*m + 42. Let h(x) = -17*x**3 - 8*x**2 + 142*x + 81. Let j(y) = 6*h(y) - 13*o(y). Solve j(i) = 0 for i.
-6, -1, 5
Let p(v) be the second derivative of -v**6/10 + 3*v**5/10 + 3*v**4/4 - 11*v + 4. Suppose p(b) = 0. What is b?
-1, 0, 3
Let l(u) be the second derivative of 8/45*u**4 + 1/45*u**7 - 2/15*u**2 + 26/225*u**6 + 50*u + 17/75*u**5 - 1/45*u**3 + 0. Factor l(k).
2*(k + 1)**4*(7*k - 2)/15
Factor 189 + 381/2*d + 3/2*d**2.
3*(d + 1)*(d + 126)/2
Let l = 5149/17507 + -21/2501. Factor -l*j**2 + 4/7*j + 16/7.
-2*(j - 4)*(j + 2)/7
Let v(p) = -7*p**2 - 34*p + 32. Let o(y) = 2*y**2 + y. Let s(x) = 6*o(x) + 2*v(x). Factor s(l).
-2*(l - 1)*(l + 32)
Let z(f) be the first derivative of f**6/6 + 38*f**5/5 + 459*f**4/4 + 1894*f**3/3 + 1504*f**2 + 1536*f + 949. Let z(r) = 0. Calculate r.
-16, -3, -2, -1
Let d(x) be the second derivative of -x**5/70 - x**4/6 + 4*x**3/3 - 20*x**2/7 + 221*x - 1. Find f such that d(f) = 0.
-10, 1, 2
Let a(t) = -5*t**2 - 2*t + 3. Let g be a(-1). Let z(v) be the third derivative of 1/20*v**5 + 0*v + 0*v**4 + 0 + g*v**3 + 1/40*v**6 - 9*v**2. Factor z(r).
3*r**2*(r + 1)
Let h = -2419/3 + 807. Find c such that h - c - 1/3*c**4 - 1/3*c**2 + c**3 = 0.
-1, 1, 2
Let a(p) = p**3 + 3*p**2 - 11*p - 31. Let s be a(-3). Let j(n) be the first derivative of -n**s - 4/3*n**3 - 6 + 0*n. Factor j(i).
-2*i*(2*i + 1)
Let z be ((-36)/910 - (-16)/104)*14/2. Solve -2/5*a**5 + 0 + z*a**4 + 0*a**3 - 4/5*a**2 + 2/5*a = 0 for a.
-1, 0, 1
Let n(q) be the second derivative of q**6/150 + q**5/50 - q**4/5 - 4*q**3/15 + 16*q**2/5 - 318*q. Determine k, given that n(k) = 0.
-4, -2, 2
Let y(g) be the first derivative of g**5/4 - 33*g**4/16 + 3*g**3 + 5*g**2/2 + 816. Factor y(u).
u*(u - 5)*(u - 2)*(5*u + 2)/4
Suppose 24 = 7*n - 10*n. Let t = n + 12. Factor -17*w - t*w**3 + 4*w**4 + 17*w.
4*w**3*(w - 1)
Suppose -8*g = -25*g + 51. Factor 14*b**3 - 13*b**3 + g*b**4 - 3 + 6*b - 7*b**3.
3*(b - 1)**3*(b + 1)
Let r = -90248/13 + 6946. Factor 2/13*z**3 - r + 18/13*z**2 + 30/13*z.
2*(z - 1)*(z + 5)**2/13
Find g such that -4/9*g**2 + 4/9*g + 8/3 = 0.
-2, 3
Let n(i) be the first derivative of -5/12*i**4 + 2/3*i**2 + 8/3*i - 1/15*i**5 - 2/3*i**3 - 1. Factor n(w).
-(w - 1)*(w + 2)**3/3
Let y = 787089/5 - 61393139/390. Let v = -1/195 - y. Factor -1/2*d + 0*d**4 + d**3 + 0 + 0*d**2 - v*d**5.
-d*(d - 1)**2*(d + 1)**2/2
Factor 7/5*w**5 + 6/5 - 22/5*w**2 - 7/5*w + 48/5*w**3 - 32/5*w**4.
(w - 2)*(w - 1)**3*(7*w + 3)/5
Let t(f) be the third derivative of -f**7/385 - 7*f**6/660 - f**5/110 + f**4/44 + 2*f**3/33 - 258*f**2. Factor t(l).
-2*(l + 1)**3*(3*l - 2)/11
Let l = -1 - 3. Let a(m) = m**2 - 2*m + 13. Let o(n) = -n**2 + 3*n - 12. Let w = 71 + -74. Let v(b) = l*o(b) + w*a(b). Determine d so that v(d) = 0.
3
Let t(o) be the first derivative of o**6/63 + 2*o**5/105 - o**4/42 - 2*o**3/63 - 269. Find d, given that t(d) = 0.
-1, 0, 1
Let v(o) be the first derivative of 7*o**6/36 + 8*o**5/15 + o**4/6 - 7*o**3/9 - 11*o**2/12 - o/3 - 27. Factor v(b).
(b - 1)*(b + 1)**3*(7*b + 2)/6
Let r(b) be the third derivative of -b**8/896 - 23*b**7/560 - b**6/2 - 15*b**5/8 - 6*b**2 - 5. Let r(o) = 0. What is o?
-10, -3, 0
Let o(s) be the second derivative of -s**9/3024 + 5*s**8/672 - 25*s**7/504 - 19*s**4/6 + 17*s - 1. Let m(x) be the third derivative of o(x). Factor m(b).
-5*b**2*(b - 5)**2
Let t(l) be the first derivative of -l**7/735 - l**6/60 - l**5/14 - 13*l**4/84 - 4*l**3/21 - l**2 + 6. Let m(w) be the second derivative of t(w). Factor m(s).
-2*(s + 1)**3*(s + 4)/7
Let j(g) be the second derivative of 0*g**4 + 1/10*g**3 + 5*g - 3/100*g**5 + 0*g**2 + 0. Factor j(o).
-3*o*(o - 1)*(o + 1)/5
Suppose 0 = 2*b + 1 - 13. Let o(x) = 4*x**3 - 8*x**2 + 6. Let c(a) = -5*a**3 + 9*a**2 - 7. Let z(f) = b*c(f) + 7*o(f). Solve z(y) = 0 for y.
-1, 0
Let o = -269 + 275. Let y be (-6)/9 + 17/3. Solve -o*t**5 + 8*t**4 - 3*t**5 + 4*t**2 + 10*t**3 + 11*t**y = 0 for t.
-2, -1, 0
Let n be 5 - (-12)/4 - 3*(-120)/(-75). Determine q, given that n + 4/5*q**3 - 12/5*q**2 + 0*q = 0.
-1, 2
Let y(s) be the first derivative of -s**5/24 - s**4/24 + 8*s**2 + 4. Let p(g) be the second derivative of y(g). Solve p(u) = 0 for u.
-2/5, 0
Let s = 2787 - 2785. Factor -2/5 + 4/15*r + 2/15*r**s.
2*(r - 1)*(r + 3)/15
Factor -38/5*o - o**2 + 16/5.
-(o + 8)*(5*o - 2)/5
Suppose -4*y = 34 + 6. Let d(z) = -14*z**2 + 26*z - 22. Let x(p) = p**2 - p + 1. Let q(o) = y*x(o) - d(o). Factor q(k).
4*(k - 3)*(k - 1)
Suppose -7*i - 2*i - 27 = 0. Let y be (-45)/(-80)*(0 - 4/i). Factor y*s**3 + 5/4*s**2 + 0 + 1/2*s.
s*(s + 1)*(3*s + 2)/4
Solve -5*m**5 + 16*m**3 + 64*m**3 + 40 - 7270*m + 7195*m - 10*m**2 - 30*m**4 = 0 for m.
-8, -1, 1
Let m(x) be the third derivative of -5/56*x**4 + 31*x**2 + 0*x + 0 + 3/14*x**3 - 1/840*x**6 + 1/60*x**5. Factor m(a).
-(a - 3)**2*(a - 1)/7
Let i(p) be the first derivative of -p**6/24 - 41*p**5/20 - 219*p**4/8 - 80*p**3/3 + 100*p**2 + 270. Solve i(g) = 0 for g.
-20, -2, 0, 1
Factor -2 + 11*p**3 - 20*p**3 + 24*p**2 - 36*p + 5*p**3 + 18.
-4*(p - 4)*(p - 1)**2
Suppose 2/5*c**2 + 176/5 + 38/5*c = 0. What is c?
-11, -8
Let p(b) be the first derivative of -5*b**3/3 + 180*b**2 - 6480*b - 264. Factor p(f).
-5*(f - 36)**2
Suppose -m + j + 12 = -0*j, -4*m + 62 = 3*j. Suppose -11 = 2*l + 3*c, 5*c + 11 = -m. Determine p, given that -4/9 - 10/9*p - 4/9*p**l = 0.
-2, -1/2
Let r be 5/(-4)*(-39)/195. Find v, given that -1 - r*v**2 + v = 0.
2
Let s(w) = -149*w + 153. Let o be s(1). Find f such that 3/5*f**5 - 9/5*f**o + 0 + 12/5*f**2 + 0*f**3 + 0*f = 0.
-1, 0, 2
Let m = 1/259 + 219/10360. Let t(v) be the second derivative of 0*v**2 + 8*v + 1/12*v**4 + 1/12*v**3 + 0 + m*v**5. Factor t(y).
y*(y + 1)**2/2
Let c(n) be the second derivative of 3*n**5/160 - 3*n**4/32 - n**3/16 + 9*n**2/16 + 11*n - 2. Let c(h) = 0. Calculate h.
-1, 1, 3
Suppose -2*h - 19*h = 10*h. Suppose -1/4*z**3 - z + z**2 + h = 0. Calculate z.
0, 2
Suppose -2323 - 467 = -18*r. Let w = -461/3 + r. What is x in 0*x + 1/3*x**4 + 0 - w*x**3 + 4/3*x**2 = 0?
0, 2
Let x(a) be the third derivative of a**8/1680 - a**7/210 + a**6/72 - a**5/60 - 2*a**3/3 + 5*a**2. Let i(p) be the first derivative of x(p). Factor i(r).
r*(r - 2)*(r - 1)**2
Let i(w) = 1 + 7 + w + 5. Let v be i(-11). Find k, given that -3 - 24*k**v - 12*k**4 + 3 + 26*k**3 + 2*k**5 + 8*k = 0.
0, 1, 2
Factor -2 + 1/2*y**2 + 3/2*y.
(y - 1)*(y + 4)/2
Let w = -6247/612 + 174/17. Let u(v) be the second derivative of 0 + w*v**4 + 15*v - 2/3*v**2 + 1/6*v**3. Factor u(h).
(h - 1)*(h + 4)/3
Suppose 5/6*o**2 - 85/3 + 25/2*o = 0. What is o?
-17, 2
Let b(i) = 8*i**4 - 45*i**3 + 104*i**2 + 3*i - 169. Let s(k) = -9*k**4 + 45*k**3 - 102*k**2 - 4*k + 172. Let l(q) = -4*b(q) - 3*s(q). Factor l(z).
-5*(z - 4)**2*(z - 2)*(z + 1)
Let y(p) be the first derivative of p**5 - 20*p**3 - 40*p**2 + 72. Factor y(t).
5*t*(t - 4)*(t + 2)**2
Let y(q) = 2*q**2 - 58*q - 58. Let n be y(30). Let c = -1 + 3/2. Solve 1/2*l + 0 - c*l**n = 0.
0, 1
Let x = -13 + 5. Let l = -3 - x. Determine h, given that -6 + 3*h + 1 - 3*h**3 + l = 0.
-1, 0, 1
Let s(f) = 2*f + 28. Let y be s(23). Let p = y - 221/3. Factor 0 - p*g - 4/3*g**3 + 5/3*g**2.
-g*(g - 1)*(4*g - 1)/3
Let s(n) be the second derivative of 0 + 8*n + 6/5*n**2 - 2/5*n**3 + 1/20*n**4. Factor s(k).
3*(k - 2)**2/5
Let b = 92 + -95. Let w be (-2 - -1)*b + -5 + 6. Factor 0*n**3 + 0 + 2/5*n**2 + 0*n - 2/5*n**w.
-2*n**2*(n - 1)*(n + 1)/5
Suppose 2*h = -l + 84, 0*h + 4*l - 84 = -2*h. Factor 4*z**2 + 26 - 17*z + 5*z - h.
4*(z - 4)*(z + 1)
Suppose 2*d + 19*d = -126. Let c be ((-32)/24)/(4/d). Factor -1/4 - 1/4*r + 1/4*r**3 + 1/4*r**c.
(r - 1)*(r + 1)**2/4
Let a(l) be the second derivative of -l**6/180 + 3*l**5/40 + 5*l**4/36 + 281*l. What is n in a(n) = 0?
-1, 0, 10
Let z(a) be the second derivative of a**6/24 + a**5/4 + 5*a**4/12 + 3*a**2 + 12*a. Let t(n) be the first derivative of z(n). Factor t(j).
5*j*(j + 1)*(j + 2)
Let z(q) be the second derivative of 5*q**4/4 + 355*q**3/6 - 60*q**2 + 47*q. Let z(a) = 0. What is a?
-24, 1/3
Let c = -80 + 119. Find f, given that -75*f**4 + 8000*f + 1200*f**2 + c*f**4 + 38*f**4 + 80*f**3 + 20000 = 0.
-10
Let c(w) be the third derivative of 1/300*w**6 + 0*w + 0*w**3 + 10*w**2 - 1/50*w**5 + 0 + 1/30*w**4. Determine q so that c(q) = 0.
0, 1, 2
Factor 4/5*w**3 - 26/5*w**2 + 0 - 14/5*w.
2*