4*m - 12. Let g be c(13). Suppose -g = -y - 2*y + 5*u, -2*u = 4*y - 10. Factor 4*f + 2*f**4 + 15*f**y - 10*f**4 + 2*f**3 + 3*f**4 - 5 + 1.
-(f - 2)*(f + 1)**2*(5*f - 2)
Let j(z) = z**3 - z**2 - z - 2. Let c(b) = -b**4 + b**3 - 9*b**2 - b - 8. Let q(l) = c(l) - 6*j(l). Solve q(y) = 0 for y.
-4, -1, 1
Let z(c) be the first derivative of -23/7*c**4 - 26/7*c**2 + 36/7*c**3 + 4/5*c**5 + 6 + 8/7*c. Find g such that z(g) = 0.
2/7, 1
Let j(w) be the second derivative of -w**6/285 + w**5/95 + w**4/38 - 22*w. Factor j(g).
-2*g**2*(g - 3)*(g + 1)/19
Let v(u) be the third derivative of u**7/525 - u**6/60 - u**5/50 + 17*u**4/60 - 2*u**3/3 - 14*u**2 - u. Let v(q) = 0. Calculate q.
-2, 1, 5
Suppose -4*t - 3*p + 28 = -0*p, 2*t + 5*p = 28. Factor 14 + 13 + 2*a + t*a**2 - 27.
2*a*(2*a + 1)
Let f(a) = -45*a**4 - 8370*a**3 - 518905*a**2 - 10724725*a. Let q(k) = -5*k**4 - 930*k**3 - 57656*k**2 - 1191636*k. Let h(y) = -4*f(y) + 35*q(y). Factor h(j).
5*j*(j + 62)**3
Let x be 44356/2016 + -12 - 10. Let h(t) be the third derivative of 0 + 0*t**3 + 0*t - x*t**8 - 1/180*t**6 + 0*t**5 + 2*t**2 + 2/315*t**7 + 0*t**4. Factor h(z).
-2*z**3*(z - 1)**2/3
Let q be (-32)/36*12/8. Let s = 88/21 + q. Factor 4*k - 8/7 - s*k**2.
-4*(k - 1)*(5*k - 2)/7
Let a = -32280 + 32282. Factor 3/5*d**a - 3/5*d + 0.
3*d*(d - 1)/5
Let a = 1011 + -40439/40. Let v(o) be the second derivative of -1/6*o**2 + 0 + 1/72*o**4 - a*o**5 + 1/180*o**6 - 5*o + 1/12*o**3. Find r, given that v(r) = 0.
-1, 1, 2
Suppose t - 2 = o, 0 = -t - t - o + 7. Let m be ((-12)/9)/((-10)/15). Factor 11*u**t + 3*u**2 - 2*u - 9*u**3 - 2 - u**m.
2*(u - 1)*(u + 1)**2
Let d = -20 + 22. Suppose -5*o + 27 = 4*y - 7*y, -5*y - 29 = -3*o. Determine c so that -3*c**d + 3*c**3 - 4*c**4 + 7*c**4 - c**4 - o*c**5 + c**4 = 0.
-1, 0, 1
Let s(z) = 35*z**3 - 35*z**2 - 10*z + 10. Suppose 4*n - 9*n = -125. Let f(x) = -x**2 + x. Let h(y) = n*f(y) + s(y). Factor h(l).
5*(l - 1)**2*(7*l + 2)
Let x(h) be the second derivative of h**9/7560 + h**8/420 + h**7/60 + h**6/20 - h**4/2 + 14*h. Let m(v) be the third derivative of x(v). Factor m(u).
2*u*(u + 2)*(u + 3)**2
Let r(s) be the second derivative of s**6/150 + 2*s**5/25 + s**4/4 - 4*s**3/15 - 8*s**2/5 + 89*s. Factor r(x).
(x - 1)*(x + 1)*(x + 4)**2/5
Let l(w) = 17*w**3 - 87*w**2 + 114*w - 44. Let k(z) = -z**3 + z**2. Let r(q) = -22*k(q) - 2*l(q). Suppose r(f) = 0. Calculate f.
2/3, 1, 11
Let k(j) = j**2 - 5*j - 9. Let r be k(6). Let f be (r - -2)/(1/(-5)). Factor -2*n**3 + 6*n**f - 5*n**2 - 8*n**4 - 5*n**2 + 14*n**2.
2*n**2*(n - 1)**2*(3*n + 2)
Suppose -5*r - 16 = -4*l, -5*r = 3*l - 39 + 27. Let p(s) be the first derivative of s**4 + 4/5*s**5 - 4 + 0*s + r*s**2 + 0*s**3. Factor p(h).
4*h**3*(h + 1)
Let y be 2/27*-4*(-45)/60. Let t(u) be the second derivative of 0 + 0*u**2 - 1/18*u**4 + 5*u - y*u**3. Find q such that t(q) = 0.
-2, 0
Let z be 1468/7 - 0 - 168/(-588). Let u = -210 + z. Factor -1/2*p**2 + u + 0*p.
-p**2/2
Let i(r) be the second derivative of -r + 0*r**4 + 3/20*r**5 + 0*r**3 + 1/14*r**7 + 0 - 1/5*r**6 + 0*r**2. Factor i(o).
3*o**3*(o - 1)**2
Let a(r) be the second derivative of -r**6/40 - 3*r**5/80 + r**4/8 - 228*r. Suppose a(d) = 0. Calculate d.
-2, 0, 1
Let b(r) be the first derivative of 2/9*r**3 + 0*r**2 + 11 + 9*r - 1/9*r**4. Let u(z) be the first derivative of b(z). Factor u(t).
-4*t*(t - 1)/3
Let -98/15*x**2 - 4/15*x**3 + 8/5 + 14/15*x**4 - 56/15*x = 0. What is x?
-2, -1, 2/7, 3
Let r(y) be the third derivative of -y**6/320 - y**5/40 - y**4/16 - 2*y**2 + 178*y. Factor r(x).
-3*x*(x + 2)**2/8
Suppose 3*n = -21, -3*l + 26 + 6 = -2*n. Find a such that 21/4*a - 3/2 + 9/4*a**3 - l*a**2 = 0.
2/3, 1
Let y(u) be the second derivative of -u**7/1260 - u**6/675 + u**5/900 + 2*u**3 - 20*u. Let m(c) be the second derivative of y(c). Factor m(l).
-2*l*(l + 1)*(5*l - 1)/15
Let n(b) be the second derivative of b**7/780 - b**6/1170 - 7*b**5/780 + b**4/78 + 11*b**3/6 - 13*b. Let i(w) be the second derivative of n(w). Factor i(g).
2*(g - 1)*(g + 1)*(7*g - 2)/13
Let k(g) = -g**3 - 10*g**2 - 4*g + 45. Let u be k(-9). What is n in 4/5*n - 2*n**2 + u = 0?
0, 2/5
Let b(f) be the second derivative of f**4/22 + 14*f**3/11 + 34*f - 5. Factor b(a).
6*a*(a + 14)/11
Let a(x) = -53*x - 3*x**2 + 65*x - x**3 + 11*x**2 - 27. Let v be a(9). Factor v*t + 2/3*t**2 - 2/3.
2*(t - 1)*(t + 1)/3
Suppose -2*f + f = -u + 29, 3*f = u - 87. Let l be (-32)/80*(-1 + f). Factor 7*c**4 - 9*c**4 + 12*c**4 - 50*c + 5*c**3 - 54*c**2 - l - 11*c**3.
2*(c - 3)*(c + 1)**2*(5*c + 2)
Suppose 4*k - 5*k = 2*w - 8, -2*w - 4*k + 2 = 0. Let i(r) = r**2 - 2*r. Let f(o) = -30*o**2 + 50*o + 20. Let a(g) = w*i(g) - f(g). Factor a(l).
5*(l - 2)*(7*l + 2)
Let a be (-11 + 8 - -11)/2. Let p(j) be the third derivative of 5*j**2 + 0*j - 2/3*j**3 + 7/12*j**a + 0 + 1/12*j**6 - 3/10*j**5 - 1/105*j**7. Factor p(m).
-2*(m - 2)*(m - 1)**3
Let w(s) = 147*s + 887. Let h be w(-6). Let r(x) be the third derivative of 0*x + 2/3*x**3 + 11/12*x**4 - h*x**2 + 0 + 3/10*x**5. Solve r(i) = 0 for i.
-1, -2/9
Suppose 0 = 16*s - 13*s - 3. Let t be 2 - 3/s - (-11)/9. Suppose -10/9*w - 8/9 - t*w**2 = 0. What is w?
-4, -1
Suppose 14*z + 760 = 18*z. Let b = 192 - z. Let 0*l - 5/2 + 5/2*l**b = 0. What is l?
-1, 1
Let z = 7436/35 - 1058/5. Factor 10/7*b - z*b**2 - 2/7*b**3 - 4/7 + 2/7*b**4.
2*(b - 1)**3*(b + 2)/7
Let m = 83 - 746/9. Let i(s) be the first derivative of 4/9*s**3 + 0*s - 1/3*s**2 + 0*s**4 - 2 + m*s**6 - 4/15*s**5. What is t in i(t) = 0?
-1, 0, 1
Let c be (-7)/(-15) + 0/(-80). Let w(t) be the second derivative of -7*t + 1/6*t**4 + 0 + 2/5*t**2 + c*t**3. Find r such that w(r) = 0.
-1, -2/5
Suppose -6*y = -3*y - 3*x - 18, 2*x = -4*y + 6. Let j(w) be the second derivative of -1/42*w**4 + w + 2/21*w**y - 1/7*w**2 + 0. Factor j(n).
-2*(n - 1)**2/7
Let c(f) be the third derivative of -f**7/105 + 3*f**6/40 - 7*f**5/30 + 3*f**4/8 - f**3/3 - 952*f**2. Find t such that c(t) = 0.
1/2, 1, 2
Let p(b) be the first derivative of 4*b**4 - 280*b**3/3 + 137*b**2/2 - 17*b - 7. Factor p(g).
(g - 17)*(4*g - 1)**2
Let q be (-20)/(-28)*21/(-9)*-3. Suppose -32 - 102*u + 5*u**2 + 26*u + q*u**2 + 0*u**2 = 0. What is u?
-2/5, 8
Let y(j) be the first derivative of 5 - 4/15*j**3 + 12/5*j**2 + 28/5*j. Factor y(v).
-4*(v - 7)*(v + 1)/5
Factor -195/4*p - 49/2 + 1/4*p**3 - 24*p**2.
(p - 98)*(p + 1)**2/4
Suppose 0 = 6*o + 1490 - 1550. Let j(s) be the second derivative of 0 + 2*s**3 + 1/5*s**5 + o*s + 0*s**2 + 4/3*s**4. Factor j(l).
4*l*(l + 1)*(l + 3)
Let j(b) be the first derivative of -b**5/60 - b**4/24 + b**3/3 + 12*b**2 - 3. Let t(r) be the second derivative of j(r). Factor t(g).
-(g - 1)*(g + 2)
Factor 2/11*j**4 + 0 - 24/11*j**2 + 0*j**3 + 32/11*j.
2*j*(j - 2)**2*(j + 4)/11
Let p(s) be the second derivative of s**8/420 + s**7/42 + s**6/10 + 7*s**5/30 + s**4/3 + s**3/6 + 11*s. Let q(a) be the second derivative of p(a). Factor q(w).
4*(w + 1)**3*(w + 2)
Let y(f) = -f**4 + f**3 - 4*f + 1. Let h(o) = 4*o**5 - 2*o**4 - 18*o**3 + 32*o**2 + 8*o - 6. Let l(m) = h(m) + 6*y(m). Factor l(r).
4*r*(r - 2)*(r - 1)**2*(r + 2)
Let y(f) be the first derivative of f**4/28 - 5*f**3/7 + 19*f**2/7 - 24*f/7 - 155. Factor y(t).
(t - 12)*(t - 2)*(t - 1)/7
Factor 2/11*j**4 - 8*j + 48/11 - 18/11*j**3 + 60/11*j**2.
2*(j - 3)*(j - 2)**3/11
Factor 0*b**2 + 0 + 0*b - 9/4*b**3 - 3/4*b**4.
-3*b**3*(b + 3)/4
Let c(z) be the first derivative of -z**3 + 120*z**2 - 237*z + 129. Factor c(u).
-3*(u - 79)*(u - 1)
Let x(o) = -2*o**2 - 171*o + 164. Let u(j) = -12*j**2 - 856*j + 820. Let r(v) = 3*u(v) - 16*x(v). Let r(f) = 0. What is f?
1, 41
Factor -2/5*g**2 - 80802/5 - 804/5*g.
-2*(g + 201)**2/5
Let y = 535/341 - 43/31. Find l, given that 0*l**3 - 2/11*l**2 + 0 + 0*l + y*l**4 = 0.
-1, 0, 1
Let h be ((-245)/21)/((-21)/9). Find u such that 0*u**3 + 0*u**2 + 3/7*u**4 + 0*u + 3/7*u**h + 0 = 0.
-1, 0
Let p be -170*-2*2/10. Let l be p/18 - (-10)/45. Factor -l*s**4 - 3*s**4 + 8*s**3 - 6*s**3.
-s**3*(7*s - 2)
Let -12*r + 341*r**4 - 116*r**4 + 12*r**2 + r**3 - 113*r**4 + 2*r**3 - 115*r**4 = 0. Calculate r.
-2, 0, 1, 2
Let c = 1/1926 + 7699/9630. Factor 6/5 - 2/5*g**2 + c*g.
-2*(g - 3)*(g + 1)/5
Let p be 23/(-184) - (93/(-40) - -2). Factor 2/5 - 1/5*a**2 - p*a.
-(a - 1)*(a + 2)/5
Let y = 43177681/2184 - 19770. Let p(z) be the third deriva