*2*(s + 6)
Let z(p) = 6*p**2 - 7*p + 8. Let u be z(2). Let v be (54/24)/(u/24). Factor 0 - 10/3*l**4 + 0*l + 0*l**2 - 5/3*l**5 - 5/3*l**v.
-5*l**3*(l + 1)**2/3
Solve -64 + 9*r**4 + 23732*r**2 + 296*r - 47481*r**2 - 74*r**3 + 23729*r**2 = 0.
-2, 2/9, 2, 8
Let -a**3 + 14*a**2 - 124*a**2 - 223*a - 114*a**2 = 0. What is a?
-223, -1, 0
Let s(r) be the first derivative of -15*r**3 + 425*r**2/2 - 180*r - 871. Let s(c) = 0. Calculate c.
4/9, 9
Suppose -6*x + 644 = -2*k - 10*x, 2*k = 3*x - 651. Let p = k - -326. Suppose 10*u**3 + 10 - 15/2*u**p - 10*u - 5/2*u**4 = 0. What is u?
-1, 1, 2
Let r be ((-40)/(-100))/((-11)/(-10) - 1). Suppose 4*l - 9 = -0*l + l. What is a in -4/5*a**r - 16/5 + 12/5*a**2 + 8/5*a**l - 16/5*a = 0?
-1, 2
Suppose 4*t + 192 = 4*p, 2*p = 4*t + 46 + 154. Let l = 55 + t. Factor -16*k - 17*k**2 - 7*k**2 - 15*k**3 + 3*k**3 + k**4 - l*k**4.
-2*k*(k + 2)**3
Let a(r) be the second derivative of r**6/10 + 4773*r**5/10 + 2534461*r**4/4 + 2529690*r**3 + 3792150*r**2 - 5613*r. Factor a(y).
3*(y + 1)**2*(y + 1590)**2
Let j(y) be the first derivative of y**4/32 + 3*y**3/4 - 39*y**2/16 + 5*y/2 - 1156. Factor j(k).
(k - 1)**2*(k + 20)/8
Let m = 3987 + -3984. Let a(q) be the third derivative of 0 - 1/204*q**4 + 0*q - 1/510*q**5 + 0*q**m + 5*q**2. Factor a(t).
-2*t*(t + 1)/17
Let d(h) be the first derivative of -1/10*h**4 + 2*h**2 - 7/25*h**5 + 4/5*h + 7/5*h**3 + 67. Let d(n) = 0. What is n?
-1, -2/7, 2
Factor 602*a - 147*a**2 - 1849/3.
-(21*a - 43)**2/3
Let a(h) = 5*h**2 - 537*h - 1890. Let m(r) = -r**2 + 90*r + 315. Let c(k) = 2*a(k) + 13*m(k). Factor c(u).
-3*(u - 35)*(u + 3)
Suppose 2047*g + 156 = 2086*g. Let a(f) be the first derivative of 0*f**3 - 1/12*f**2 - 1/36*f**6 + 0*f**5 + 1/12*f**g - 43 + 0*f. Factor a(u).
-u*(u - 1)**2*(u + 1)**2/6
Let a = 193 - 191. Find x such that 2*x**3 + 2*x**a + 7*x**2 + 151*x - 141*x + 3*x**2 = 0.
-5, -1, 0
Factor 1144*w - 4*w**2 + 2278 + 2967 - 6385.
-4*(w - 285)*(w - 1)
Suppose 31/2*s**3 - 147/2*s + 171/5 - 185/2*s**2 + 3/10*s**4 = 0. Calculate s.
-57, -1, 1/3, 6
Suppose -14*z = -59 + 3. Let v be (3/(-9))/(z/(-36)). Factor -7/2*f**4 + 0 + 5/2*f**v - 1/2*f**2 + 0*f + 3/2*f**5.
f**2*(f - 1)**2*(3*f - 1)/2
Let q(k) be the first derivative of k**4/28 - 73*k**3/21 - 113*k**2/7 - 152*k/7 + 911. Factor q(v).
(v - 76)*(v + 1)*(v + 2)/7
Suppose 44 = -28469*i + 28474*i - 3*o, 8*o = 4*i + 32. Find y, given that 17/4*y**2 - 20*y - 1/4*y**3 + i = 0.
1, 8
Let o(a) be the first derivative of a**7/7140 + 11*a**6/3060 + 238*a**3/3 + 87. Let n(w) be the third derivative of o(w). Factor n(k).
2*k**2*(k + 11)/17
Let o(n) = -n**5 + 421*n**4 + 1415*n**3 + 319*n**2. Let i(u) = 140*u**4 + 472*u**3 + 116*u**2. Let r(f) = -11*i(f) + 4*o(f). Let r(x) = 0. Calculate x.
-3, 0, 39
Suppose -z + 4*r + 1 = 2*z, -16 = -2*z - 5*r. Factor -533 + 521 - 18*p**3 + 3*p**z - 39*p**2 - p**4 - 37*p.
-(p + 1)**3*(p + 12)
Let y(t) = 2*t**2 - 4237*t + 2115. Let s(z) = -11*z**2 + 25423*z - 12690. Let n(a) = 4*s(a) + 25*y(a). Find l, given that n(l) = 0.
1/2, 705
Let g(o) be the third derivative of o**8/1344 - o**7/840 - 7*o**6/240 + 7*o**5/60 + o**4/12 - 4*o**3/3 + 690*o**2. Factor g(r).
(r - 2)**3*(r + 1)*(r + 4)/4
Let p(v) be the third derivative of 11/720*v**6 - 6*v**2 - 17/1260*v**7 + 0 + 5/2016*v**8 - 1/9*v**4 + 1/9*v**3 + 13/360*v**5 + 0*v. Solve p(i) = 0.
-1, 2/5, 1, 2
Let x = -819 - -835. Let z(c) be the first derivative of -x + 3/8*c**4 + 0*c + 0*c**3 + 0*c**2 + 1/10*c**5. Factor z(y).
y**3*(y + 3)/2
Let a(d) = 2*d**3 + 3*d - 3. Suppose 5 = -422*j + 427*j. Let q be a(j). Solve 0 + 0*n - 6/7*n**3 + 0*n**q = 0 for n.
0
Let i(q) = 3 + 453*q**3 + 4*q - 3*q**2 - 458*q**3 - 3*q. Let t(n) = -11*n**3 - 5*n**2 + 3*n + 7. Let c(y) = -5*i(y) + 2*t(y). Factor c(h).
(h + 1)**2*(3*h - 1)
Let a = -117 - -103. Let j be 2/6 - a/30. Suppose -1/5*b**4 - 6/5*b**2 - j*b - 4/5*b**3 - 1/5 = 0. What is b?
-1
Let i(q) be the third derivative of 19*q**6/90 + 79*q**5/90 + 11*q**4/9 + q**3/3 + 678*q**2 - 3*q. Factor i(g).
2*(g + 1)**2*(38*g + 3)/3
Let w be ((-8)/(-252) + 0)/(12/9). Let p(c) be the third derivative of w*c**7 - 5/6*c**3 + 0*c + 13*c**2 + 0*c**5 + 0 - 5/12*c**4 + 1/12*c**6. Factor p(s).
5*(s - 1)*(s + 1)**3
Let j(x) be the second derivative of x**4/66 - 4*x**3/11 - 288*x**2/11 - 17*x + 6. Factor j(f).
2*(f - 24)*(f + 12)/11
Let x = 43 - 41. Factor x*i**3 - 22*i**2 - 25*i - 4 + 51*i + 40*i - 14*i**2 - 28.
2*(i - 16)*(i - 1)**2
Let u(d) = -d**4 + 84*d**3 - 265*d**2 + 290*d - 124. Let z(m) = 2*m**4 - 83*m**3 + 265*m**2 - 295*m + 123. Let t(b) = -3*u(b) - 4*z(b). Factor t(p).
-5*(p - 12)*(p - 2)*(p - 1)**2
Let l(j) be the first derivative of 2/7*j**3 - 8/7*j + 82 + 1/7*j**2. Factor l(a).
2*(a - 1)*(3*a + 4)/7
Let z be (-3)/(-27) + (-136)/(-72). Factor 16*b**4 - 3*b**3 - 6*b**2 - 3*b**3 - 2*b - 20*b**4 + z*b**4.
-2*b*(b + 1)**3
Let p(n) be the second derivative of -n**7/21 - n**6/15 + 6*n**5/5 + 536*n + 2. Let p(g) = 0. Calculate g.
-4, 0, 3
Let q(n) = 14*n**3 + 238*n**2 + 1422*n + 2262. Let l(f) = -6*f**3 - 96*f**2 - 569*f - 905. Let x(o) = -12*l(o) - 5*q(o). Suppose x(h) = 0. What is h?
-3, 25
Let d = 8543/79317 - -30/8813. What is s in 37/9*s - 20/9*s**2 - 2 + d*s**3 = 0?
1, 18
Suppose 15*y - 104 - 631 = 0. Factor 0*r**2 - 123*r**3 + y*r**5 - 2*r**2 + 96*r**3 - 84*r**4.
r**2*(r - 2)*(7*r + 1)**2
Let v(m) be the third derivative of 0 + 289/24*m**3 + 0*m + 25*m**2 + 1/240*m**5 + 17/48*m**4. Factor v(w).
(w + 17)**2/4
Factor -620/3*g**2 + 2/3*g**3 + 48050/3*g + 0.
2*g*(g - 155)**2/3
Let i(d) be the first derivative of d**4/10 + 374*d**3/15 - 386*d**2/5 - 3024*d/5 - 12788. Factor i(o).
2*(o - 4)*(o + 2)*(o + 189)/5
Suppose -2*n + 18 = 4*t, 0 = 3*t - 1289*n + 1287*n - 3. Let -2/9*b**5 + 10/3*b**2 - 8/3 - 2/3*b**4 + 10/9*b**t - 8/9*b = 0. What is b?
-3, -2, -1, 1, 2
Let b(m) be the third derivative of m**7/195 - 103*m**6/780 - 71*m**5/195 - 8*m**4/39 - 2*m**2 - 105*m. Suppose b(o) = 0. What is o?
-1, -2/7, 0, 16
Let h(j) be the first derivative of 0*j**2 + 7*j - 1/3*j**3 - 5 + 1/12*j**4. Let t(v) be the first derivative of h(v). Find f, given that t(f) = 0.
0, 2
Let c(g) = -3*g**4 + g**3 - g + 2. Let t(d) = -13*d**4 + 562*d**3 + 2470*d**2 + 1091*d + 10. Let l(z) = -5*c(z) + t(z). Factor l(n).
n*(n + 4)*(n + 274)*(2*n + 1)
Let u be (0 + -15)/(8/(-32)). Solve -86*x**3 + 360 - 86*x**3 - 50*x**2 + 274*x**3 + u*x - 97*x**3 = 0 for x.
-2, 6
Let m(u) = -2*u**2 - 34*u - 58. Let c be m(-15). Factor 107*b**c + 2*b + 0*b**3 - 3*b**3 - 68*b**2 - 38*b.
-3*b*(b - 12)*(b - 1)
Let b(g) be the second derivative of 2*g**7/63 - 368*g**6/45 - 748*g**5/15 - 752*g**4/9 - 10218*g. Determine q, given that b(q) = 0.
-2, 0, 188
Let q(k) be the first derivative of -2*k**3/33 - 167*k**2/11 - 3251. Factor q(g).
-2*g*(g + 167)/11
Let q = 1462 - 1463. Let m be 3 + q - (-480)/(-280). Let 242/7 - 44/7*p + m*p**2 = 0. Calculate p.
11
Solve -1119/5*q**2 + 834774/5*q + 1/10*q**3 - 207580468/5 = 0 for q.
746
Let f(w) be the first derivative of w**4/40 + 14*w**3/15 - 59*w**2/20 + 3*w + 486. Factor f(x).
(x - 1)**2*(x + 30)/10
Determine k so that -5994722 - 2*k**4 - 92*k**3 + 1568*k**3 + 5994722 + 5*k**4 = 0.
-492, 0
Suppose 0 = 5*b + u - 34, 90 = 268*b - 256*b + 3*u. Factor -3/2*m**b + 0 - 243*m + 24*m**3 - 135/2*m**2.
-3*m*(m - 9)**2*(m + 2)/2
Let i = -26 - -28. Suppose -i*u = 46 - 54. Factor w**4 + 17*w + 6*w**2 - 12*w**3 + 19*w - 4*w**u - 25 - 2.
-3*(w - 1)**2*(w + 3)**2
Let b(r) = 9*r**5 - 27*r**4 - 16*r**3 + 5*r**2 + 5*r. Let s(f) = -5*f**5 + 16*f**4 + 8*f**3 - 2*f**2 - 2*f. Let a(y) = -2*b(y) - 5*s(y). Factor a(i).
i**3*(i - 4)*(7*i + 2)
Let c(g) = 2*g**2 + 449*g + 16022. Let p be c(-180). Determine i, given that -20/9*i + 22/9*i**p + 0 - 2/9*i**3 = 0.
0, 1, 10
Let q = -73377 - -73379. Solve -4/3*d**q + 80/3*d + 0 = 0.
0, 20
Factor 1/6*m**3 + 91/6*m + 0 + 10/3*m**2.
m*(m + 7)*(m + 13)/6
Let d be (69/9 - (-17 - -25))*-39. Let l(o) be the first derivative of 1/18*o**4 + 4/27*o**3 + d + 0*o - 1/3*o**2. Let l(t) = 0. What is t?
-3, 0, 1
Let b(h) = -54*h**3 - 146*h**2 + 152*h + 309. Let t(o) = 33*o**3 + 88*o**2 - 91*o - 186. Let s(g) = -8*b(g) - 13*t(g). Factor s(r).
3*(r - 2)*(r + 1)*(r + 9)
Let a(y) be the first derivative of -25*y**6/6 - 560*y**5 - 18889*y**4 + 52974*y**3 - 100035*y**2/2 + 19494