Let r be s(12). Let b be 1 + r + (-512)/272 - -5. Determine c so that -2/17*c**5 - 2/17*c**2 + 0 + 2/17*c**4 + b*c**3 + 0*c = 0.
-1, 0, 1
Let u(l) be the second derivative of -l**7/84 - l**6/20 - l**5/40 + l**4/8 + l**3/6 - 56*l + 2. Suppose u(d) = 0. Calculate d.
-2, -1, 0, 1
Suppose -100*f + 98*f = 5*t + 11, 5 = -5*f - 5*t. Let -4/7*z**4 + 0*z**f + 8/7*z + 4/7 - 8/7*z**3 = 0. What is z?
-1, 1
Suppose -5*u - 19 = -2*z - 0*u, z + 13 = -5*u. Factor 626 + 2*f**3 - 16*f**z - 602 - 4*f - 6*f**3.
-4*(f - 1)*(f + 2)*(f + 3)
Find g, given that 1/5*g**5 + 6/5*g**4 + 0 + 9/5*g**3 + 4/5*g**2 + 0*g = 0.
-4, -1, 0
Let h(b) be the third derivative of b**5/12 + 5*b**4/8 - 10*b**3/3 + 251*b**2. Factor h(v).
5*(v - 1)*(v + 4)
Suppose 0*l - l = 5*m - 11, 22 = 2*l + 4*m. Let p = l + -1. Suppose 48*v**3 + 18*v**3 - 74*v**2 - p*v**4 + 4*v**5 - 2*v**3 - 16*v**4 - 8 + 40*v = 0. What is v?
1/2, 1, 2
Let n(o) be the first derivative of o**5/10 + 2*o**4/3 + 5*o**3/3 + 2*o**2 + o - 10. Let t(g) be the first derivative of n(g). Suppose t(z) = 0. Calculate z.
-2, -1
Let b(y) be the first derivative of 5 - 3/2*y - 1/6*y**3 + y**2. Let b(h) = 0. What is h?
1, 3
Let h = -36305/11 - -3305. Factor -h - 20/11*w - 2/11*w**2.
-2*(w + 5)**2/11
Factor -36/13 - 22/13*q - 2/13*q**2.
-2*(q + 2)*(q + 9)/13
Let q(h) be the first derivative of -2*h**3/9 + 14*h**2 + 86*h/3 + 192. Suppose q(w) = 0. Calculate w.
-1, 43
Let o(k) = -k**3 + k - 1. Let l(a) = 45*a**3 - 40*a**2 - 9*a + 7. Let u(s) = 2*l(s) + 6*o(s). Let u(r) = 0. Calculate r.
-1/3, 2/7, 1
Let n(k) be the second derivative of -k**5/90 - 37*k**4/54 + 38*k**3/27 - 286*k. Let n(i) = 0. Calculate i.
-38, 0, 1
Let d be (-7 - 678/(-120))*(-10)/12. What is x in -3/8*x**2 - d*x - 3/4 = 0?
-2, -1
Let u(a) be the second derivative of -a**4/42 + 26*a**3/21 - 169*a**2/7 - 33*a. What is o in u(o) = 0?
13
Let s be 138/345 + 0/(-1) - 0. Solve -6/5*y**2 - 2/5*y**4 + 0 - s*y - 6/5*y**3 = 0 for y.
-1, 0
Let n be 2/(-5) - 31/5 - -7. Factor n*i**3 + 6/5*i + 2/5 + 6/5*i**2.
2*(i + 1)**3/5
Let q(f) be the third derivative of f**10/30240 - f**9/3780 + f**8/1344 - f**7/1260 - f**4/6 - 9*f**2. Let o(u) be the second derivative of q(u). Factor o(j).
j**2*(j - 2)*(j - 1)**2
Let i be (-4)/((-5)/(-2 + -8)*-10). Determine d, given that i - 12/5*d + 1/5*d**4 - 6/5*d**3 + 13/5*d**2 = 0.
1, 2
Let d = -228 + 232. Let i(x) be the second derivative of d*x - 1/14*x**4 + 0*x**2 + 3/140*x**5 + 0*x**3 + 0. Factor i(z).
3*z**2*(z - 2)/7
Factor -22*g**3 - 2*g**4 - 1923*g**2 + 1893*g**2 + 6*g**3.
-2*g**2*(g + 3)*(g + 5)
Let k be 5 - (-2 + 6 + -4). Solve 125*i**3 - 35*i**3 + 30*i + 10*i - 11*i**5 + 16*i**k + 100*i**2 + 35*i**4 = 0.
-2, -1, 0
Let p(n) = n**3 + n + 1. Let r(q) = -5*q**3 - 9*q - 8. Let x(u) = 6*p(u) + r(u). Suppose x(g) = 0. Calculate g.
-1, 2
Factor -9/2*w**2 + 1/4*w**3 - 15/2 + 47/4*w.
(w - 15)*(w - 2)*(w - 1)/4
Let n(q) = -5*q**2 + 6*q - 5. Let l(b) = -81*b**2 + 96*b - 81. Let j be (2 - 0)*18 - (-11 + 14). Let s(u) = j*n(u) - 2*l(u). Factor s(k).
-3*(k - 1)**2
Let o(j) = j**2 + 5*j + 6. Let m be o(-4). Let y(d) = 2*d**2 - 3*d. Let p be y(m). What is c in 4*c**2 - 6*c**p + 4 + 5*c**2 - 4*c**2 = 0?
-2, 2
Let n(m) be the second derivative of -m**4/60 - 7*m**3/10 + 11*m**2/5 + 3*m - 25. Solve n(s) = 0 for s.
-22, 1
Let n(m) be the second derivative of m**4/126 - 2*m**3/7 - 19*m**2/21 - 25*m. Let n(g) = 0. Calculate g.
-1, 19
Let f = 2223 + -2218. Factor -4*a**2 + a**3 + 7/2*a - 1 + a**4 - 1/2*a**f.
-(a - 1)**4*(a + 2)/2
Let n be (-3 + 3)/(4 + -8 - -6). Let z(q) be the third derivative of n*q**4 + 0 - 4*q**2 + 1/180*q**5 + 0*q**3 + 0*q. Factor z(c).
c**2/3
Let t be 54/54 + 5/1. Let a(k) be the second derivative of 1/12*k**4 + 4*k**5 - 5/6*k**t - 6*k**2 - 22/3*k**3 + 0 + 4*k. Factor a(p).
-(p - 3)*(p - 1)*(5*p + 2)**2
Let v(r) be the third derivative of r**8/1344 - r**7/252 + r**6/144 - 5*r**4/12 + 12*r**2. Let g(a) be the second derivative of v(a). Factor g(s).
5*s*(s - 1)**2
Suppose 83*k - 55*k - 40 - 44 = 0. Determine c so that 50/3 + 2*c**2 + 2/15*c**k + 10*c = 0.
-5
Factor 22707 + 103*v**2 + 101*v**2 + 522*v - 306*v**2 + 105*v**2.
3*(v + 87)**2
Let b(g) be the third derivative of 125*g**8/672 - 5*g**7/28 - 97*g**6/48 + 299*g**5/120 - 5*g**4/4 + g**3/3 - 109*g**2. Solve b(a) = 0 for a.
-2, 1/5, 2
Factor -205*t - 5/4*t**2 - 8405.
-5*(t + 82)**2/4
Determine c, given that -94*c**3 + 4*c - 17*c**2 - 36 - 10*c**2 + 64*c**3 + 49*c + 67*c + 9*c**4 = 0.
-2, 1/3, 2, 3
Let r be 26208/8892 - (-1)/19. Factor -3/8*j**r + 117/8*j**2 + 6591/8 - 1521/8*j.
-3*(j - 13)**3/8
Suppose -a**4 - 35*a**3 - 382*a**2 + 80*a - 4*a**4 - 419*a**2 + 761*a**2 = 0. What is a?
-4, 0, 1
Suppose 40 = -5*k + 7*k. Let -17 + 30*y**2 + 43 + 0*y**4 - 20*y**3 + 5*y**4 - k*y - 21 = 0. What is y?
1
Let o = -4428 - -4428. Solve -4/5*i - 2/5*i**2 + o = 0 for i.
-2, 0
Factor -2*x**2 + 235*x - 2*x**2 + 453*x - x**2 - 29584 + x**2.
-4*(x - 86)**2
Determine i so that 2/15*i**2 + 64/15 - 8/5*i = 0.
4, 8
Suppose 3*w - 7 = -52. Let x be ((-8)/(-14) - w/35)*0. Factor 2/5*i**5 + 0 + 4/5*i**4 + 0*i**3 + 0*i + x*i**2.
2*i**4*(i + 2)/5
Let r(b) be the second derivative of -b**4/24 + 19*b**3/12 + 2*b + 9. Factor r(a).
-a*(a - 19)/2
Let o(d) be the third derivative of -1/20*d**3 + 1/100*d**5 + 0 + 0*d + 17/240*d**4 + 9*d**2. Factor o(s).
(s + 3)*(6*s - 1)/10
Let k(y) be the third derivative of y**10/151200 + y**9/30240 - 13*y**5/60 - 16*y**2. Let i(t) be the third derivative of k(t). Let i(b) = 0. Calculate b.
-2, 0
Let h = 1303 + -1303. Factor -3*p + 1/3*p**5 + 8/3*p**3 + 2*p**2 + h - 2*p**4.
p*(p - 3)**2*(p - 1)*(p + 1)/3
Let l(f) = 22*f**3 + 40*f**2 + 18*f - 40. Let r(i) = -2*i**3 - i**2 - 2*i + 1. Let g(u) = -l(u) - 10*r(u). Factor g(s).
-2*(s - 1)*(s + 1)*(s + 15)
Let s be -1 + 1 + (-11 - -14). Factor -3*a**s + a**3 + 5*a**3 + 5 + 15*a**2 + 2*a**3 + 15*a.
5*(a + 1)**3
Let i(l) be the second derivative of -1/36*l**4 - 2/3*l**3 + 7*l + 0 - 6*l**2. Factor i(o).
-(o + 6)**2/3
Suppose -9*x**3 + 53*x**4 + 11*x**3 + 68 - 13*x**2 - 54*x**4 - 72*x + 16*x**3 = 0. What is x?
-2, 1, 2, 17
Let g = 80 - 75. Factor 5 - g - 4*n**4 - 7*n - n + 12*n**2.
-4*n*(n - 1)**2*(n + 2)
Let s(i) be the third derivative of 0*i**4 - 4/525*i**7 - 1/50*i**6 + 0*i + 0*i**3 + 0*i**5 + 0 - 15*i**2 + 1/420*i**8. Find w, given that s(w) = 0.
-1, 0, 3
Let d(k) = k**2 - 4. Let v be d(3). Suppose -a = -2*b - 3, v*a - b = -0*b + 24. Factor 0*i**2 - i**4 + 6 - a*i + 3*i**2 - 4 + i**3.
-(i - 1)**3*(i + 2)
Let m be ((-15)/45)/(32/(-72)). Solve m*a + 3/8*a**2 - 9/8 = 0 for a.
-3, 1
Factor 111*h**2 - 54*h**2 + 4*h**5 + 40*h**4 + 53*h**2 + 28*h + 105*h**3 + h**5 + 12*h.
5*h*(h + 1)**2*(h + 2)*(h + 4)
Suppose 0 = 3*q - 2*q - 3. Let f(u) be the first derivative of -3*u - q*u + u**3 - u + 4*u + 6. Determine b, given that f(b) = 0.
-1, 1
Let f = -112 - -117. What is l in -l**2 + f*l**2 + 0*l**2 + 609*l - 613*l = 0?
0, 1
Let r(u) be the second derivative of 2*u**6/105 - u**5/70 - u**4/42 - 58*u - 1. Determine s so that r(s) = 0.
-1/2, 0, 1
Suppose 839*z = 835*z. Let o(h) be the second derivative of z + 1/42*h**4 - 2/7*h**2 + 6*h - 1/21*h**3. Solve o(u) = 0 for u.
-1, 2
Suppose -4*o - 16 = 0, -a - 4*o + 0*o - 14 = 0. Factor -5*n**5 + a*n**3 - 3*n - n - n + 8*n**3.
-5*n*(n - 1)**2*(n + 1)**2
Suppose -4*m = -2*m + 2*r - 10, -4*r - 10 = -2*m. Suppose 5 = -m*o + 135. Solve 34*n**4 - 7*n**4 + 5*n**3 - 6*n**2 - o*n**3 = 0.
-2/9, 0, 1
Let c be (-1)/(-6 - (-11 - -8)). Let j(q) be the first derivative of 0*q - 3/2*q**2 - c*q**3 + 7. Factor j(r).
-r*(r + 3)
Let r(z) be the second derivative of -z**9/30240 + z**7/5040 + 7*z**4/12 - 7*z. Let b(h) be the third derivative of r(h). Factor b(p).
-p**2*(p - 1)*(p + 1)/2
Let j = -8/101 + 335/404. Determine n, given that 1/2*n + j - 1/4*n**2 = 0.
-1, 3
Let h(v) be the third derivative of 1/180*v**6 - 1/36*v**4 + 0 - 1/90*v**5 + 0*v + 1/9*v**3 + 12*v**2. Factor h(a).
2*(a - 1)**2*(a + 1)/3
Let t = 38 - 30. Suppose 4*w - 5*w = 4*n + 8, -4*n = -2*w + t. Suppose -2*o**3 - 1/3*o + w - 7/3*o**2 = 0. Calculate o.
-1, -1/6, 0
Let f be (12/(-14))/(-3) - 15/175. Let z(b) be the first derivative of b**2 - 4 + 0*b**3 - 1/2*b**4 + f*b**5 - b. Factor z(j).
(j - 1)**3*(j + 1)
Let v be (-8118)/(-1107) - 16/3. Factor 1/11*r**v + 0 + 2/11*r.
r*