z(w). Factor p(o).
-(o + 1)**4*(o + 4)
Suppose 68*a - 49 = 61*a. Suppose 0 = -13*s + a*s + 18. Factor -10/11*t + 2/11 + 14/11*t**2 - 6/11*t**s.
-2*(t - 1)**2*(3*t - 1)/11
Suppose -9*q + 32 = 5. Factor -140*u - 24 - 62*u**2 - 243*u - 40*u**q + 471*u + 8*u**4.
2*(u - 6)*(u + 2)*(2*u - 1)**2
Let u(b) = 3*b**4 - 303*b**3 - 1893*b**2 - 2982*b - 1359. Let v(r) = r**4 - 150*r**3 - 947*r**2 - 1492*r - 680. Let o(n) = 4*u(n) - 9*v(n). Solve o(k) = 0.
-38, -6, -1
Let w(j) = j**3 - 3*j**2 + 5*j - 2. Let i = 11 + -9. Let b be w(i). Find a, given that -a**4 + 0*a**4 - 2*a**b - 2*a**2 - 6*a**3 + 5*a**4 + 6*a = 0.
-1, 0, 1, 3
Let x(j) = 374*j - 2242. Let a be x(6). Let w(q) be the second derivative of -1/36*q**6 + 0 - 5/4*q**a - 8*q - 1/4*q**5 - 25/18*q**3 - 5/6*q**4. Factor w(p).
-5*(p + 1)**3*(p + 3)/6
Let m(i) be the third derivative of -i**5/15 + 83*i**4/6 - 108*i**3 - 46*i**2 + 3. Factor m(y).
-4*(y - 81)*(y - 2)
Let u(v) = 17*v**3 + 24*v**2 - 86*v. Let n(x) = 8*x**3 + 12*x**2 - 40*x. Let w(z) = 9*n(z) - 4*u(z). Find b, given that w(b) = 0.
-4, 0, 1
Let b(l) = 5*l**3 - 271780*l - 54*l**2 - 2*l**3 + 271830*l + 19. Let k be b(17). Factor 0 - 1/4*y**k - 1/2*y.
-y*(y + 2)/4
Let o(i) be the first derivative of 0*i**2 + 0*i + 45/4*i**4 + 7*i**3 + 6/5*i**5 - 53. Let o(h) = 0. What is h?
-7, -1/2, 0
Let o(n) be the second derivative of 1/66*n**4 + 0*n**3 - 52*n + 0 - 4/11*n**2. Factor o(y).
2*(y - 2)*(y + 2)/11
Factor 24/7*j**3 - 6*j + 15/7*j**2 + 0 + 3/7*j**4.
3*j*(j - 1)*(j + 2)*(j + 7)/7
Let q be (-1234)/12 + -30 + 23. Let t = q - -352/3. Factor 0 + t*l**2 + 5*l + 5/2*l**3.
5*l*(l + 1)*(l + 2)/2
Let t(d) be the second derivative of d**7/84 + d**6/4 - 107*d**5/20 + 11*d**4/2 + 174*d**3 + 432*d**2 + 43*d - 46. Solve t(i) = 0.
-24, -2, -1, 6
Let p(r) be the first derivative of 0*r - 4/5*r**5 - r**4 + 8/3*r**3 - 58 + 0*r**2. Factor p(b).
-4*b**2*(b - 1)*(b + 2)
Let l(u) be the second derivative of 2*u**7/21 + 8*u**6/15 - 51*u**5/5 - 18*u**4 - 321*u + 1. Factor l(d).
4*d**2*(d - 6)*(d + 1)*(d + 9)
Let y(l) be the second derivative of 0*l**2 - 4/3*l**4 + 41*l + 0 + 2/15*l**6 - 8/3*l**3 + 1/5*l**5. Factor y(j).
4*j*(j - 2)*(j + 1)*(j + 2)
Factor 652/5*d**2 - 4/5*d**3 - 3888/5 - 624/5*d.
-4*(d - 162)*(d - 3)*(d + 2)/5
Let h(c) = 8*c**2 + 1030*c + 1781. Let y be h(-127). Factor 2/7*r**y + 0 + 0*r - 4/7*r**2.
2*r**2*(r - 2)/7
Let z(t) be the first derivative of -t**6/2 - 36*t**5/5 - 51*t**4/2 + 12*t**3 + 105*t**2/2 - 127. What is r in z(r) = 0?
-7, -5, -1, 0, 1
Let p(o) be the second derivative of o**6/120 - 13*o**5/10 + 169*o**4/2 - 6*o**3 + 2*o + 28. Let w(a) be the second derivative of p(a). Factor w(c).
3*(c - 26)**2
Let o(k) = -31*k**2 - 18*k - 82. Let p(x) = 108*x**2 + 54*x + 247. Let s(u) = -7*o(u) - 2*p(u). Let s(z) = 0. Calculate z.
-10, -8
Suppose -t + 8*t = 175. Solve 217 - 405*y - 3*y**4 + 45*y**2 + t*y**3 - 2*y**4 + 213 + 58 + 52 = 0 for y.
-4, 3
Suppose -2*i - 2*l + l - 2 = 0, -17 = -19*i - 5*l. Determine u, given that 8/5*u**2 + 0 - 9/5*u + 1/5*u**i = 0.
-9, 0, 1
Let q(p) be the first derivative of -4*p**5/35 + 109*p**4 - 1016*p**3/7 + 12931. Factor q(c).
-4*c**2*(c - 762)*(c - 1)/7
Let x(k) be the first derivative of 3/5*k**5 + 0*k**2 - 33/4*k**4 + 49 + 10*k**3 + 0*k. Solve x(o) = 0 for o.
0, 1, 10
Let i(t) be the second derivative of 46*t + 1/20*t**6 - 3211/4*t**3 + 6591/2*t**2 + 0 + 585/8*t**4 - 123/40*t**5. Suppose i(p) = 0. Calculate p.
2, 13
Suppose -8*o + 32 = 16. Suppose 9 = -4*m + o*r + 19, -2 = -3*m - 4*r. Factor -1/2*h - 3 + 1/2*h**m.
(h - 3)*(h + 2)/2
Let j = 1174031/116127 - -68089/621. Let g = j + -1316/11. Determine i so that -g*i**2 - 338/17 - 52/17*i = 0.
-13
Let u(s) be the second derivative of s**4/6 + 2696*s**3/3 + 1817104*s**2 - 4*s - 17. Factor u(x).
2*(x + 1348)**2
Let 2/9*z**2 - 452/3 + 446/9*z = 0. What is z?
-226, 3
Let m be 1/(-3) - (-5)/6. Let v(k) = 3*k**3 - 32*k**2 - 159*k + 1631. Let s be v(11). Factor -3/4*q + 1/4*q**s + m*q**2 + 0.
q*(q - 1)*(q + 3)/4
Let c(w) be the second derivative of w**5/90 - w**4/4 + 33*w**2 + 117*w. Let z(h) be the first derivative of c(h). Determine u, given that z(u) = 0.
0, 9
Suppose u + 4*u**4 + 2480 - 4*u - 13*u + 24568*u**3 - 12506*u**3 - 1860*u**2 - 12670*u**3 = 0. Calculate u.
-2, 1, 155
Factor -c**2 - 2*c**2 - 43*c - 60 + 75*c - c**2.
-4*(c - 5)*(c - 3)
Let f(r) be the first derivative of 1/10*r**5 + 13 + 0*r + 0*r**2 - 1/90*r**6 - 1/3*r**4 - 8/3*r**3. Let g(d) be the third derivative of f(d). Factor g(l).
-4*(l - 2)*(l - 1)
Let a = 469 + -466. Factor 60*t - 9 - 57*t - t**3 - 3*t**3 + t**a + 9*t**2.
-3*(t - 3)*(t - 1)*(t + 1)
Suppose 819*w = 789 + 849. Factor 1/8*u**w - 3/4*u + 9/8.
(u - 3)**2/8
Let u be ((3 + -206)/7)/((-1)/(-4)). Let f = -104 - u. Let -91*g**2 - 392 - 82*g**2 + f*g**3 + 389*g + 311*g - 3*g**2 = 0. Calculate g.
2/3, 7
Let v = 4045/8638 + -49/1234. Factor 6/7 - 3/7*h**3 + v*h - 6/7*h**2.
-3*(h - 1)*(h + 1)*(h + 2)/7
Suppose 283*r - 771 - 78 = 0. Let p(j) be the third derivative of 0*j + 4*j**r + 0 - 1/15*j**5 + 1/6*j**4 - 20*j**2. Factor p(c).
-4*(c - 3)*(c + 2)
Let q(t) be the first derivative of -t**5/10 - 4*t**4/3 - 7*t**3/3 + 77*t + 22. Let i(u) be the first derivative of q(u). Suppose i(b) = 0. Calculate b.
-7, -1, 0
Let o(n) be the third derivative of n**5/15 - 6*n**4 + 520*n**3/3 - 1980*n**2. Factor o(c).
4*(c - 26)*(c - 10)
Let u(o) be the first derivative of -o**4 - 716*o**3/3 - 15840*o**2 + 32400*o + 10858. Solve u(v) = 0.
-90, 1
Let h(p) = 17*p**5 - p**4 - 8*p**3 + p**2. Let u(d) = 4*d**5 - 2*d**3. Let z(a) = -8*a - 121. Let b be z(-14). Let i(t) = b*u(t) + 2*h(t). Solve i(f) = 0.
-1, 0, 1
Suppose -p = -2*u - 60, -2*p + 2*u + 77 = -33. Suppose 6*i - p = i. Factor 7*r**4 - r**2 - 2*r**2 - 19*r**4 + i*r**3 + 5*r**3.
-3*r**2*(r - 1)*(4*r - 1)
Factor -g**3 + 2*g**3 - 5072 + 135*g**2 + 3820*g - 5*g**3 + 1121*g**2.
-4*(g - 317)*(g - 1)*(g + 4)
Let c = -262 + 264. Suppose 735 + 170 + s**c - 84*s + 419 + 440 = 0. What is s?
42
Let a(d) be the first derivative of d**6/6 + 89*d**5/5 - 116*d**4 + 568*d**3/3 + 184*d**2 - 752*d - 1999. Factor a(n).
(n - 2)**3*(n + 1)*(n + 94)
Suppose 5*p = 5*w + 40, -10*p - 5*w = -6*p + 40. Let a = -8/7 - -71/56. Factor a*o**2 + p*o + 0.
o**2/8
Factor -5*b - 60*b**2 - 9*b**2 - b**3 + 16*b**2 - 37*b - 10*b.
-b*(b + 1)*(b + 52)
Let w = 873/344 - 415/172. Solve 3/8 + w*f**2 + 1/2*f = 0.
-3, -1
Let m(b) = 2*b**2 + 15*b + 6. Let k be m(-4). Let o be ((-15)/k)/3*72/45. Find p such that o*p + 6/11*p**2 + 0 = 0.
-2/3, 0
Let n(z) = z**2 - 396*z - 782. Let a(s) = -4*s**2 + 1588*s + 3129. Let r(o) = 2*a(o) + 9*n(o). Factor r(c).
(c - 390)*(c + 2)
Let j = -8230/99 - -749/9. Let t(n) be the third derivative of 1/66*n**5 - 13*n**2 + 0 + 0*n + j*n**3 + 4/33*n**4. Factor t(d).
2*(d + 3)*(5*d + 1)/11
Suppose -1617 = -7*r + 14*r. Let d be 2/(-1*14) - 4037/r. Let 36*y**2 + 28/3*y**4 + 8/3 - d*y - 92/3*y**3 = 0. Calculate y.
2/7, 1
Let j(g) be the second derivative of g**6/1620 - g**5/540 - g**3/6 + g**2 - g + 35. Let i(a) be the second derivative of j(a). Find s, given that i(s) = 0.
0, 1
Solve -1/2*p**2 - 598418 - 1094*p = 0.
-1094
Let s(i) = -6*i**2 + 1433*i - 1405. Let f(l) = 3*l**2 - 716*l + 703. Let w(c) = 11*f(c) + 5*s(c). Factor w(v).
3*(v - 236)*(v - 1)
Let o be 7 + 1*3/((-15)/25). Factor 0*l**4 + 237*l**2 + 42*l**3 + 33*l**o + 2*l**4 + 486*l.
2*l*(l + 3)*(l + 9)**2
Factor -6*z**2 + 1708470*z - 2160 + 2*z**2 - 1709026*z.
-4*(z + 4)*(z + 135)
Let j(a) = -a**2 + 9*a - 5. Let n be j(7). Let r be 1/(-3) - (-21)/n. Factor 162*o**r + 0 + 0 - 165*o**2 + 6*o.
-3*o*(o - 2)
Let d = 146864/7 - 20980. Factor 2*t - 10/7*t**2 - d.
-2*(t - 1)*(5*t - 2)/7
Let r be 74/296 + 4/(-192)*11. Let x(g) be the third derivative of 16*g**2 + 0*g - 1/480*g**6 + 0 - r*g**5 - 1/8*g**3 - 7/96*g**4. Factor x(c).
-(c + 1)**2*(c + 3)/4
Let p(i) be the first derivative of 5*i**3/3 + 5*i**2/2 - 450*i - 3709. Factor p(b).
5*(b - 9)*(b + 10)
Let b(j) be the second derivative of j**6/240 + 41*j**5/16 + 1173*j**4/2 + 164152*j**3/3 + 314432*j**2 + 5413*j. Factor b(y).
(y + 2)*(y + 136)**3/8
Factor -1029*l + 352947/2 + 3/2*l**2.
3*(l - 343)**2/2
Let m(p) = -2*p**4 - 38*p**3 + 78*p**2 - 38*p + 4. Let h(s) = -2*s**3 + 3*s**2 - s + 1. Let x(t) = -4*h(t) + m(t). Determine c so that x(c) = 0.