**r - 7/120*b**6 + 0*b**2 - 2*b + 1/24*b**4 + 0 + 1/16*b**5. Find i such that s(i) = 0.
-2/7, 0, 1
Let 0 - 1/4*g**3 + 5/8*g**4 + 0*g + 0*g**2 = 0. Calculate g.
0, 2/5
Let u(a) be the second derivative of -a**2 - 1/60*a**5 + 0 - 1/24*a**4 - 2*a + 1/3*a**3. Let m(v) be the first derivative of u(v). Let m(j) = 0. What is j?
-2, 1
Let c(o) = 6*o**2 + 16*o. Let h(q) = -6*q + q + 0*q - 2*q**2. Suppose 4*m + 14 - 54 = 0. Let k(f) = m*h(f) + 3*c(f). Factor k(l).
-2*l*(l + 1)
Let t be (-1 - -4) + -10 + 11. Solve 5*b**3 + 9*b**t + 4*b**5 + b**2 + 6*b**3 - 5*b**3 = 0 for b.
-1, -1/4, 0
Let v(g) be the first derivative of -1/30*g**4 + 2/5*g**2 - 2*g + 2 - 1/15*g**3. Let u(f) be the first derivative of v(f). Factor u(q).
-2*(q - 1)*(q + 2)/5
Let s(x) be the first derivative of -9*x**4/4 - 5*x**3/3 + 2*x**2 - 2*x - 1. Let q(l) = -l**3 + l - 1. Let g(r) = 2*q(r) - s(r). Factor g(i).
i*(i + 1)*(7*i - 2)
Factor -3/4*w - 1/4*w**3 + 1/4 + 3/4*w**2.
-(w - 1)**3/4
What is m in -32/3*m - 4/3*m**3 + 20/3*m**2 + 16/3 = 0?
1, 2
Factor 0*c + 4/9*c**2 - 2/9*c**3 + 0.
-2*c**2*(c - 2)/9
Let c(y) be the second derivative of -3*y**6/70 + 3*y**5/28 + y**4/2 - 10*y**3/7 - 12*y**2/7 - 5*y. Determine b, given that c(b) = 0.
-2, -1/3, 2
Let b(t) = -3*t - 9. Let n be b(-3). Let k(u) be the second derivative of 0*u**2 - 1/9*u**3 - u + n + 1/18*u**4. Factor k(r).
2*r*(r - 1)/3
Determine h so that 4/11*h - 10/11*h**4 + 0 - 14/11*h**2 + 18/11*h**3 + 2/11*h**5 = 0.
0, 1, 2
Let x = -10 - -17. Suppose x = 2*r - 3. Suppose -2*s**4 + 6*s - 2 + 0*s + 8*s**r - 4*s + 6*s - 16*s**3 + 4*s**2 = 0. What is s?
-1, 1/4, 1
Let i(p) = -3*p**5 + 6*p**4 + 9*p**3 - 6*p**2 - 6*p. Let b(y) = -2*y**5 + 7*y**4 + 9*y**3 - 7*y**2 - 7*y. Let d(t) = 6*b(t) - 5*i(t). Factor d(h).
3*h*(h - 1)*(h + 1)*(h + 2)**2
Let l(x) = -12*x. Let o be l(-1). Let 2*c**5 + 5*c**5 + 7*c**2 - o*c**4 + 8*c**3 - 7*c**4 - 3*c**2 = 0. Calculate c.
-2/7, 0, 1, 2
Let c(y) be the first derivative of 4/3*y**4 + 2 + 2/5*y**5 - 2/3*y + 4/3*y**3 + 0*y**2. Factor c(w).
2*(w + 1)**3*(3*w - 1)/3
Let l = 2 + 0. Find p such that 2*p - l*p**3 + 15*p**2 - 9*p**2 - 2*p**4 - 4*p**2 = 0.
-1, 0, 1
Let d(v) be the first derivative of v**9/1008 - v**8/840 + v**7/2520 - 2*v**3/3 - 2. Let h(n) be the third derivative of d(n). Solve h(l) = 0 for l.
0, 1/3
Let p(m) be the third derivative of -3/80*m**5 - 4*m**2 - 1/8*m**3 + 5/48*m**4 + 0 + 1/240*m**6 + 0*m. Determine k, given that p(k) = 0.
1/2, 1, 3
Let k = -68 + 68. Let x(d) be the third derivative of 4*d**2 + k + 0*d**3 + 0*d + 1/270*d**5 + 0*d**4 - 1/540*d**6. Factor x(l).
-2*l**2*(l - 1)/9
Let n be (-1)/6 + 16515/(-30). Let l = -544 - n. Factor -l*b**3 + 10/3*b**4 + 20/3*b**2 + 2/3 - 2/3*b**5 - 10/3*b.
-2*(b - 1)**5/3
Let h(y) be the second derivative of -y**4/6 + y**3/3 + 2*y. Suppose h(n) = 0. Calculate n.
0, 1
Factor -4/3*l**2 + 1/3*l**4 + 1 - 2/3*l + 2/3*l**3.
(l - 1)**2*(l + 1)*(l + 3)/3
Let d(u) = -u**3 - 6. Let q be d(-2). Factor -2/9*r + 2/9*r**q - 4/9.
2*(r - 2)*(r + 1)/9
Let j be 2 + (8/5 - 2). Suppose -15 = -5*y + 3*u, -35*y - 2*u = -32*y - 9. What is k in 8/5*k**y + 8*k - j - 34/5*k**2 = 0?
1/4, 2
Let k(j) be the first derivative of -5*j**3/6 - 9*j**2/2 + 4*j - 10. Suppose k(t) = 0. What is t?
-4, 2/5
Let s(d) be the third derivative of 1/8*d**4 - 2*d**2 + 0*d**3 + 0*d + 3/10*d**5 + 0. Factor s(b).
3*b*(6*b + 1)
Let d(a) be the third derivative of 1/420*a**7 + 0*a**6 + 0*a + 0 - 4*a**2 - 1/672*a**8 + 0*a**4 + 0*a**5 + 0*a**3. Solve d(f) = 0.
0, 1
Let -4/3*x**2 + 4/3*x + 8/3 = 0. Calculate x.
-1, 2
Let j(f) be the first derivative of 8/15*f**5 + 0*f**2 + 1/6*f**4 + 0*f + 4/9*f**6 + 0*f**3 + 2. Factor j(o).
2*o**3*(2*o + 1)**2/3
Let a = -31/4 - -8. Let g(u) be the second derivative of u**2 + 0 + u - 7/6*u**3 + a*u**4. Factor g(v).
(v - 2)*(3*v - 1)
Let a(t) = -t**2 - 2*t + 5. Let j be a(5). Let h be ((-3)/(-10))/(j/(-25)). Factor 0 - 1/4*s + h*s**2.
s*(s - 1)/4
Let j(m) = m**2 + 46*m - 44. Let x be j(-47). Factor 6/5*p**x - 8/5*p + 0 + 0*p**2 - 2/5*p**4.
-2*p*(p - 2)**2*(p + 1)/5
Suppose l + 5*w - 125 = 0, -5*l + 2*l = 2*w - 336. What is v in -110 - 18*v**2 + l - 3*v**3 - 27*v = 0?
-3, 0
Let b be 3 + 1*42/2. Let -27*j**2 + b*j**2 + 0*j**3 + 6*j**3 - 3*j**4 = 0. What is j?
0, 1
Suppose -5*b + 3 + 17 = 0. Factor 12*n**b - 28*n**2 - 22*n**3 + 6*n + 6*n - 7*n**3 + n**3.
4*n*(n - 3)*(n + 1)*(3*n - 1)
Let u(r) be the second derivative of 0*r**2 - 1/6*r**3 + 1/24*r**4 + 3/40*r**5 + 0 + 6*r. Factor u(v).
v*(v + 1)*(3*v - 2)/2
Suppose 20 = 11*m - 6*m. Factor 2/15*d + 0 + 2/15*d**5 + 0*d**m + 0*d**2 - 4/15*d**3.
2*d*(d - 1)**2*(d + 1)**2/15
Suppose 6 = -0*j + 2*j. What is o in 3/4*o**2 + 1/4 - 9/4*o**j + 5/4*o = 0?
-1/3, 1
Suppose -7*l = -5*l. Let n(d) be the third derivative of 0*d + 0*d**3 + d**2 + l - 1/30*d**6 + 0*d**4 + 1/60*d**5. Let n(t) = 0. Calculate t.
0, 1/4
Suppose 4*r = -5*h + 2*h + 28, 0 = r - h. Determine f so that 1 + f + 8*f**3 - 9*f + 1 - 6*f**4 + r*f**2 = 0.
-1, 1/3, 1
Let p(s) be the second derivative of -s**7/21 + 2*s**6/15 - s**4/3 + s**3/3 - 6*s. Factor p(c).
-2*c*(c - 1)**3*(c + 1)
Let c(o) be the second derivative of -1/9*o**3 + 0*o**2 + 2*o + 0 + 1/9*o**4. Solve c(r) = 0 for r.
0, 1/2
Let y**2 + 3*y**3 + 0*y**3 - y**3 - 3*y**3 = 0. Calculate y.
0, 1
Let a be 6/(-25)*620/(-6). Let l = 25 - a. Solve 0 - 1/5*p**4 + 1/5*p**2 + 1/5*p - l*p*