*7/336 - j**6/60 - 3*j**5/80 - j**4/24 - j**3/48 + j + 10. Factor m(n).
-n*(n + 1)**4/8
Let j(d) = -14*d**2 - 143*d - 149. Let n(b) = -33*b**2 - 357*b - 372. Let q(u) = -12*j(u) + 5*n(u). Let q(l) = 0. Calculate l.
-1, 24
Let o(n) be the first derivative of -n**3/3 - 75. Let o(m) = 0. Calculate m.
0
What is o in -135202*o**5 - 41930*o**3 + 4 - 196822*o**5 - 325*o + 6379*o**4 + 113*o + 185505*o**4 + 4321*o**2 = 0?
1/14, 2/11
Let g(x) be the second derivative of 5*x**7/42 - 16*x**6/3 + 221*x**5/4 + 1445*x**4/6 + 270*x. Find t, given that g(t) = 0.
-2, 0, 17
Factor 14*b + 0*b**2 - 2*b**2 + 24*b - 28*b - 8.
-2*(b - 4)*(b - 1)
Let k(i) = -i**2 - 8*i - 8. Suppose -4*r + 5*d + 3 = 36, 4*d - 30 = 5*r. Let a be k(r). Factor -1/2*c + 1/2*c**3 + 1/2*c**2 + 0 - 1/2*c**a.
-c*(c - 1)**2*(c + 1)/2
Solve -124/5*t + 1922/5 + 2/5*t**2 = 0 for t.
31
Let y(n) = -259*n - 10099. Let w be y(-39). Factor w*r**2 - 20/3*r + 50/9.
2*(3*r - 5)**2/9
Let j = -1716 + 1740. Suppose 3*o + 18 = 66. Factor -o - 8*t**2 - 4*t**3 - 1/2*t**5 + 3*t**4 + j*t.
-(t - 2)**4*(t + 2)/2
Suppose 2 = -65*w + 66*w. Factor 9*a - 12*a**w + 10*a**3 + 0*a**3 - 7*a**3.
3*a*(a - 3)*(a - 1)
Let z(c) be the third derivative of -c**7/1050 - c**6/600 + c**5/150 + 50*c**2. Factor z(n).
-n**2*(n - 1)*(n + 2)/5
Let w(l) = -l**2 - 5*l - 2. Let f be w(-4). Let d(m) be the third derivative of 1/420*m**5 + 0 + 0*m**4 + 1/210*m**6 + 0*m + 0*m**3 - m**f. Factor d(h).
h**2*(4*h + 1)/7
Let l be (6/(-4))/(2*6/(-32)). Factor -20 - 48*o - 3*o**2 + 21*o - l.
-3*(o + 1)*(o + 8)
Let x(s) be the first derivative of 0*s - 3/4*s**4 - 21 + 3*s**3 - 1/2*s**6 + 3*s**2 - 9/5*s**5. Determine l, given that x(l) = 0.
-2, -1, 0, 1
Let f(s) be the first derivative of 1/20*s**5 - 1/24*s**6 + 1/8*s**4 - 1/6*s**3 - 1/8*s**2 - 2 + 1/4*s. What is o in f(o) = 0?
-1, 1
Let d(x) be the first derivative of -26 - 1/4*x**2 - 1/3*x**3 + 1/8*x**4 + x. Factor d(o).
(o - 2)*(o - 1)*(o + 1)/2
Let q be ((-100)/60)/((-5)/6). Let h(v) be the second derivative of -1/18*v**4 + 2/9*v**3 + 0 + 2*v + v**q. Factor h(c).
-2*(c - 3)*(c + 1)/3
Let p = 32 - 32. Let z be (-5)/2 - -3 - (p - 1). Factor -z*v + 0 + 21/4*v**2 - 9/4*v**3.
-3*v*(v - 2)*(3*v - 1)/4
Suppose 4*k = 6*k. Suppose k = 5*u - 10 - 15. Let -3*i - i - u*i**2 + i**2 = 0. Calculate i.
-1, 0
Let z(n) be the third derivative of -n**6/300 - 4*n**5/225 - n**4/45 - 230*n**2. Factor z(k).
-2*k*(k + 2)*(3*k + 2)/15
Let c be 12/(-56)*(-94)/141. Factor 0 - 1/7*d**2 + c*d.
-d*(d - 1)/7
Factor 2/15*c - 2/15*c**2 + 4/5.
-2*(c - 3)*(c + 2)/15
Suppose -4*w + 5*w - 11 = 0. Suppose -3*y + w + 0 = -2*x, -4*y = 2*x - 24. Factor 131*r**2 - 62*r**2 - 67*r**x + 4*r.
2*r*(r + 2)
Let w be (-1 - 5)*(-14)/28 - 1. Let u(b) be the second derivative of -b**w + 1/9*b**3 - 1/30*b**5 + 13*b + 0 + 1/6*b**4. Factor u(o).
-2*(o - 3)*(o - 1)*(o + 1)/3
Let f(w) = w**2 + 30*w - 62. Let x be f(-32). Factor -10 + 24*r + r**2 - 21*r + 5*r + r**x.
2*(r - 1)*(r + 5)
What is u in 183 - 81*u**2 + 15*u + 53*u - 3*u**3 - 270 + 98*u + 5*u = 0?
-29, 1
Suppose 32*n**2 + 20*n**2 - 4*n**3 + 13*n**2 - 84*n - 17*n**2 + n**3 = 0. What is n?
0, 2, 14
Suppose -16*w**2 - 4 + 9*w**2 + 3*w**2 - 44*w + 52 = 0. What is w?
-12, 1
Factor 1/2*l - 10 + 1/2*l**2.
(l - 4)*(l + 5)/2
Let k(n) = -n**3 + 3*n**2 + 4. Let l be k(3). Solve -48*x**2 - 8 - 3*x + 17*x**l - 12*x**2 - 33*x - 44*x**3 - 29*x**4 = 0.
-1, -2/3
Suppose z - 3 = 2*r, -z = -5*r - 3 + 9. Find a, given that -72*a**2 + 22*a**2 - 17*a - 9 - 43*a - z = 0.
-3/5
Let o(b) be the first derivative of -1/4*b**4 + 3/4*b**2 + 1/2*b - 34 + 1/3*b**3 - 3/10*b**5 - 1/12*b**6. Solve o(w) = 0 for w.
-1, 1
Let u(v) be the second derivative of -7*v**6/15 - 34*v**5/5 + 9*v**4/2 + 68*v**3/3 - 20*v**2 + 21*v + 2. Find p such that u(p) = 0.
-10, -1, 2/7, 1
Let a be (-86)/(-30) - 4/(-30). Let r(o) be the first derivative of 3*o**a + 6*o + 0*o**2 + 4 + 3*o**2 + 3*o - 8*o. Solve r(w) = 0.
-1/3
Let q = -62/11 + 259/44. Let h(r) be the second derivative of 7/16*r**4 + 0*r**2 + q*r**3 + 0 + 4*r. Factor h(l).
3*l*(7*l + 2)/4
Let t(l) be the first derivative of -l**4/22 + 2*l**3/11 + 4*l**2/11 - 24*l/11 - 65. Find x such that t(x) = 0.
-2, 2, 3
Find h, given that -2/5*h**4 - 2/5*h**5 + 4/5*h + 2*h**2 + 6/5*h**3 + 0 = 0.
-1, 0, 2
Suppose -4*j - 5 = -r, 5*j + 11 = -4. Let x(a) = a**2 + 4*a - 13. Let b be x(r). Factor -b*c**2 - 3*c**2 - 2*c**3 + 18 - 6*c + 4*c**2 - 3*c**2.
-2*(c - 1)*(c + 3)**2
Let w be 0 + 4/10 - (-325)/(-1125). Solve -1/9*h**2 - w - 2/9*h = 0 for h.
-1
Let l(w) = -20*w**3 + 6*w**2 + 6*w - 34. Let q be (-20)/(-4) + 1 + -1 + -2. Let g(z) = -4*z**3 + z**2 + z - 7. Let a(t) = q*l(t) - 14*g(t). Factor a(y).
-4*(y - 1)**2*(y + 1)
Let f(d) be the second derivative of -d**6/10 - 24*d**5/5 - 143*d**4/2 - 240*d**3 - 675*d**2/2 + d - 14. Factor f(p).
-3*(p + 1)**2*(p + 15)**2
Let t(l) be the second derivative of -l**4/12 - 11*l**3/6 + 2*l**2 - 9*l. Let i be t(-11). Factor -5*c + 4*c**2 + 5*c - 8*c + i.
4*(c - 1)**2
Let k(b) = -b**3 - 11*b**2 + 2*b + 10. Let q be k(-11). Let d be 6/4*q/(-18). Solve -26*x - d + 5 + 20*x + 2*x**3 = 0 for x.
-2, 1
Let n(f) = -f**2 + 33*f + 4. Let r(h) = h**2 - 33*h - 3. Let a(d) = 3*n(d) + 4*r(d). Solve a(g) = 0 for g.
0, 33
Let t(n) be the second derivative of 0*n**2 + 1/30*n**5 + 0 - 1/6*n**4 - n + 2/9*n**3. Factor t(m).
2*m*(m - 2)*(m - 1)/3
Let g(s) be the third derivative of -s**7/10080 - s**6/480 - s**4/8 + 20*s**2. Let k(j) be the second derivative of g(j). Factor k(v).
-v*(v + 6)/4
Factor -1/2*w**2 + 0*w + 1/2*w**3 + 0.
w**2*(w - 1)/2
Suppose -8*b + 93 = 77. Let -b - 3/2*c**2 - 3*c - 1/4*c**3 = 0. What is c?
-2
Let r(b) = -b**2 - 2*b - 1. Let t(y) = 4*y**3 - 449*y**2 + 16418*y - 202617. Let p(d) = 5*r(d) - t(d). Determine n so that p(n) = 0.
37
Let c(w) = -6*w**2 + 156*w + 3038. Let k(p) = 8*p**2 - 156*p - 3037. Let m(l) = 5*c(l) + 4*k(l). Determine v so that m(v) = 0.
-39
Let c(s) = s**3 + s**2 - s + 1. Suppose -5*n - 4*f = 3 - 0, 1 = -n - f. Let u(q) = -9*q**3 - 7*q**2 + 6*q - 4. Let p(h) = n*u(h) + 4*c(h). Factor p(j).
-j*(j + 1)*(5*j - 2)
Let w(l) be the third derivative of -1/270*l**5 + 0*l**6 + 0 + 1/945*l**7 + 0*l**3 + 16*l**2 + 0*l + 0*l**4. Factor w(s).
2*s**2*(s - 1)*(s + 1)/9
What is f in 3/5*f**5 - 6/5*f**2 + 6/5*f**4 + 0 - 3/5*f + 0*f**3 = 0?
-1, 0, 1
Let s(x) = 2*x**4 + 451*x**3 + 32849*x**2 + 810448*x + 14. Let w(p) = -p**4 - 226*p**3 - 16424*p**2 - 405224*p - 8. Let o(y) = 4*s(y) + 7*w(y). Factor o(i).
i*(i + 74)**3
Let g = 38 + -38. Suppose -m = -g*m. Factor 0*i**3 + m + i**4 - 1/2*i - i**2 + 1/2*i**5.
i*(i - 1)*(i + 1)**3/2
Let r be (1 - 4)*108/(-81). Let w be 436/126 + r/36. Factor 10/7*g - w - 1/7*g**2.
-(g - 5)**2/7
Let v = -23 + 27. Factor 8*t**2 + 0*t**3 + 4*t + 0*t**3 - t**v - 4*t**5 - 7*t**4.
-4*t*(t - 1)*(t + 1)**3
Let p be (-160 + 160)/((-2)/(-6)*(-20 + -1)). Factor p*b + b**3 - 1/2*b**2 - 1/2*b**4 + 0.
-b**2*(b - 1)**2/2
Let 4*j**5 - 3*j**5 + 653180*j + 33*j**4 - 653212*j + 31*j**3 - 33*j**2 = 0. What is j?
-32, -1, 0, 1
Let d = 4 + 19. Let q = -14 + d. Factor -3 + 5*v**3 - 3 - 2*v**3 - q*v.
3*(v - 2)*(v + 1)**2
Factor -42*d**3 - 100*d - 180*d**2 - 50*d - 51 - 3*d**4 + 426.
-3*(d - 1)*(d + 5)**3
Let r(i) be the first derivative of 237*i**3 + 705*i**2/2 - 6*i + 226. Factor r(b).
3*(b + 1)*(237*b - 2)
Let y be 90/4*12/10. Suppose -y*j = -29*j. Solve -8/9*r**2 - 4/3*r**4 + 0*r + 20/9*r**3 + j = 0.
0, 2/3, 1
Let c(p) be the second derivative of -p**4/54 + 25*p**3/27 - 10*p - 8. What is u in c(u) = 0?
0, 25
Let r be (12/(-135))/(12/(-18)) + 33/495. Factor -3/5 - r*d**2 - 4/5*d.
-(d + 1)*(d + 3)/5
Let r(l) be the first derivative of l**5/5 - 9*l**4/4 - 7*l**3 - 11*l**2/2 + 258. Factor r(f).
f*(f - 11)*(f + 1)**2
Let z = 175 - 94. Let a = 254 - z. Factor -s**3 - 2*s + 173 - a - 3*s**2.
-s*(s + 1)*(s + 2)
Let u be (-2)/(-10) - (-2480)/2475. Let y = u + -1/495. Suppose -21/5*s**5 + 12/5*s**2 - 6/5*s**4 - y + 42/5*s**3 - 21/5*s = 0. Calculate s.
-1, -2/7, 1
Let p(c) = 3*c**2 + 1320*c + 85801. Let x(t) = 8*t**2 + 3965*t + 257401. Let o(s) = -7*p(s) + 2*x(s). Factor o(f).
-5*(f + 131)**2
Let i(s) be the third derivative of s**8/2184 - 2*s**7/1365 - 7*s**6/390 - 4*s**5/195 + s**4/12 + 10*s**3/39 - 206*s**2. Suppose i(j) = 0. What is j?
-2, -1, 1, 5
Let a(l) be the firs