*2 + 1 - r**2 - 3*r**2 + 4*r**2. Let j(f) = -4*f**2 + 18*f + 86. Let a(b) = 3*j(b) - 15*z(b). Suppose a(q) = 0. Calculate q.
-9
Let k(t) be the second derivative of -t**5/100 - t**4/30 + 2*t**3/15 + 4*t**2/5 + 237*t - 2. Suppose k(a) = 0. Calculate a.
-2, 2
Suppose 4*q = -2*o + 10, -2*o + 3 = -4*q + q. Suppose -2*m + 6 = -2*b, -4*m + 3*m + o = -4*b. Let -57 - 16 - m*f**2 + 46 - 18*f = 0. What is f?
-3
Let v = -439 - -446. Let m(n) be the third derivative of 0*n**4 + 0 - 1/18*n**3 + 0*n - v*n**2 + 1/180*n**5. Factor m(o).
(o - 1)*(o + 1)/3
Factor 10*l**3 - 64*l**2 + 1440*l - 17*l**3 + 12*l**3 - 111*l**2 + 1620.
5*(l - 18)**2*(l + 1)
Let u(n) be the first derivative of n**7/56 - n**6/24 + n**5/40 + 42*n - 43. Let x(l) be the first derivative of u(l). Let x(p) = 0. What is p?
0, 2/3, 1
Suppose 3/7*g**2 - 78/7*g - 24 = 0. Calculate g.
-2, 28
Let g(s) be the first derivative of s**3/3 + 5*s**2 + 25*s + 215. Factor g(n).
(n + 5)**2
Let f(u) be the first derivative of 2*u**6/105 + 4*u**5/35 + 5*u**4/21 + 4*u**3/21 - 11*u - 1. Let z(q) be the first derivative of f(q). Factor z(h).
4*h*(h + 1)**2*(h + 2)/7
Factor 22*g**2 - 80/3*g - 20/3*g**3 + 32/3 + 2/3*g**4.
2*(g - 4)**2*(g - 1)**2/3
Let z(w) be the second derivative of -3*w**6/10 - 51*w**5/20 - 9*w**4/4 + 41*w**3/2 - 18*w**2 - 3*w + 8. Find l, given that z(l) = 0.
-4, -3, 1/3, 1
Let n(d) be the second derivative of 2*d**7/63 - d**6/9 + d**5/30 + d**4/9 - 404*d. What is r in n(r) = 0?
-1/2, 0, 1, 2
Factor 17190*v + 6*v**2 - 17090*v + 12 - 23*v**2.
-(v - 6)*(17*v + 2)
Determine w so that -7*w**5 - 1185*w**2 - 8*w**5 + 1165*w**2 + 35*w**4 = 0.
-2/3, 0, 1, 2
Let b(l) = 25*l - 850. Let u be b(34). Determine w so that -12/5*w + u - 3/5*w**3 - 12/5*w**2 = 0.
-2, 0
Let i be 4/(-42) + (-31311)/(-37044). Factor -3/4*l**2 - 1/4*l**3 - i*l - 1/4.
-(l + 1)**3/4
Let v = 0 + -3. Let k be 9/6*4 + v. Determine p, given that 6*p**3 - k*p**4 - p**3 - p**3 - p**3 = 0.
0, 1
Suppose -8 = 2*f - 3*r - 4, 0 = 2*f - 4*r + 8. Let v(g) be the second derivative of 1/72*g**f + 0 + 12*g - 1/4*g**2 + 1/18*g**3. Let v(s) = 0. Calculate s.
-3, 1
Let k be 4/(-10) + (-56)/(-90). Let y = 156665/9 - 17407. Factor -k*v**2 - y*v**4 + 0 + 4/9*v**3 + 0*v.
-2*v**2*(v - 1)**2/9
Factor 22/5*k + 2 + 14/5*k**2 + 2/5*k**3.
2*(k + 1)**2*(k + 5)/5
Let r(k) = k**3 + 6*k**2 + k - 17. Let j be -5 - (-2 - 1) - 3. Let g be r(j). Factor -z**2 - 1/4*z**4 - z**g + 0*z + 0.
-z**2*(z + 2)**2/4
Let b be 28/(16/(-4)) + 1. Let r = b - -8. Factor -2 + 2*m**2 + r*m + 0*m**2 - 2.
2*(m - 1)*(m + 2)
Let l(a) be the first derivative of -5 + 3/7*a**2 + 1/14*a**4 + 0*a + 8/21*a**3. Find d such that l(d) = 0.
-3, -1, 0
Let v(b) = 2*b**3 - b**2 + 4*b - 2. Let u be v(1). Let a(p) be the first derivative of 8/3*p**u - 8*p - 3*p**4 + 6*p**2 - 5. Let a(m) = 0. Calculate m.
-1, 2/3, 1
Let j(v) be the first derivative of -v**6/24 + 3*v**4/16 + v**3/6 + 100. What is z in j(z) = 0?
-1, 0, 2
Let -2/5*r**2 - 6/5*r + 0 = 0. Calculate r.
-3, 0
Factor 0 + 2/3*k**3 - 14/3*k + 4*k**2.
2*k*(k - 1)*(k + 7)/3
Let x(k) be the third derivative of -5*k**2 - 1/3*k**5 + 0 + 0*k - 1/24*k**6 + 0*k**3 + 0*k**4. Suppose x(v) = 0. What is v?
-4, 0
Let y(l) = 11*l**2 + 160*l + 149. Let q(v) = -100*v**2 - 1440*v - 1340. Let f(h) = 6*q(h) + 55*y(h). Factor f(c).
5*(c + 1)*(c + 31)
Let n be 90/2 + -1 + -2. Suppose 30 = 18*a - n. Factor -8/5*z**3 + 0*z**a + 6/5*z + 2/5*z**5 + 4/5 - 4/5*z**2.
2*(z - 2)*(z - 1)*(z + 1)**3/5
Factor -2904/7*w - 21296/7 - 2/7*w**3 - 132/7*w**2.
-2*(w + 22)**3/7
Let j be (48/(-36))/((-104)/24). Factor -j*o + 2/13*o**3 + 2/13*o**2 + 0.
2*o*(o - 1)*(o + 2)/13
Let j(u) be the second derivative of 2*u**6/75 - 2*u**5/25 - u**4/15 + 4*u**3/15 - 68*u. Factor j(t).
4*t*(t - 2)*(t - 1)*(t + 1)/5
Let k(j) = 5 + 11*j**2 - j**2 - 3 - 5*j - 3*j**2. Let b be k(-3). Determine m, given that 0*m**3 + b*m**2 - 80*m**2 - 3*m**3 = 0.
0
Suppose -7*l - 6 = -20. Determine j, given that -6*j**2 - 7*j**2 + 9*j**l + j**3 + j + 6 = 0.
-1, 2, 3
Let l(i) be the first derivative of -4/69*i**3 + 1/23*i**2 + 20 - 1/46*i**4 + 4/23*i. Factor l(s).
-2*(s - 1)*(s + 1)*(s + 2)/23
Let b(h) be the first derivative of -h**4/12 - 5*h**3/9 + 14*h**2/3 + 32*h/3 - 395. Factor b(g).
-(g - 4)*(g + 1)*(g + 8)/3
Let c be 61/12 - (2 - 9/(-3)). Let l(a) be the second derivative of 3*a + 1/3*a**3 + 0 + 0*a**2 - c*a**4. Find o such that l(o) = 0.
0, 2
What is p in -3*p**2 + 5*p**4 - 20*p**2 - 7*p**3 + 25*p**2 = 0?
0, 2/5, 1
Let h(y) be the first derivative of 0*y - 3/5*y**5 + 0*y**2 - 1/3*y**3 - 3/4*y**4 - 1/6*y**6 - 15. Factor h(p).
-p**2*(p + 1)**3
Let a(b) be the third derivative of 5*b**2 + 0 + 0*b + 1/39*b**3 - 7/156*b**4 + 4/195*b**5 + 4/195*b**6. Factor a(r).
2*(r + 1)*(4*r - 1)**2/13
Suppose -2/13*z**4 - 968/13 + 84/13*z**3 - 1848/13*z - 794/13*z**2 = 0. What is z?
-1, 22
Let b(a) be the third derivative of a**9/5040 - a**7/840 + a**4/3 + 8*a**2. Let h(t) be the second derivative of b(t). Factor h(s).
3*s**2*(s - 1)*(s + 1)
Let h(m) = 2*m**4 - 3*m**3 + 3*m. Let a(k) = -19*k**4 - 15*k + 4*k**4 + 20*k**3 - 5*k. Let o(g) = 3*a(g) + 20*h(g). Factor o(n).
-5*n**4
Let y(o) be the first derivative of o**4/3 - 2*o**3 + 4*o**2 + 4*o + 6. Let t(a) be the first derivative of y(a). Solve t(c) = 0 for c.
1, 2
Let d be ((-6)/((-24)/(-5)))/((-2)/8). Let i(f) = 3*f**2 - 20*f + 22. Let n(h) = 5*h**2 - 40*h + 45. Let x(y) = d*i(y) - 2*n(y). Factor x(t).
5*(t - 2)**2
Factor -41*j**2 + 16*j**2 + 7*j**2 + 10*j**2 + 980 + 13*j**2 - 140*j.
5*(j - 14)**2
Suppose -1 = 3*k - 16. Factor -2*b**k + 4*b**2 - 2*b**4 + 5*b**3 + 5*b - 7*b - b**3 - 2.
-2*(b - 1)**2*(b + 1)**3
Let x = -26361 + 26363. Find i such that 0 + 4/5*i**3 - 4*i - 16/5*i**x = 0.
-1, 0, 5
Let j(o) be the second derivative of 1/120*o**6 + 1/2*o**2 - 1/16*o**4 - 39*o + 0 + 1/6*o**3 - 1/40*o**5. Factor j(n).
(n - 2)**2*(n + 1)**2/4
Let 17/6 + 44*o**2 - 45/2*o + 8/3*o**3 = 0. What is o?
-17, 1/4
Let r(l) be the first derivative of -10/3*l**3 + 7 - 1/210*l**5 + 0*l**4 + 0*l + 0*l**2 - 1/1260*l**6. Let x(m) be the third derivative of r(m). Factor x(p).
-2*p*(p + 2)/7
Let d(s) = s - 1. Let r(x) = -4*x**3 + 52*x**2 - 164*x + 172. Let t(n) = -20*d(n) + r(n). Determine c, given that t(c) = 0.
2, 3, 8
Let q(i) = -i + 16. Let s be q(12). Let t be ((-80)/9)/(-4) - s/2. Determine k, given that 0 + t*k**2 - 2/9*k = 0.
0, 1
Let o(r) be the second derivative of r**8/560 + r**7/140 + r**6/120 - 11*r**3/6 + 8*r. Let l(n) be the second derivative of o(n). Suppose l(u) = 0. Calculate u.
-1, 0
Let y(t) = -2*t**5 - 42*t**4 + 2*t**3 + 50*t**2 + 8*t - 16. Let o(p) = p**5 + 28*p**4 - p**3 - 33*p**2 - 5*p + 10. Let l(m) = -8*o(m) - 5*y(m). Factor l(i).
2*i**2*(i - 7)*(i - 1)*(i + 1)
Let t(x) = 17*x**3 - 3*x**2 - 17*x + 29. Let z be 254/10 + 21/35. Let l(h) = -4*h**3 + h**2 + 4*h - 7. Let y(g) = z*l(g) + 6*t(g). Factor y(w).
-2*(w - 4)*(w - 1)*(w + 1)
Let u(c) be the third derivative of 5*c**8/48 + 2*c**7/7 - 25*c**6/24 - 11*c**5/6 + 15*c**4/2 - 20*c**3/3 - 5*c**2 + 9*c. Suppose u(n) = 0. Calculate n.
-2, 2/7, 1
Let r(y) be the second derivative of y**6/40 - 9*y**5/5 + 48*y**4 - 512*y**3 + 175*y. Factor r(u).
3*u*(u - 16)**3/4
Find d such that -1/4*d**4 - 3/2*d**3 - 3/4*d**2 + 5/2*d + 0 = 0.
-5, -2, 0, 1
Determine v so that -2/15*v**3 - 12/5*v**2 - 8*v + 80/3 = 0.
-10, 2
Let r(h) be the second derivative of -h**5/80 - h**4/16 + 3*h**3/8 - 5*h**2 - 11*h. Let y(s) be the first derivative of r(s). Solve y(g) = 0.
-3, 1
Let o(v) = -18*v**3 + v**2 + 2. Let y be o(2). Let q be y/(-45) - (32/(-20))/(-4). Suppose 4/9*x**4 - q*x + 2/3*x**3 - 14/9*x**2 - 8/9 = 0. What is x?
-2, -1, -1/2, 2
Let c(m) be the first derivative of -20*m + 10*m**2 + 5/3*m**3 + 26 - 5/4*m**4. Factor c(a).
-5*(a - 2)*(a - 1)*(a + 2)
Let v(l) = 20*l**4 - 20*l**3 - 180*l**2 + 202*l. Let q(u) = -5*u**4 + 5*u**3 + 45*u**2 - 51*u. Let w(x) = 11*q(x) + 3*v(x). Factor w(n).
5*n*(n - 3)*(n - 1)*(n + 3)
Factor 6 + 722/3*m**2 + 76*m.
2*(19*m + 3)**2/3
Suppose 6 = 2*n + 4*n. Let h be ((-25)/(-20) - 2)*n/(-3). Factor 0*d - h*d**2 + 1/4.
-(d - 1)*(d + 1)/4
Factor -39*q**2 + 72*q**2 + 2 + q - 34*q**2 + 0.
-(q - 2)*(q + 1)
Let l(t) = t**3 - 2*t**2 - 5. Let g be l(3). Suppose 3*f = 2*a + 11, -g*a - 2*f + 28 = 2*f. Factor a*j**3 - 9*j**2 + 10*j**2 + 8*j -