112. Let l(m) = 2*m**3 + m**2 + 2*m + 1. Let w(h) = 5*d(h) + 10*l(h). What is k in w(k) = 0?
-5, 1, 22
Let l(r) be the first derivative of -r**6/4 - 6*r**5/5 + 3*r**4/8 + 2*r**3 - 51. Solve l(t) = 0 for t.
-4, -1, 0, 1
Let g = -199 - -3583/18. Let f(b) be the third derivative of -g*b**3 + 0*b - 1/180*b**5 + 0 - 5*b**2 + 1/36*b**4. What is r in f(r) = 0?
1
Factor 657*r**4 + 4*r**5 + 2*r**3 - 5*r**5 - 656*r**4.
-r**3*(r - 2)*(r + 1)
Let k(u) = 2*u**2 + u - 1. Let b be k(0). Let o be 3 + (-3 - -4) + b. Suppose 0 + 0*i**2 + 2/3*i**o + 0*i = 0. Calculate i.
0
Let s be ((-6)/(-7))/(4/168). Suppose -d = w, s = 4*w - d - 4*d. Determine x, given that 71*x**w - 3*x**3 + 2*x**2 - 69*x**4 - x**3 = 0.
0, 1
Suppose 0 = 2*g - 24*c + 28*c - 4, 0 = 3*g + c - 16. Let f(a) be the second derivative of -4/3*a**3 + 1/6*a**4 - g*a + 4*a**2 + 0. Determine s so that f(s) = 0.
2
Let d be (-4)/(-10) + 208/130. Factor 4*k**3 + 75*k + 12*k - 27*k + k**3 - 40 - 30*k**d.
5*(k - 2)**3
Let l be (-5 - -11)*(-71)/(-10). Let u = 43 - l. Factor u*c + 0 + 1/5*c**2.
c*(c + 2)/5
Suppose 0 = -5*t - 5*c + 30, -7*t = -8*t + c. Let x be 0/(4 + -2 + -4). Determine h so that x + 0*h**2 + 0*h - 1/4*h**4 - 1/4*h**5 + 0*h**t = 0.
-1, 0
Let c be (-32)/48 - (-2 - 22/(-30)). Let h(s) be the first derivative of -c*s**2 - 8 + 1/5*s**3 - 9/5*s. What is j in h(j) = 0?
-1, 3
Let h(w) be the third derivative of -1/70*w**7 + 0*w - 1/8*w**4 + 1/40*w**6 + 1/20*w**5 + 0*w**3 + 3*w**2 + 0. Factor h(z).
-3*z*(z - 1)**2*(z + 1)
Suppose -12*s + 13*s + 2*w = 3, 0 = -2*w. Suppose -512/3 + 512/3*j - 64*j**2 + 32/3*j**s - 2/3*j**4 = 0. What is j?
4
Let q be (-10)/(-8)*((-1 - -15) + 13950/(-1125)). Let 2/5*k**3 - 2/15*k**4 + 0 + 0*k - 4/15*k**q = 0. Calculate k.
0, 1, 2
Let v be (-6*2/8)/9*1042. Let i = -172 - v. What is x in 4/3*x**4 + i*x**2 - 11/3*x**3 + 2/3*x + 0 = 0?
-1/4, 0, 1, 2
Let y be 9 - (7/15)/((-123)/(-1845)). Find x, given that 120/11*x - 72/11 - 50/11*x**y = 0.
6/5
Let -18/5*u**5 - 1556/5*u**2 + 214/5*u**4 - 372/5*u**3 - 98/5 - 210*u = 0. Calculate u.
-1, -1/9, 7
Factor -26 + 42 + 14*u**2 - 5*u**3 + 3*u**3 - 28*u.
-2*(u - 4)*(u - 2)*(u - 1)
Let q = -50 - -50. Let t(j) be the second derivative of 4*j + 0 + 0*j**3 + 0*j**4 + q*j**5 + 0*j**2 - 1/84*j**7 - 1/30*j**6. Solve t(f) = 0 for f.
-2, 0
Let m(g) be the second derivative of 0 + g - g**2 + 3/8*g**4 + 1/10*g**5 + 1/120*g**6 + 0*g**3. Let r(w) be the first derivative of m(w). Factor r(h).
h*(h + 3)**2
Suppose 7 - 2 - 17 - 21 - 5 - p**2 - 39*p = 0. What is p?
-38, -1
Suppose 21 = -a + 24. Let n(c) be the first derivative of 0*c**2 + 3 - 2/3*c**3 + 4/3*c**6 + 0*c + a*c**4 - 18/5*c**5. Let n(s) = 0. Calculate s.
0, 1/4, 1
Let l(b) be the second derivative of -b**8/2240 + 13*b**7/3360 + b**6/144 + 3*b**3 - 8*b. Let d(f) be the second derivative of l(f). What is c in d(c) = 0?
-2/3, 0, 5
Let a(n) = 4*n**5 - 13*n**4 + 10*n**3 + 41*n**2 - 72*n + 33. Let c(v) = 2*v**5 - v**4 + v**2 + 1. Let r(p) = -a(p) + c(p). Suppose r(h) = 0. What is h?
-2, 1, 2, 4
Let d(w) = 135*w + 1218. Let s be d(-9). Factor s + 15/4*a**2 - 9*a.
3*(a - 2)*(5*a - 2)/4
Let p(n) be the second derivative of -31*n**7/252 - n**6/90 + 31*n**5/120 + n**4/36 - 2*n - 26. Let p(z) = 0. What is z?
-1, -2/31, 0, 1
Let s(q) = -q**5 - q**3 + q**2 + q + 1. Let r = -38 - -37. Let w(n) = -138*n**5 + 87*n**3 + 43*n**2 + 8*n + 3. Let i(g) = r*w(g) + 3*s(g). Factor i(p).
5*p*(p - 1)*(3*p + 1)**3
Let r = 16 - 9. Suppose 5*q - 15 = -3*f, -3*q + r*f - 5 = 6*f. Find s, given that 5/3*s**3 - s**5 + 4/3*s**4 - 2/3*s**2 + 0*s + q = 0.
-1, 0, 1/3, 2
Let s = -5 + 8. Suppose -s + 2 = -3*f - 2*v, -23 = -f + 5*v. Let k - k**4 + 4*k - 2*k - 3*k**2 + 3*k**f - 2*k = 0. Calculate k.
0, 1
Let h(f) be the first derivative of -1 - 23*f**4 - 4*f**2 - 14*f**4 + 12*f**3 + 30*f**4. Factor h(s).
-4*s*(s - 1)*(7*s - 2)
Let w be (-1 - (-101)/5) + -2. Let x = w + -17. Factor 1/5*u - 2/5 - x*u**3 + 2/5*u**2.
-(u - 2)*(u - 1)*(u + 1)/5
Let w(h) = -2*h**3 + 21*h**2 - 51*h + 40. Let o(q) = 2*q**3 - 22*q**2 + 52*q - 40. Let p(l) = 3*o(l) + 4*w(l). Factor p(a).
-2*(a - 5)*(a - 2)**2
Let j be (-3)/7*(-1 + -6). Suppose 2*f = j*f - 4. Let 6*x**5 - 4*x**f + x**2 + 2*x**3 - 8*x**5 + 3*x**2 = 0. What is x?
-2, -1, 0, 1
Let m(q) = -q**2 - 17*q - 14. Let w be m(-16). Factor -x**3 + x**3 + 2*x**4 + 6*x**2 - 8*x**w.
2*x**2*(x - 1)*(x + 1)
Determine z, given that 122/3 + 368/3*z + 2*z**2 = 0.
-61, -1/3
Let f(j) = 8*j**2 + 196*j + 96. Let x be f(-24). Let 3/2*p**4 + 0*p**3 + 3*p - 9/2*p**2 + x = 0. Calculate p.
-2, 0, 1
Suppose 52*b + 20*b = 0. What is d in 0 - 4/13*d + 2/13*d**4 - 6/13*d**2 + b*d**3 = 0?
-1, 0, 2
Suppose 2*m - 25 - 5 = 0. Suppose m = 3*j - 5*p, -7 = -5*p - 22. Solve 2/9*y**2 + 0*y + j = 0 for y.
0
Factor -9/8*y**3 + 3/4*y**2 + 21/8*y + 3/4.
-3*(y - 2)*(y + 1)*(3*y + 1)/8
Let t(a) = 10*a**3 + 654*a**2 + 10896*a - 11544. Let o(g) = -2*g**3 - 131*g**2 - 2179*g + 2309. Let q(l) = 16*o(l) + 3*t(l). Factor q(n).
-2*(n - 1)*(n + 34)**2
Let p(d) be the second derivative of -d**5/140 - d**4/56 + d**3/7 - 2*d**2 + 28*d. Let s(m) be the first derivative of p(m). Factor s(f).
-3*(f - 1)*(f + 2)/7
Let a(i) be the first derivative of -i**3 + 51*i**2/2 + 54*i - 92. Factor a(v).
-3*(v - 18)*(v + 1)
Let p(m) be the first derivative of m**6/45 + m**5/30 - m**4/18 - m**3/9 - 4*m - 2. Let k(y) be the first derivative of p(y). Let k(u) = 0. Calculate u.
-1, 0, 1
Let a(v) = -v**3 + 45*v**2 - 57*v + 574. Let k be a(44). Solve -1/2*d**4 + 2*d**k + 4*d - d**3 + 0 = 0 for d.
-2, 0, 2
Let j(v) be the third derivative of v**8/112 - v**7/14 + 7*v**6/40 - 3*v**5/20 - 390*v**2. Factor j(l).
3*l**2*(l - 3)*(l - 1)**2
Suppose -1863*v = -1880*v + 51. Factor 3 - 1/2*r**v - 13/2*r + 4*r**2.
-(r - 6)*(r - 1)**2/2
Let m = 40 + -36. Factor -28*g + 4*g**m - 8*g**3 + 4 + 4*g**5 - 12 - 32*g**2 + 4*g**4.
4*(g - 2)*(g + 1)**4
What is v in 1/11*v**5 + 0 + 6/11*v**3 + 7/11*v**4 + 0*v**2 + 0*v = 0?
-6, -1, 0
Let 0*s - 4/3 + 1/3*s**2 = 0. Calculate s.
-2, 2
Let o(g) be the first derivative of -g**6/27 + 8*g**5/45 + g**4/18 - 8*g**3/27 + 387. What is n in o(n) = 0?
-1, 0, 1, 4
Factor -2/3*o**4 + 14/3*o**2 + 0 + 0*o + 9*o**3.
-o**2*(o - 14)*(2*o + 1)/3
Let c(h) be the third derivative of -15*h**2 - 1/300*h**6 + 1/15*h**4 - 1/150*h**5 + 0 + 4/15*h**3 + 0*h. Factor c(b).
-2*(b - 2)*(b + 1)*(b + 2)/5
Let u(l) be the first derivative of 3*l**4/4 + 7*l**3 + 65. Factor u(f).
3*f**2*(f + 7)
Let c(x) be the first derivative of x**5 + 5*x**4/4 - 5*x**3/3 - 5*x**2/2 - 59. Factor c(p).
5*p*(p - 1)*(p + 1)**2
Let j(d) be the third derivative of d**8/84 - 4*d**7/35 + 7*d**6/15 - 16*d**5/15 + 3*d**4/2 - 4*d**3/3 + 9*d**2 - 24. Solve j(s) = 0.
1, 2
Let n = -69 + 74. Suppose -7*r + 10*r**3 + 5*r**n + 17*r**4 + 20*r**2 - 8*r - 37*r**4 = 0. What is r?
-1, 0, 1, 3
Suppose 0 = 452*y - 456*y + 12. Let d(r) be the first derivative of 0*r + 0*r**y + 0*r**2 + 3*r**4 + 7/2*r**6 + 5 + 48/5*r**5. What is c in d(c) = 0?
-2, -2/7, 0
Let j(k) be the first derivative of 2*k**3/21 + 470*k**2/7 + 110450*k/7 + 319. Let j(m) = 0. What is m?
-235
Let b(t) be the third derivative of -t**8/840 + t**7/175 + t**6/75 - 7*t**2 - 1. Factor b(f).
-2*f**3*(f - 4)*(f + 1)/5
Let o(v) be the first derivative of 11*v**3/3 + v**2 + 2*v - 17. Let f(a) = -44*a**2 - 8*a - 9. Let d(u) = -2*f(u) - 9*o(u). Factor d(y).
-y*(11*y + 2)
Let z(x) be the third derivative of 5*x**8/336 + x**7/6 + 5*x**6/8 + 3*x**5/4 - 30*x**2. Find i, given that z(i) = 0.
-3, -1, 0
Let h(x) be the second derivative of x**4/48 + x**3/8 + x**2/4 - 83*x - 1. Factor h(j).
(j + 1)*(j + 2)/4
Let u = -211 + 211. Suppose -60*k + 55*k + 10 = u. Determine l, given that 0*l + 1/5*l**5 + 0*l**k + 1/5*l**3 + 2/5*l**4 + 0 = 0.
-1, 0
Let d(r) = -8*r**3 + 9*r**2 + 43*r + 5. Let y(p) = 9*p**3 - 9*p**2 - 42*p - 6. Let l(o) = -6*d(o) - 7*y(o). Factor l(u).
-3*(u - 2)*(u + 1)*(5*u + 2)
Factor 0 - 1/4*w**2 + 41/4*w.
-w*(w - 41)/4
Let h be 6/(-4) - 68/8. Let x = h + 12. Factor 2/3 - x*k - 2/3*k**3 + 2*k**2.
-2*(k - 1)**3/3
Let m(k) = -k - 5. Let q be m(-7). Suppose i - q - 1 = 0. Factor -i*c**3 - 2*c**2 - 4*c - 4 + 9*c**3 + 4.
2*c*(c - 1)*(3*c + 2)
Let h be 4*(-3)/(-10)*120/48. Factor 2*g**4 - h*g**4 - 20*g**3 + 0*g**2 + g**2 + 21*g**3 - g**5.
-g**2*(g - 1)*(g + 1)**2
Let h