 = -17*k**3 + 27*k**2 + 30*k + 19. Suppose -14*v = -31 + 115. Let g(r) = v*s(r) + 11*w(r). Factor g(p).
(p - 4)*(p + 1)*(3*p + 1)
Let s = -8103 + 8106. Factor -32/5*k - 2/5*k**s + 24/5 + 14/5*k**2.
-2*(k - 3)*(k - 2)**2/5
Let k be 3*16/6 + -4. Suppose 4*w = 3*w + 13. Solve 8*v**4 + v**4 - w*v**3 + v**3 - v**4 + k*v**2 = 0.
0, 1/2, 1
Let t(n) be the second derivative of -n**6/40 - 9*n**5/40 - 9*n**4/16 - n**3/2 - 133*n. Solve t(k) = 0.
-4, -1, 0
Let y = 3 + 33. What is u in u**5 + 2*u**4 - 36 + 3*u**3 + y - 5*u**4 - u**2 = 0?
0, 1
Determine m, given that 14*m + 18*m**2 - 60 + 0*m + 10*m - 15*m**2 = 0.
-10, 2
Let m(p) be the second derivative of p**5/100 + p**4/6 - 2*p**3/15 - 4*p**2 - 244*p. Let m(y) = 0. What is y?
-10, -2, 2
Suppose 909/2*h**2 + 91809/2*h + 3090903/2 + 3/2*h**3 = 0. What is h?
-101
Factor -8*q**3 + 166/3*q**2 + 121/3 - 88*q + 1/3*q**4.
(q - 11)**2*(q - 1)**2/3
Let q be (0 + -4)/4 - -3. Solve -15*k - 3*k**q + 13 - 19 - 12 = 0 for k.
-3, -2
Let a(o) be the first derivative of 1/48*o**4 - 4 + o - 1/8*o**2 + 1/24*o**3 - 1/80*o**5. Let k(y) be the first derivative of a(y). Factor k(l).
-(l - 1)**2*(l + 1)/4
Let p(n) be the second derivative of -n**5/40 + n**4/16 + n**3/3 - 3*n**2/2 - 127*n. Solve p(l) = 0 for l.
-2, 3/2, 2
Let d(j) = -2*j - 15. Let x be d(-13). Determine w, given that 3*w - 3 + 0*w**2 + x + 5*w - 2*w**3 - 2*w**2 = 0.
-2, -1, 2
Factor -2304*m + 96*m**2 - 4/3*m**3 + 18432.
-4*(m - 24)**3/3
Suppose 3*y - 3 = 9. Factor -3*g**2 + 1 - 4*g**4 - 1 + 7*g**y.
3*g**2*(g - 1)*(g + 1)
Let m = -11 - 30. Let f = m - -43. Factor 1/3*q**f - 1/3*q + 0.
q*(q - 1)/3
Let n(h) be the second derivative of -h**4/4 - 102*h**3 - 15606*h**2 - 2*h + 62. Factor n(u).
-3*(u + 102)**2
Let c(b) be the third derivative of 0*b - 10*b**2 + 0 - 1/30*b**5 + 1/12*b**4 + 0*b**3. Factor c(p).
-2*p*(p - 1)
Let b = 4/319 - -311/638. Factor -1/3*t + 1/6*t**5 + 0 + 1/6*t**3 - b*t**2 + 1/2*t**4.
t*(t - 1)*(t + 1)**2*(t + 2)/6
Suppose 7/5 + 6/5*g - 1/5*g**2 = 0. Calculate g.
-1, 7
Suppose -4*z + 98 = -2. Suppose -5*b = -0*b - z. Factor b*x**3 - 9*x**2 + 0*x**3 - 3*x**4 + 3*x + 4*x**3.
-3*x*(x - 1)**3
Suppose -5*r + 23 = 4*g, -5*r + 7 + 6 = -g. Let l be r/(-9)*(4 + (-848)/14). Let -16/7*v - 74/7*v**4 - 2*v**5 - l*v**3 - 88/7*v**2 + 0 = 0. What is v?
-2, -1, -2/7, 0
Let z(q) be the second derivative of -q**5/80 - 9*q**4/4 - 243*q**3/2 + 2*q + 556. Factor z(k).
-k*(k + 54)**2/4
Let v be 7/(-21)*3*-4 + 1. Factor -4/9*h**4 + 0*h**2 + 0*h + 2/9*h**3 + 0 + 2/9*h**v.
2*h**3*(h - 1)**2/9
Let u be (1/(-3))/(-4 - 47/(-12)). Suppose -2*g = -6, 9*g - u*g = 4*c + 7. Let -1/2*h**c - 1 + 3/2*h = 0. What is h?
1, 2
Let n = -129 - -115. Let d be (-1)/((7/n)/((-10)/(-8))). Factor -1 + 1/2*y**4 + d*y - 1/2*y**3 - 3/2*y**2.
(y - 1)**3*(y + 2)/2
Let f(d) be the first derivative of -d**5/20 - d**4/4 - 5*d**3/12 - d**2/4 - 242. Factor f(v).
-v*(v + 1)**2*(v + 2)/4
Let w(l) = -4*l**5 - 18*l**4 - 8*l**2 + 4*l. Let y(q) = -2*q**5 - 8*q**4 - 4*q**2 + 2*q. Let h(t) = 6*w(t) - 13*y(t). Solve h(b) = 0 for b.
-1, 0, 1
Let b(j) be the second derivative of -9/10*j**5 - 1/21*j**7 + 0*j**4 + 2/5*j**6 + 0*j**2 + 23*j + 0*j**3 + 0. Factor b(t).
-2*t**3*(t - 3)**2
Factor 12/5*y**2 + 0*y + 0 + 3/5*y**4 + 3*y**3.
3*y**2*(y + 1)*(y + 4)/5
Factor -2/15*l**3 - 8/5 + 2/15*l + 8/5*l**2.
-2*(l - 12)*(l - 1)*(l + 1)/15
Let j(w) be the second derivative of w**6/600 - w**5/100 - 3*w**4/40 - 11*w**3/6 + w. Let p(y) be the second derivative of j(y). Find l, given that p(l) = 0.
-1, 3
Let q(b) be the first derivative of 43 + 3/10*b**4 - 4/5*b**3 + 9/5*b - 3/5*b**2 + 3/25*b**5. What is l in q(l) = 0?
-3, -1, 1
Let v(s) be the first derivative of s**5/15 + 5*s**4/12 - 14*s**3/9 - 6*s**2 + 24*s + 411. Factor v(y).
(y - 2)**2*(y + 3)*(y + 6)/3
Suppose 9/7*c**2 - 33/7*c - 3 + 33/7*c**3 + 12/7*c**4 = 0. Calculate c.
-7/4, -1, 1
Let n be (-41364)/(-18576) + (-6)/(-258). Determine g so that -3/4*g**4 + n*g**2 - 3*g + 3/2*g**3 - 3 = 0.
-1, 2
Let r(m) be the first derivative of 5*m**4/12 - 5*m**3/6 - 15*m + 3. Let t(p) be the first derivative of r(p). Find z such that t(z) = 0.
0, 1
Let c(f) be the third derivative of f**7/630 - f**6/90 + f**5/30 - 3*f**4/8 - 15*f**2. Let a(p) be the second derivative of c(p). Find z, given that a(z) = 0.
1
Let q(a) be the third derivative of -a**5/20 + 7*a**4/36 + 4*a**3/9 - 166*a**2. Factor q(v).
-(v - 2)*(9*v + 4)/3
Let t(s) be the third derivative of -s**7/735 + 3*s**6/140 + 11*s**5/70 + 5*s**4/12 + 4*s**3/7 - 3*s**2 + 16*s. Let t(g) = 0. Calculate g.
-1, 12
Let o be 2 - ((-96)/(-45) + (-2)/15). Factor 0*n**3 + o - 1/4*n + 3/8*n**2 - 1/8*n**4.
-n*(n - 1)**2*(n + 2)/8
Factor 22*f + 221*f**3 - 6*f**2 - 26*f - 223*f**3.
-2*f*(f + 1)*(f + 2)
Let d(t) = -t**2 - 34*t - 49. Let b(g) = -35*g - 50. Let q(r) = -4*b(r) + 5*d(r). Determine j so that q(j) = 0.
-3
Factor -7/4*m**2 - 2 + 7/2*m + 1/4*m**3.
(m - 4)*(m - 2)*(m - 1)/4
Factor 0 + 16 + 1 + 8 + 20*l - 5*l**2.
-5*(l - 5)*(l + 1)
Let b be (51/27 + -2)/(21/(-252)). Let z(a) be the second derivative of 0 - b*a**3 - 3*a - 1/3*a**4 - 2*a**2. Solve z(c) = 0.
-1
Let q be (-36)/(-6) - 6/(2/1). What is l in 6*l**2 - 5*l**2 + 2*l**q - 4*l**3 + l**3 = 0?
0, 1
Determine z, given that 15*z**3 - 112*z**2 - 1/2*z**4 - 15*z + 225/2 = 0.
-1, 1, 15
Factor -26/5*s - 4/5*s**2 + 2/5*s**3 - 4.
2*(s - 5)*(s + 1)*(s + 2)/5
Let l = -26 + 19. Let n(o) = o**2 - 125*o**3 + 1 - 7*o + 74*o**2 - 2 - 6*o. Let b(k) = -375*k**3 + 225*k**2 - 38*k - 4. Let x(p) = l*n(p) + 2*b(p). Factor x(a).
(5*a - 1)**3
Let p(f) = f**3 - 6*f**2 + 9*f - 4. Let u = -14 - -18. Let z be p(u). Factor -4/7*i**2 + 0 + z*i.
-4*i**2/7
Let a(t) = 5*t**3 - 10*t**2 + 10*t + 5. Let g(f) = -5*f**3 + 10*f**2 - 11*f - 6. Let n = -4 - 1. Let r(h) = n*g(h) - 6*a(h). Factor r(j).
-5*j*(j - 1)**2
Let v = -783 - -786. Determine b, given that 1/2*b**v + 1/2*b - b**2 + 0 = 0.
0, 1
Factor 1/4*x**2 + 4*x - 57/4.
(x - 3)*(x + 19)/4
Let 35/2*k**3 - 3/2*k**5 + 0*k + 0 + 9/2*k**2 + 23/2*k**4 = 0. Calculate k.
-1, -1/3, 0, 9
Let u be (-42)/(-4)*6/9. Let n(c) = 2*c**2 - 10*c - 26. Let p be n(u). Factor -2/9*a + 2/9*a**3 - 2/9*a**4 + 0 + 2/9*a**p.
-2*a*(a - 1)**2*(a + 1)/9
Let j(o) be the third derivative of 0 - 1/12*o**4 + 0*o + 23*o**2 + 1/70*o**5 + 2/21*o**3. Factor j(q).
2*(q - 2)*(3*q - 1)/7
Let o be 12*((-17)/(-3) - (-5 - -9)). Let y be 2*(56/o + -1). Determine s so that 54/5 + 54/5*s + 2/5*s**3 + y*s**2 = 0.
-3
Let j(v) = v**3 + 8*v**2 + 8*v + 13. Let b be j(-7). Factor b*c**3 + 37*c - 34*c**2 - 13 + 7*c - 3.
2*(c - 4)*(c - 1)*(3*c - 2)
Let t(z) be the third derivative of -z**5/12 - 125*z**4/24 - 5*z**2 + 16. Find y such that t(y) = 0.
-25, 0
Let y = 26329/520 - 613/40. Let t = -35 + y. Factor -16/13*u**2 - t - 14/13*u - 4/13*u**3 + 2/13*u**5 + 4/13*u**4.
2*(u - 2)*(u + 1)**4/13
Let t be (-8)/(-600)*-5*(0 + -3). Let -4/5*j + 3/5 + t*j**2 = 0. What is j?
1, 3
Let m = -22 - -18. Let s = m - -7. Let -2/11*t + 0*t**s + 4/11*t**4 - 4/11*t**2 + 0 + 2/11*t**5 = 0. What is t?
-1, 0, 1
Let x(o) be the first derivative of 2*o**3/21 + 9*o**2/7 - 44*o/7 + 52. Factor x(d).
2*(d - 2)*(d + 11)/7
Let m(u) be the first derivative of 8*u**6/3 - 20*u**5 + 54*u**4 - 208*u**3/3 + 44*u**2 - 12*u + 83. Factor m(n).
4*(n - 3)*(n - 1)**3*(4*n - 1)
Let m(t) be the second derivative of 1/96*t**4 + 0 + 1/24*t**3 + 7*t + 1/16*t**2. Determine i so that m(i) = 0.
-1
Let w(c) be the third derivative of -c**6/240 - 7*c**5/60 - 43*c**4/48 - 5*c**3/2 - 453*c**2. Factor w(x).
-(x + 1)*(x + 3)*(x + 10)/2
Let o(k) be the second derivative of k**6/75 + 2*k**5/25 + k**4/30 - 2*k**3/5 + 2*k - 24. Find b, given that o(b) = 0.
-3, -2, 0, 1
Let o(b) be the second derivative of -b**6/840 + b**5/280 - 5*b**3/3 + 2*b. Let f(w) be the second derivative of o(w). Determine n, given that f(n) = 0.
0, 1
Let y(j) be the second derivative of 1/8*j**2 - 1/12*j**3 + 5*j + 1/40*j**5 + 0*j**4 - 1/120*j**6 + 0. Factor y(d).
-(d - 1)**3*(d + 1)/4
Let d(a) be the first derivative of 4*a**3/3 - 56*a**2 + 560. Factor d(s).
4*s*(s - 28)
Let i(y) be the first derivative of -1/28*y**4 + 2 + 4/21*y**3 - 5/14*y**2 + 2/7*y. Solve i(n) = 0 for n.
1, 2
Let d(q) be the second derivative of q**7/14 - 4*q**6/5 - 18*q**5/5 + 155*q**4/2 - 425*q**3/2 - 1125*q**2 + 210*q - 1. Let d(j) 