
Let n = 3034 + -3018. Factor -18/7*p**4 - n*p**2 + 2/7*p**5 + 96/7*p + 64/7*p**3 - 32/7.
2*(p - 2)**4*(p - 1)/7
Let t(l) = 10*l**2 + 106*l + 768. Let u(i) = 28*i**2 + 316*i + 2307. Let m(c) = -11*t(c) + 4*u(c). Suppose m(h) = 0. Calculate h.
-39, -10
Let n be (-306)/18 - -9 - (-228)/27. Let 1/9*u**3 - 5/9*u - n*u**2 + 0 = 0. Calculate u.
-1, 0, 5
Let z = 110/9 - 877/72. Let a(p) be the first derivative of -1/6*p**2 - 1/6*p**3 - z*p**4 + 6 + 0*p. Factor a(v).
-v*(v + 1)*(v + 2)/6
Let x be 14*25/(-13475)*-42. Factor -9/11*w - 5/11*w**3 - x*w**2 - 2/11.
-(w + 1)**2*(5*w + 2)/11
Let p(u) be the second derivative of u**7/28 - 2*u**6/5 - 57*u**5/40 - 5*u**4/4 + 192*u + 1. Factor p(h).
3*h**2*(h - 10)*(h + 1)**2/2
Let m(u) = 4*u**5 + 429*u**4 + 10346*u**3 - 46640*u**2 + 48400*u - 5. Let k(h) = h**4 - 2*h**3 - 1. Let n(l) = -5*k(l) + m(l). Solve n(b) = 0 for b.
-55, 0, 2
Suppose -24 = -7*i - p, -603*i = -598*i - 4*p - 3. Factor 4/11*h**2 - 2/11*h + 0*h**i - 4/11*h**4 + 0 + 2/11*h**5.
2*h*(h - 1)**3*(h + 1)/11
Let x(t) be the third derivative of 2*t**7/105 + 323*t**6/30 + 11663*t**5/5 + 1293737*t**4/6 + 4900172*t**3/3 - 1221*t**2. Factor x(u).
4*(u + 2)*(u + 107)**3
Let j be 13 + (-7)/(-14)*-16. Suppose 3*x + 32 = -48*b + 52*b, -j*x - 30 = -2*b. Determine z so that -2*z**2 + 0*z + 2*z**3 + 1/2*z**4 + 0 - 1/2*z**b = 0.
-2, 0, 1, 2
Solve 133/3*k**5 + 12 + 1823/3*k**3 - 92*k - 907/3*k**4 - 809/3*k**2 = 0 for k.
-2/7, 2/19, 1, 3
Suppose 88*w - 85*w + 19 = -a, 3*a + w + 1 = 0. Let d(h) be the second derivative of 0 - a*h**2 + 14/3*h**4 - 11/3*h**3 - 7*h - 3/2*h**5. What is b in d(b) = 0?
-2/15, 1
Suppose 7 = -3*x - 29, 1 = 3*k - 3*x - 41. Factor -21/2*u + 11 - 1/2*u**k.
-(u - 1)*(u + 22)/2
Let x(u) be the second derivative of u**6/42 - 17*u**5/10 - 101*u**4/84 + 17*u**3/3 + 48*u**2/7 - 129*u + 8. Solve x(b) = 0 for b.
-1, -2/5, 1, 48
Let b(n) be the third derivative of 3/200*n**6 + 1/350*n**7 + 1/100*n**5 - 1/5*n**3 - 5*n**2 + 0 + 13*n - 3/40*n**4. Factor b(k).
3*(k - 1)*(k + 1)**2*(k + 2)/5
Let v(g) = 21*g**2 + 768*g - 1540. Let k(f) = 92*f**2 + 3076*f - 6160. Let r(n) = 2*k(n) - 9*v(n). Factor r(o).
-5*(o - 2)*(o + 154)
Let t be ((-4)/4)/((-319)/(-64) - 5). Solve -t*c**2 - 35*c**4 - 37951*c**5 - 21*c**4 - 124*c**3 + 37955*c**5 = 0.
-1, 0, 16
Let v(x) be the second derivative of x**8/336 + x**7/28 + x**6/6 + x**5/3 - x**3/3 + 59*x. Let f(h) be the second derivative of v(h). Factor f(d).
5*d*(d + 2)**3
Let d(n) be the third derivative of n**7/70 + n**6/10 + 3*n**5/20 - n**4/2 - 2*n**3 + 73*n**2 + 2*n. Suppose d(p) = 0. What is p?
-2, -1, 1
Let o be (1575/(-28))/(-15)*40. Suppose -o*v = -154*v + 8. What is c in 0*c**4 + 2/11*c**3 + 0 + 0*c**v + 0*c - 2/11*c**5 = 0?
-1, 0, 1
Suppose 5*i = 2*u - 12, -2*u + 6*u - 3*i = -4. Let c be (4/(-7))/(u/14). Factor -n**3 + n**c - 785 + 785.
-n**2*(n - 1)
Suppose 301 = 5*j + 4*c, j - 68 = -2*c - 3. Suppose -3*b = -3*v + v + j, -v = 2*b - 46. Solve -32*o**3 + 22*o**4 + 26*o**4 - v*o**2 + 36*o + 58 - 66 = 0 for o.
-1, 1/2, 2/3
Let o(x) = -5*x**2 - x. Let q(p) = 17*p**2 - 3146*p - 826875. Let n(y) = -4*o(y) - q(y). Let n(i) = 0. What is i?
-525
Let y(c) be the first derivative of c**8/1680 + c**7/840 - c**6/360 - c**5/120 - 91*c**3/3 + 19. Let h(u) be the third derivative of y(u). Factor h(z).
z*(z - 1)*(z + 1)**2
Let v be 11 - (14 + (-22 - -15)). Let x(g) be the second derivative of 0*g**3 + 0*g**2 - 1/66*g**v + 0 + 7*g. Factor x(a).
-2*a**2/11
Let k be (24/28)/((-14464)/(-448) - 32). Factor -1/7*o**k - 16/7*o**2 - 52/7*o - 48/7.
-(o + 2)**2*(o + 12)/7
Let a = 3 - -2. Let d(s) = -s**2. Let c(t) = -3*t - 12*t + 2*t**2 - 1381 + 2761 - 1380. Let p(u) = a*d(u) + c(u). Factor p(z).
-3*z*(z + 5)
Determine v so that 2/5*v**2 + 179560 - 536*v = 0.
670
Suppose 37 = 3*n + 1. Let u(p) = 8*p - 3*p**2 - 20 + p**2 - 7*p**2 + p**2. Let f(q) = q**2 - q + 1. Let v(b) = n*f(b) + u(b). Solve v(w) = 0 for w.
-1, 2
Let f(i) be the second derivative of -i**6/20 - 3*i**5/2 - 51*i**4/8 + 18*i + 32. Factor f(w).
-3*w**2*(w + 3)*(w + 17)/2
Let g = -32276/15 - -258253/120. Determine d so that 15/4*d - g*d**2 + 33/8 = 0.
-1, 11
Let h(n) be the second derivative of -12/5*n**5 + 6 + 3*n + 36*n**2 - 34*n**3 + 44/3*n**4. Factor h(a).
-4*(2*a - 3)**2*(3*a - 2)
Let x(h) be the second derivative of h**4/60 + 733*h**3/3 + 2686445*h**2/2 - 9226*h. Factor x(b).
(b + 3665)**2/5
Let q(i) be the first derivative of i**6/30 + 3*i**5/20 - i**4/6 - 2*i**3 - 4*i**2 + 2*i + 2. Let h(o) be the first derivative of q(o). Factor h(u).
(u - 2)*(u + 1)*(u + 2)**2
Factor 2/5*s**4 + 0 + 28798/5*s**2 + 478/5*s**3 + 28322/5*s.
2*s*(s + 1)*(s + 119)**2/5
Find s, given that 0 - 36/5*s**3 + 34/5*s**2 + 2/5*s**4 + 0*s = 0.
0, 1, 17
Let j(i) be the first derivative of 7/12*i**2 - 5/18*i**3 + 1/24*i**4 - 84 - 1/2*i. Solve j(y) = 0 for y.
1, 3
Let d(y) be the second derivative of -y**5/45 - 25*y**4/18 - y**2 - 2*y - 10. Let o(t) be the first derivative of d(t). What is v in o(v) = 0?
-25, 0
Let a(y) be the third derivative of 7*y**3 + 0 - 5*y**2 + 17*y + 9/4*y**5 - 43/8*y**4 - 17/40*y**6 + 1/70*y**7. Suppose a(i) = 0. What is i?
1, 14
Let l(s) be the first derivative of 4*s**2 - 3*s - 4*s**3 - 32*s**2 - 100 + 10*s**3 - 17*s - 2*s**3. Factor l(w).
4*(w - 5)*(3*w + 1)
Let t be (-44)/(-28) + -1 + (-17490)/30485. Let d = t - -7849/4355. Find a, given that 0 - 3*a**4 + 36/5*a**2 - 12/5*a - d*a**3 = 0.
-2, 0, 2/5, 1
Let g(w) be the third derivative of w**5/45 + 2153*w**4/9 + 9270818*w**3/9 + 49*w**2 + 22*w. Factor g(u).
4*(u + 2153)**2/3
Let c = -1001898 - -9017102/9. What is j in c*j - 14/3 - 2/9*j**2 = 0?
3, 7
Let t(q) be the third derivative of -q**8/40320 + q**7/180 - 49*q**6/90 + q**5/2 + 122*q**2. Let h(y) be the third derivative of t(y). Let h(o) = 0. What is o?
28
Suppose -120*t + 12297 + 6474 = 6137*t. Let -54/11 - 18/11*d**2 - 2/11*d**t - 54/11*d = 0. Calculate d.
-3
Find s such that -3*s**4 + 31*s - 2*s - 21*s**2 - 74*s + 21*s**3 = 0.
-1, 0, 3, 5
Let p = -127/4149 + 366763/53937. What is s in p*s**2 + 28/13*s**3 + 80/13*s + 2/13*s**4 + 0 = 0?
-10, -2, 0
Let l(b) be the second derivative of 5/8*b**4 + 0 + 15/2*b**2 - 126*b - 27/4*b**3. What is c in l(c) = 0?
2/5, 5
Let h(z) be the third derivative of 0*z - 12/5*z**3 - 1/12*z**6 + 2/5*z**4 + 15*z**2 + 7/30*z**5 + 2. Let h(q) = 0. What is q?
-1, 6/5
Let i(g) be the second derivative of 8/15*g**6 + 0*g**3 + 0 - 64/3*g**4 - 2/21*g**7 + 16/5*g**5 + 0*g**2 + 16*g. Factor i(k).
-4*k**2*(k - 4)**2*(k + 4)
Let a be 22/(-77) - ((-23)/7 + 0). Suppose 15*q**5 - 19*q**5 + 9*q**a - 12*q + 7*q**3 - 35*q**2 + 27*q**2 + 8*q**4 = 0. Calculate q.
-1, 0, 1, 3
Let t be 2*9/42 - 522/(-7). Suppose -r - 4*r = -t. Factor 5*p**2 - 6 + r*p + 13*p + 2*p - 4*p**3 - 7*p.
-(p - 3)*(p + 2)*(4*p - 1)
Let m(o) = -8*o**2 - 29*o - 9. Let l(t) = 7*t**2 + 30*t + 10. Let d = -40 - -91. Let y = d - 48. Let z(u) = y*l(u) + 2*m(u). Factor z(b).
(b + 6)*(5*b + 2)
Let w = -5/85668 - -16064/21417. Find a such that 1/4*a**2 + 0 + w*a**3 - 1/2*a = 0.
-1, 0, 2/3
Let t(q) be the third derivative of q**7/42 + q**6/4 + q**5/4 - 25*q**4/12 + 49*q**2 + 6. Factor t(f).
5*f*(f - 1)*(f + 2)*(f + 5)
What is h in -788/9*h**2 - 16/3 + 1600/9*h = 0?
6/197, 2
Let m be (1 - (-219)/18) + (0 + (-132)/24 - -10). Suppose 20*j**3 - m*j**2 + 0*j + 49/3*j**4 + 4/3 - 20*j**5 = 0. Calculate j.
-1, -1/4, 2/5, 2/3, 1
Let t(v) = -16*v**2 - 173*v - 482. Let d(r) = 123*r**2 + 1209*r + 3375. Let h(s) = 2*d(s) + 15*t(s). Factor h(k).
3*(k - 32)*(2*k + 5)
Let 9 + 81/2*q + 83/2*q**4 - 97/2*q**3 - 101/2*q**2 + 8*q**5 = 0. What is q?
-6, -1, -3/16, 1
Let d = -6609 - -132183/20. Let j(k) be the second derivative of 0*k**3 + 0 + d*k**5 + 0*k**2 + 1/4*k**4 + 11*k. Factor j(p).
3*p**2*(p + 1)
Let a = 94 - 82. Let c(m) = m**2. Let w(q) = -q**3 + 3*q**4 + 5*q**2 + 4*q**3 - 2*q**4. Let t(j) = a*c(j) - 4*w(j). Solve t(u) = 0 for u.
-2, -1, 0
Let r(j) = -j + 149. Let f be r(-26). Suppose f*b - 45 = 160*b. Find y such that 0*y + 1/4*y**2 + 0 + 1/4*y**5 - 1/4*y**4 - 1/4*y**b = 0.
-1, 0, 1
Factor -275*d - 253*d + 1608 - 1076*d - 4*d**2.
-4*(d - 1)*(d + 402)
Let s = -10651/60 - -888/5. Let c(n) be the first derivative of -16/3*n - n**3 - s*n**4 + 7 - 4*n**2. Find o such that c(o) = 0.
-4, -1
Let z be 26 - 655/30 - 12/8