t o be q(h). Determine v, given that 2/19*v**4 + 0*v**2 - 4/19*v + 4/19*v**o - 2/19 = 0.
-1, 1
Let f(b) be the third derivative of b**7/70 - 27*b**6/40 - 25*b**5/4 + 27*b**4/8 + 62*b**3 + 168*b**2 - 4*b. Find s such that f(s) = 0.
-4, -1, 1, 31
Let i(d) be the first derivative of 2/11*d + 6/11*d**3 - 94 + 7/22*d**4 + 4/55*d**5 + 5/11*d**2. Find v such that i(v) = 0.
-1, -1/2
Let j = -3062289/13 + 235561. Factor -14/13*o**2 - j*o + 0.
-2*o*(7*o + 2)/13
Let x(r) be the first derivative of -5*r**3/3 + 15*r**2 - 40*r + 1591. What is g in x(g) = 0?
2, 4
Let k(u) = -u**3 + 6*u**2 + 17*u - 65. Let c be k(7). Determine s so that -s**4 - 4*s**c + 17*s - 3*s + 50*s + 17*s**4 - 64*s**2 = 0.
-2, 0, 2
Let z(t) be the first derivative of -132 + 1/4*t**4 - 1/2*t**2 - 11/12*t**3 + 5*t. Factor z(s).
(s - 2)**2*(4*s + 5)/4
Let n = -24977/2 + 174851/14. What is p in n*p**2 - 8/7 + 8/7*p - 8/7*p**3 + 2/7*p**4 = 0?
-1, 1, 2
Let f(l) be the second derivative of -l**7/21 - 11*l**6/15 - 2*l**5/5 + 10*l**4 - 15*l - 127. Determine t, given that f(t) = 0.
-10, -3, 0, 2
Let w = 100 - 78. Solve -23*y**2 - 55 - 105*y - w*y**2 - 34*y**3 + 14*y**3 + 25*y**3 = 0 for y.
-1, 11
Suppose 0 = 3*d - 3*w + 36, 0 = 307*w - 152*w - 160*w + 75. Factor -d*v**4 + 9*v**3 + 0*v + 0*v**2 + 0 + 1/4*v**5.
v**3*(v - 6)**2/4
Let w(f) = -2*f. Let g be ((-1)/2)/(29/(-58)). Let o(l) = -2*l**3 - 18*l**2 - 36*l. Let x(i) = g*o(i) - 10*w(i). Find k, given that x(k) = 0.
-8, -1, 0
Let u(q) be the second derivative of 1/24*q**5 + 23*q + 0 - 1/180*q**6 - 1/252*q**7 + 1/72*q**4 - 2/9*q**3 + 1/3*q**2. What is n in u(n) = 0?
-2, 1
Let z be ((-24)/(-10))/((-21)/(-70)). Let q be 26/7 - z/(-28). Suppose 159 + 32*m - 6*m**2 + 4*m**2 - 31 + q*m**2 = 0. Calculate m.
-8
Let c(d) = 6*d**2 - 486*d + 513. Let g(k) = -7*k**2 + 487*k - 524. Let m(r) = 4*c(r) + 3*g(r). Solve m(b) = 0 for b.
1, 160
Let i(h) = -111*h**3 - 2724*h**2 + 2109*h + 834. Let w(v) = -16*v**3 - 389*v**2 + 301*v + 119. Let q(m) = -5*i(m) + 36*w(m). Determine l, given that q(l) = 0.
-19, -2/7, 1
Factor 0 - 2/5*x**2 - 114/5*x.
-2*x*(x + 57)/5
Let u(n) be the second derivative of 6*n**5 + 521*n**4/6 - 170*n**3/3 + 9*n**2 - 8942*n - 2. Find k, given that u(k) = 0.
-9, 1/15, 1/4
Let g(p) = -3*p**4 - 7*p**3 + 7*p**2 - 2*p + 10. Let z(c) = -3*c**4 - 6*c**3 + 7*c**2 - 2*c + 8. Let w(n) = -4*g(n) + 5*z(n). Let w(k) = 0. What is k?
-2, 0, 1/3, 1
Find j such that 0 + 310*j**3 - 313/2*j**2 - 309/2*j**4 + j = 0.
0, 2/309, 1
Factor 693*u**3 - 1124*u**2 + 1153*u**4 - 820*u**3 - 273*u - 1149*u**4.
u*(u - 39)*(u + 7)*(4*u + 1)
Suppose 4*p = -11*r + 16*r, -5*p = 2*r. Suppose 5*d = 4*v + 20, 26*d - 28*d + 8 = r. Factor 8/9*t + v - 2/9*t**2.
-2*t*(t - 4)/9
Let h be -1 + -1 - ((-5)/200 + (-11766)/2960). Let k = 1288/5 - 256. Factor 12/5*o**3 - 28/5*o + 8/5 + k*o**h.
4*(o - 1)*(o + 2)*(3*o - 1)/5
Let o = -6315 + 6320. Let m(l) be the third derivative of 0*l**4 + 1/90*l**6 + 0*l + 0*l**3 + 1/630*l**7 + 0 + 1/60*l**o + 9*l**2. Factor m(n).
n**2*(n + 1)*(n + 3)/3
Let t(q) = -q**2 - 16*q - 30. Let d be t(-14). Let u be (5 - (-2 - d))*(-18)/(-30). Factor 10*y**3 - u*y**4 + 2*y**2 - 4*y**3 - 5*y**2.
-3*y**2*(y - 1)**2
Let c be 2 + (-3669)/189 + (-164)/(-123). Let p = c + 139/7. Let 16/9*h**2 - 2/3*h**4 + 0 - p*h**3 + 8/3*h = 0. Calculate h.
-6, -2/3, 0, 1
Suppose -169 = -2*t + 2*k + 61, -4*t - k = -460. Suppose 3*j = t - 25. Find x such that -29*x - 11*x + x**4 + 0*x**4 + 4*x**4 - 15 - j*x**2 = 0.
-1, 3
Find v, given that 40 - 469*v + 356*v + 405*v**2 + 558*v = 0.
-1, -8/81
Let x = -90 + 93. Let t(r) = 4*r - 49. Let h be t(13). Factor -3/2*u**h + 9/4 - x*u**2 + 3/2*u + 3/4*u**4.
3*(u - 3)*(u - 1)*(u + 1)**2/4
Let q(n) be the first derivative of 44/3*n**3 - 34 + 9/10*n**5 - 8*n**2 - 19/3*n**4 + 33*n. Let g(w) be the first derivative of q(w). Factor g(t).
2*(t - 2)**2*(9*t - 2)
Let u(v) = -12*v**2 - 84*v - 16. Let w(h) be the first derivative of -4*h**3/3 - 14*h**2 - 5*h - 19. Let b(m) = 5*u(m) - 16*w(m). Solve b(k) = 0.
-7, 0
Factor -1/7*r**3 - 58*r**2 - 405/7*r + 0.
-r*(r + 1)*(r + 405)/7
Let g be 1/(-7 - (8 + 76/(-5))). Let j(t) be the second derivative of 0 - 1/18*t**4 + 11*t + 2/27*t**3 + 1/90*t**g + 0*t**2. Factor j(h).
2*h*(h - 2)*(h - 1)/9
Let a(l) be the first derivative of -1/10*l**6 - 4/25*l**5 - 3/10*l**2 + 0*l + 7/10*l**4 - 4/15*l**3 - 37. Suppose a(s) = 0. Calculate s.
-3, -1/3, 0, 1
Let m = 327329/21 - 46580/3. Determine d, given that 66/7 + 303/7*d + 24*d**3 + m*d**2 + 12/7*d**4 = 0.
-11, -2, -1/2
Let z = -1526 - -1526. Let f(b) be the second derivative of z*b**2 - 5/48*b**4 - 1/120*b**6 + 1/12*b**3 + 0 + 1/20*b**5 - 11*b. Factor f(u).
-u*(u - 2)*(u - 1)**2/4
Let v = -7711 + 7715. Let n(l) be the second derivative of 0*l**2 - 1/168*l**7 + 0*l**v + 0*l**6 + 0*l**3 + 0 + 22*l + 1/80*l**5. Factor n(i).
-i**3*(i - 1)*(i + 1)/4
Let d(f) = -15*f**2 - 420*f + 655. Let x be -48 + -10 + 7 + -4. Let z(h) = h**2 + 30*h - 47. Let j(p) = x*z(p) - 4*d(p). Factor j(k).
5*(k - 1)*(k + 7)
Let a be (-12)/54*6 + 6/(-9). Let g(v) = 5*v**3 + 19*v**2 - 41*v + 23. Let z(r) = -4*r**3 - 18*r**2 + 40*r - 22. Let x(o) = a*g(o) - 3*z(o). Factor x(n).
2*(n - 1)**2*(n + 10)
Let i(d) = d**3 - 2*d**2 - 5. Let g(q) = 33*q**3 - 180*q**2 + 237*q + 162. Let h(x) = g(x) - 36*i(x). Factor h(t).
-3*(t - 3)*(t + 1)*(t + 38)
Let q = 234 - 127. Factor -62*p**2 + q*p**2 - 49*p - 35*p - 12.
3*(p - 2)*(15*p + 2)
Let p(y) be the third derivative of 1/120*y**6 + 0 - 1/60*y**5 - 1/336*y**8 + 0*y**4 + 87*y**2 + 0*y**3 + 0*y + 1/210*y**7. Factor p(v).
-v**2*(v - 1)**2*(v + 1)
Suppose -15 = -6*h + 75. Suppose 3*f = -4*r + 7*f, f - h = -4*r. Suppose 6*v**2 - 16*v - v**2 + 16*v + 5*v**4 + 10*v**r = 0. Calculate v.
-1, 0
Let t(r) be the first derivative of r**5/5 - 19*r**4/2 + 12*r**3 + 19*r**2 - 37*r + 655. Factor t(c).
(c - 37)*(c - 1)**2*(c + 1)
Determine l, given that 322*l + 40 - 985*l + 3*l**2 + 296*l + 326*l - 2*l**2 = 0.
1, 40
Let r(m) be the second derivative of -m**5/40 + 22*m**4/3 - 2639*m**3/4 + 7569*m**2/2 + 38*m - 3. Let r(f) = 0. Calculate f.
2, 87
Let s = 13 - -13. Suppose 7 = -w - 2*k + 6*k, -4*w = 2*k - s. Suppose 16*f**3 + 5*f**2 + 8*f - 25*f**2 - 5 + w - 4*f**4 = 0. Calculate f.
0, 1, 2
Let g(j) = -j**2 - j - 16. Let o(s) = s**2 - s + 15. Let q be (-30)/(-4) + (-14)/112*12. Let v(x) = q*o(x) + 5*g(x). Factor v(w).
(w - 10)*(w - 1)
Let f(c) be the first derivative of c**3/3 + 6*c**2 + 30*c - 17. Let v(i) = 3. Let a(l) = -f(l) - 2*v(l). Factor a(h).
-(h + 6)**2
Suppose 0 = 4*k - 240 - 204. Let y = k - 109. Find c such that 1/5 + 1/5*c**4 + 1/5*c**5 - 2/5*c**y + 1/5*c - 2/5*c**3 = 0.
-1, 1
Suppose -4*p = 3*x + 48, 0 = -x + 203*p - 187*p + 244. Solve 82/17*h**3 + 0 - 82/17*h + 2/17*h**2 - 2/17*h**x = 0 for h.
-1, 0, 1, 41
Let -1/2*v**3 - 5/2*v - 1 - 2*v**2 = 0. What is v?
-2, -1
Suppose -2*k + 5*u + 37 = 47, -3*k + 4 = 2*u. Let v(i) be the first derivative of k*i + 4/3*i**3 - 10 - i**4 + 4*i**2. Factor v(c).
-4*c*(c - 2)*(c + 1)
Let u = 50 + -22. Suppose 0 = -3*n + u + 2. Let r**3 - 2 - 2*r - 9*r**3 - n*r - 16*r**2 - 2*r**2 = 0. Calculate r.
-1, -1/4
Let w(d) be the third derivative of 0 + 0*d**3 + 0*d**4 + 1/140*d**6 - d - 3/70*d**5 - 15*d**2. Solve w(k) = 0.
0, 3
Let s = -79239/35 + 2265. Let f = s + -109/140. Factor -g + 3/2*g**2 - g**3 + f*g**4 + 1/4.
(g - 1)**4/4
Factor 374352 + 10*o**2 - 15*o**2 + 2440*o - 364512.
-5*(o - 492)*(o + 4)
Let n(f) be the third derivative of -f**6/960 - 49*f**5/96 - 1829*f**4/24 + 961*f**3 - 28*f**2. Find m, given that n(m) = 0.
-124, 3
Suppose 1/4*p**5 - 17/4*p**2 + 17/4*p**4 - 1/4*p**3 + 0*p + 0 = 0. What is p?
-17, -1, 0, 1
Find q such that 8/3*q**4 + 44/3 + 1/3*q**5 - 38/3*q**3 + 37/3*q - 52/3*q**2 = 0.
-11, -1, 1, 4
Let o be (3 - (-82)/60) + 4378/(-132) + 33. Factor -o*r**4 - 9/5 + 3/5*r**5 + 39/5*r - 66/5*r**2 + 54/5*r**3.
3*(r - 3)*(r - 1)**4/5
Let x = 21224/15 - 4072/3. Factor x - 48/5*r + 2/5*r**2.
2*(r - 12)**2/5
Let d(i) be the first derivative of i**4/22 + 190*i**3/11 - 574*i**2/11 - 6918. Determine m, given that d(m) = 0.
-287, 0, 2
Suppose -i + 5735*o = 5733*o - 18, 3*o + 20 = -2*i. Suppose 4/5*q**4 + 6/5*q**3 - 8/5*q**i - 2/5*q**5 + 0 - 8/5*q = 0. What is q?
-1, 0, 2
Factor -18/7*f**3 + 260/7*f**2 + 0 + 0*f.
-2*f**2*(9*f - 130)/7
Let x(t) = 4*t