+ 15)/2
Suppose 5*a - p - 489 = -504, -5*a - 2*p = -30. Factor 2/3*z**2 + 28/3*z + a.
2*z*(z + 14)/3
Solve -34*d - 17 + 8*d**2 + 18*d + 101 + d**4 - 16*d**2 + 4*d**3 - 17*d**2 = 0 for d.
-7, -2, 2, 3
Suppose 39 + 61 = -5*h - 4*y, -3*y + 135 = -5*h. Let r be ((-6)/(-126))/((-2)/h). Factor 2/7*s**2 + r*s - 2/7*s**3 + 0.
-2*s*(s - 2)*(s + 1)/7
Let f = 98381 - 98381. Determine l so that -5 + 0*l**3 + 25/4*l**2 - 5/4*l**4 + f*l = 0.
-2, -1, 1, 2
Let t(n) be the third derivative of -n**5/300 - 18*n**4/5 - 429*n**3/10 - 6841*n**2. Determine o so that t(o) = 0.
-429, -3
Suppose 5*a = 6*h - 4*h + 10, -a = 3*h - 19. Factor 1 - 1 + 0 + h*v + 5*v**2.
5*v*(v + 1)
Let o be (-16)/4 + 30 + -4. Suppose -20 = 18*c - o*c. Factor -i**3 + 2*i**c - 10*i**2 - 6*i**3 + i**3 - 18*i + 2*i**4 + 14*i.
2*i*(i - 2)*(i + 1)**3
Factor 32/5*y**3 - 28*y + 16/5 + 92/5*y**2.
4*(y - 1)*(y + 4)*(8*y - 1)/5
Suppose 0 = -57052*s + 57095*s - 86. Factor 6/11*u**3 - 486/11*u**s + 13122/11*u - 118098/11.
6*(u - 27)**3/11
Let u(q) be the first derivative of 0*q**2 + 1/21*q**6 + 0*q - 2/7*q**5 - 2/3*q**3 - 13/14*q**4 - 26. Factor u(p).
2*p**2*(p - 7)*(p + 1)**2/7
Factor -2814*o**2 + 1407*o**2 + 1398*o**2 - 40*o + 42 + 163*o.
-3*(o - 14)*(3*o + 1)
Suppose 0 = -68*t + 183*t - 575. Let k(y) be the first derivative of -5*y**3 + 5/4*y**4 + 0*y + t + 0*y**2. Factor k(b).
5*b**2*(b - 3)
Let t = 1272 - 1272. Let i(v) be the third derivative of 11*v**2 + t + 1/420*v**6 - 1/84*v**4 + 0*v - 1/210*v**5 + 1/21*v**3. Determine p so that i(p) = 0.
-1, 1
Let k = 82/95 + 14/19. Let n(r) = -r**3 - 7*r**2 + 5*r - 22. Let a be n(-8). Factor -4/15 + 22/15*o - k*o**a.
-2*(3*o - 2)*(4*o - 1)/15
Let o(u) be the third derivative of -1/240*u**6 + 1/20*u**5 + 1/48*u**4 + 0*u - 1/2*u**3 - 4*u**2 - 12. What is p in o(p) = 0?
-1, 1, 6
Let g = -334120 - -334120. What is h in -1/2*h**2 + 3/2*h + g = 0?
0, 3
Let v(u) be the second derivative of u**8/43680 + u**7/1092 + 7*u**4/12 - u**2 + 61*u. Let i(g) be the third derivative of v(g). Let i(y) = 0. What is y?
-15, 0
Let q(k) be the second derivative of -k**6/240 - 41*k**5/160 - 173*k**4/32 - 1751*k**3/48 + 289*k**2/2 - 1789*k. Factor q(z).
-(z - 1)*(z + 8)*(z + 17)**2/8
Let o be 6/(-4)*9/18*-4. Factor 36995*p**4 + 11777*p**3 + 4 + 16 - 12005*p**5 + 1503*p + 15005*p**2 - 2543*p - 50752*p**o.
-5*(p - 1)**3*(49*p - 2)**2
Suppose 0 - 152/13*a + 2030/13*a**4 + 1072/13*a**2 - 2526/13*a**3 - 100/13*a**5 = 0. Calculate a.
0, 2/5, 1/2, 19
Let q(j) be the first derivative of -j**4/12 - 67*j**3/9 - 380*j**2/3 + 4332*j + 4347. Factor q(w).
-(w - 9)*(w + 38)**2/3
Let x = 5/397 + 1865/9528. Let j = 119/120 + x. Solve -j*c - 4/5 - 2/5*c**2 = 0.
-2, -1
Let j(u) be the second derivative of 1/15*u**4 - 236/15*u**3 + 6962/5*u**2 - 1 + 6*u. What is d in j(d) = 0?
59
Let t(m) be the third derivative of 17/54*m**4 + 0*m**3 - 7*m**2 + 0*m - 10 + 1/270*m**5. Determine p, given that t(p) = 0.
-34, 0
Factor 85*k - 29*k**2 - 536*k**2 - 106*k - 5*k**3 - 290*k**2 + 881*k.
-5*k*(k - 1)*(k + 172)
Let o be (-19)/(79 + -22) - 93/(-63). Suppose 8/7*b + 0 + o*b**2 - 2/7*b**4 - 2/7*b**3 = 0. Calculate b.
-2, -1, 0, 2
Let d = 5273/3 - 4915/3. Let p = 6092/51 - d. Suppose 2/17*t**5 + 8/17 - 10/17*t**3 - 10/17*t**2 + 8/17*t + p*t**4 = 0. Calculate t.
-2, -1, 1, 2
Let k(n) = n**3 - 22*n**2 + 13*n + 66. Let o be k(23). Let f = -6254/7 + o. Find z, given that 6/7*z**5 - 8/7*z**3 - 8/7*z**4 - f + 12/7*z**2 + 2/7*z = 0.
-1, -2/3, 1
Let w(x) = -4*x**2 - 19264*x - 7737692. Let o(y) = 3*y**2 + 12843*y + 5158462. Let j(f) = -8*o(f) - 5*w(f). Let j(q) = 0. Calculate q.
-803
Let m(w) be the second derivative of 3/20*w**5 - 17/12*w**4 + 5/2*w**2 + 0 + 3/2*w**3 + 33*w. Factor m(s).
(s - 5)*(s - 1)*(3*s + 1)
Let j(r) = r**2 - 235*r - 480. Let z(c) = 2*c + 1. Let y(a) = j(a) - 2*z(a). Factor y(o).
(o - 241)*(o + 2)
Let k(a) = 35*a**2 - 835*a + 1650. Let f(q) = 38*q**2 - 835*q + 1650. Let g(r) = -10*f(r) + 11*k(r). Factor g(y).
5*(y - 165)*(y - 2)
Let f(k) be the third derivative of -2*k**7/105 + 23*k**6/30 - 143*k**5/15 + 121*k**4/6 + 3739*k**2. Determine i so that f(i) = 0.
0, 1, 11
Let a(n) be the third derivative of -2*n**2 + 14 - 3/28*n**4 - 1/30*n**5 + 8/21*n**3 + 0*n - 1/735*n**7 + 3/140*n**6. Let a(t) = 0. Calculate t.
-1, 1, 8
Let w = -350 + 346. Let v(z) = -25*z**3 + 40*z**2 + 9*z. Let l(f) = 5*f**3 - 8*f**2 - 2*f. Let b = 49 - 71. Let k(h) = b*l(h) + w*v(h). Let k(d) = 0. What is d?
-2/5, 0, 2
Factor 738 + 3/2*b**2 + 132*b.
3*(b + 6)*(b + 82)/2
Let o be (78/(-26) + (-4 - -11))*(-2)/(-12). Let x(v) be the first derivative of -8/3*v**3 + 5/2*v**2 + 11/12*v**4 + 8 - o*v. Find m, given that x(m) = 0.
2/11, 1
Let r be ((-1)/(-23))/((-2816)/(-97152)). Factor -3/2 + r*n**2 + 3/4*n**3 - 3/4*n.
3*(n - 1)*(n + 1)*(n + 2)/4
Let o(w) = -w - 2. Let l(b) = 4*b - 1. Let g(n) = -3*n**2 + 81*n - 30. Let f(t) = g(t) - 18*l(t). Let p(i) = -f(i) + 6*o(i). Factor p(m).
3*m*(m - 5)
Let m(a) be the second derivative of 13*a**4/20 - 153*a**3/10 + 33*a**2 - 180*a + 2. Factor m(i).
3*(i - 11)*(13*i - 10)/5
Suppose 319*k - 315*k = 60. Factor 300*p - 564 - 436 - 45*p**2 + k*p**2 + p**3.
(p - 10)**3
Let a be (-52480)/(-2460) - (-2 - 6). Find w, given that 242/3 - a*w + 8/3*w**2 = 0.
11/2
Let m(l) = -l**2 + 10*l. Suppose -2*q + q + 3 = -w, -12 = q + 4*w. Let z(b) = q*b - 28*b - b**2 + 4*b**2 + 7*b. Let s(c) = -9*m(c) - 4*z(c). Factor s(f).
-3*f*(f + 2)
Suppose -22*d - 1152 = -19*d. Let c = 387 + d. Solve 0 + 8/7*b**c - 6/7*b**2 - 2/7*b = 0.
-1/4, 0, 1
Let m(g) be the second derivative of -g**4/32 + 25*g**3/16 - 63*g**2/4 - 1715*g. Factor m(y).
-3*(y - 21)*(y - 4)/8
Let k(w) be the third derivative of -w**6/720 - 7*w**5/18 - 1225*w**4/36 + 51*w**2 - w. Determine n, given that k(n) = 0.
-70, 0
Let s be (1 + (-20)/21)*(-276)/230*-5. Factor -288/7 - s*p**2 + 48/7*p.
-2*(p - 12)**2/7
Let r(v) be the first derivative of 19*v**5/330 + v**4/66 + 17*v**2/2 + 2*v - 131. Let s(i) be the second derivative of r(i). Factor s(x).
2*x*(19*x + 2)/11
Let h be (-330)/4*(-284)/(-355). Let k be 2/(-33) - 202/h. Factor 4/11*j**2 + 0*j**k - 2/11*j**5 - 4/11*j**4 + 2/11*j + 0.
-2*j*(j - 1)*(j + 1)**3/11
Factor 58/17*k**2 - 4536/17 + 2/17*k**3 + 144/17*k.
2*(k - 7)*(k + 18)**2/17
Determine k, given that -133/5*k + 1/5*k**2 + 132/5 = 0.
1, 132
Let w(p) be the first derivative of 0*p**2 + 1/36*p**3 - 16*p + 6 + 1/120*p**5 + 1/36*p**4. Let z(h) be the first derivative of w(h). Let z(a) = 0. What is a?
-1, 0
Suppose -288/11 - 10/11*b**4 - 760/11*b + 106/11*b**3 - 56/11*b**2 = 0. What is b?
-2, -2/5, 4, 9
Let c = -1099 - -1114. Suppose 3 = -a + i, -c*a = -11*a - 5*i + 17. Factor -1/4*w**a - 1/2 + 3/4*w.
-(w - 2)*(w - 1)/4
Let d(i) be the first derivative of i**3/21 + 187*i**2/7 + 34969*i/7 - 756. Factor d(f).
(f + 187)**2/7
Suppose -3*l - 9/8*l**2 - 1/8*l**3 - 2 = 0. What is l?
-4, -1
What is c in 274/11*c**2 + 2/11*c**4 + 58/11*c - 58/11*c**3 - 276/11 = 0?
-1, 1, 6, 23
Let s = 288 - 8. Let z = s - 1119/4. Factor 1/8*i**2 - 3/8*i + z.
(i - 2)*(i - 1)/8
Let x be 6 + -7 - (-11)/(2 - -9). Factor 3*z - 1/3*z**2 + x.
-z*(z - 9)/3
Let f(b) be the third derivative of b**5/390 + 71*b**4/52 + 212*b**3/39 - 200*b**2 + 2*b. Factor f(y).
2*(y + 1)*(y + 212)/13
Let h(d) = -5*d**2 - 869*d + 2628. Let o(u) = -15*u**2 - 2604*u + 7883. Let a(b) = -8*h(b) + 3*o(b). Factor a(m).
-5*(m - 3)*(m + 175)
Suppose 15*c = 10*c - 3590. Let o = -718 - c. Factor -1/2*l - 1/4*l**2 + o.
-l*(l + 2)/4
Let 717/7*b**2 + 168*b**3 + 0 - 474/7*b - 15/7*b**4 = 0. What is b?
-1, 0, 2/5, 79
Let c(j) be the first derivative of j**4/22 - 14*j**3/11 - j**2/11 + 42*j/11 - 1302. Factor c(u).
2*(u - 21)*(u - 1)*(u + 1)/11
Let r(c) be the first derivative of c**3/12 - 133*c**2/8 + 160*c - 2967. Factor r(s).
(s - 128)*(s - 5)/4
Let f(l) be the third derivative of l**7/42 - l**6/8 + 5*l**4/6 - 9*l**2 - 51*l. Factor f(n).
5*n*(n - 2)**2*(n + 1)
Let z(c) be the second derivative of -c**7/504 + c**6/18 + 11*c**4/12 - 6*c - 2. Let n(r) be the third derivative of z(r). Solve n(g) = 0 for g.
0, 8
Let r = 5942/17 + -66727/68. Let q = 632 + r. Factor s**3 + 3/2*s**2 + 1/4 + q*s**4 + s.
(s + 1)**4/4
Let d be (-44)/(-24) - (-100)/(-75). Let r = 716 - 714. Factor -5/8*h + d*h**r + 1/8.
(h - 1)*(4*h - 1)/8
Let a = 1/2812 - 112656