Suppose 0 = -2*k + 3*y + 32, 5*k = -5*y + 2*y + 38. Factor k + 8*z**2 - 13*z**2 - 4*z - z.
-5*(z - 1)*(z + 2)
Let y(r) be the third derivative of -r**5/50 + 449*r**4/60 - 298*r**3/15 - 207*r**2. Factor y(i).
-2*(i - 149)*(3*i - 2)/5
Suppose -5*d = -m - 26 + 8, d + 4*m = -9. Let c(k) be the second derivative of 1/36*k**4 + 1/18*k**d + 0 + 0*k**2 - 3*k. Factor c(t).
t*(t + 1)/3
Let l(f) be the first derivative of 3*f**5/35 - 3*f**4/4 + 15*f**3/7 - 39*f**2/14 + 12*f/7 - 79. Factor l(z).
3*(z - 4)*(z - 1)**3/7
Let a(t) be the second derivative of 2*t**4 - 9*t**3/2 + 3*t**2/2 - 16*t + 1. Solve a(z) = 0 for z.
1/8, 1
Let u(v) = 51*v**3 - 360*v**2 + 666*v + 102. Let k(t) = -152*t**3 + 1079*t**2 - 1999*t - 305. Let l(j) = 6*k(j) + 17*u(j). Factor l(a).
-3*(a - 4)**2*(15*a + 2)
Let j(i) be the second derivative of -1/15*i**6 + 1/10*i**5 + 0*i**3 - 6*i + 0*i**4 + 0*i**2 + 2. Solve j(a) = 0 for a.
0, 1
Suppose -2*r = 5*h - 3*r - 24, -4*r - 24 = -2*h. Factor -6*m**h + 13*m**4 + 2*m**5 - 5*m**4.
2*m**4*(m + 1)
Let o = -2 + 5. Suppose 24 = 2*v + 3*v - o*r, -3*v - 5*r = 6. Solve 5*m**2 + m**5 + 2*m - 5*m**2 - 2*m**2 + 2*m**4 - v*m = 0.
-1, 0, 1
Determine y, given that 24/7 + 5/7*y - 1/7*y**2 = 0.
-3, 8
What is y in 84/5*y - 84/5*y**3 + 117*y**2 - 588/5 + 3/5*y**4 = 0?
-1, 1, 14
Let k(s) be the third derivative of -s**7/630 + s**6/60 - s**5/15 - 5*s**4/12 + 14*s**2. Let t(r) be the second derivative of k(r). Let t(l) = 0. What is l?
1, 2
Let u(a) be the second derivative of 0*a**6 + 0 - 1/14*a**7 - 1/2*a**3 + 3/10*a**5 + 0*a**4 + 19*a + 0*a**2. Find p such that u(p) = 0.
-1, 0, 1
Let o(p) be the first derivative of p**3/3 + 18. Find b such that o(b) = 0.
0
Factor -1/3*w + 1/3*w**3 - 1/3*w**4 - 2/3 + w**2.
-(w - 2)*(w - 1)*(w + 1)**2/3
Let q(s) be the first derivative of 10*s**2 + 5/3*s**3 + 15*s - 28. Suppose q(c) = 0. Calculate c.
-3, -1
Determine l so that -6*l**5 - 9487*l**3 + 9441*l**3 - 7*l - 32*l**2 - l - 28*l**4 = 0.
-2, -1, -2/3, 0
Let x = 408 + -404. Let y(f) be the first derivative of 1/3*f**3 + 0*f - 1/5*f**5 + 1/10*f**2 - 1/20*f**x - 2. Factor y(d).
-d*(d - 1)*(d + 1)*(5*d + 1)/5
Let w(z) be the second derivative of -z**6/30 - 11*z**5/30 - z**4 + z**3/6 - 10*z. Let t(d) be the second derivative of w(d). What is g in t(g) = 0?
-3, -2/3
Let -192*c - 232*c**2 + 66*c**3 + 72 + 75/2*c**4 + 7/2*c**5 = 0. Calculate c.
-6, -1, 2/7, 2
Let o be (0 + (-5)/34)*(-1004)/1255. Find s, given that o + 2/17*s**2 - 4/17*s = 0.
1
Suppose -5*v + 6*v + 62 = 0. Let z = v + 62. Factor z*i**2 + 0 - 1/4*i**4 + 1/2*i**3 + 0*i.
-i**3*(i - 2)/4
Suppose -3*a - 8 - 10 = -v, -2*a - 7 = v. Let p = -281 + 286. Suppose 0*o - 2/3*o**2 + 0 - 4/3*o**4 - 1/3*o**p - 5/3*o**v = 0. Calculate o.
-2, -1, 0
Let n = 1672 + -133759/80. Let r(z) be the second derivative of -1/48*z**4 + 0*z**3 + 1/32*z**5 + 0*z**2 + 0 - 12*z + n*z**6. Suppose r(x) = 0. Calculate x.
-2, 0, 1/3
Let p be 2 - 2*(-4)/(-6). Suppose 4*g + 5*o + 20 = 0, 2*g - 6*o + 20 = -11*o. Suppose -2/3*b + g - p*b**2 = 0. What is b?
-1, 0
Suppose -9*h + 16 = 17*h - 62. Factor 8/7*z**h + 2/7*z**5 - 10/7*z + 4/7*z**2 + 4/7 - 8/7*z**4.
2*(z - 2)*(z - 1)**3*(z + 1)/7
Suppose 5*s = -187 + 202. Let l be 4 - (-24)/((-18)/s). Factor 0 + 2/3*j**3 - 2/3*j**2 - 2/3*j**5 + l*j + 2/3*j**4.
-2*j**2*(j - 1)**2*(j + 1)/3
Factor -g**2 - 1/2*g**3 + 0 + 0*g.
-g**2*(g + 2)/2
Factor -21/5*s**3 - 3/5*s**4 + 24/5*s**2 + 0 + 0*s.
-3*s**2*(s - 1)*(s + 8)/5
Let q be (-8)/18 + 3 - 1. Let h(z) = -z**3 - 7*z**2 + 2*z - 46. Let y be h(-8). Factor q*v**y - 16/9*v + 2/9.
2*(v - 1)*(7*v - 1)/9
Let x be (-2)/10 + 26/5. Find y such that 4*y**3 + 9*y**4 + 3*y**5 + 0*y**5 + x*y**3 + 3*y**2 = 0.
-1, 0
Let x = -35 - -40. Let y(z) be the third derivative of -1/42*z**4 + 1/210*z**x + 0 + 0*z + 0*z**3 - 5*z**2. Solve y(f) = 0.
0, 2
Let u = 18 - 9. What is d in 2*d**2 + 22*d**2 - u*d**3 + d**4 - 9*d - 7*d = 0?
0, 1, 4
Let o be 6/(-4) + (-129)/(-6). Let p be (-5)/o + 10*(-6)/(-112). Determine k so that p*k**3 + 0 + 4/7*k**2 + 2/7*k = 0.
-1, 0
Let r(d) be the first derivative of d**6/10 - 6*d**5/25 - 3*d**4/4 + 6*d**3/5 - 391. Find v such that r(v) = 0.
-2, 0, 1, 3
Factor 1/3 - 73/6*p**2 - 71/6*p.
-(p + 1)*(73*p - 2)/6
Let b(j) = 14*j**4 + 24*j**3 - 30*j**2 + 16. Let c(m) = -9*m**4 - 16*m**3 + 20*m**2 - 10. Let k(s) = -5*b(s) - 8*c(s). Factor k(p).
2*p**2*(p - 1)*(p + 5)
Let w(f) = -f**3 - 12*f**2 - 16*f - 14. Let l be (-132)/(-48)*(-5 + 1). Let t be w(l). Factor -48*i**2 - 4*i**4 - 24*i**3 + 4*i - t*i + 5*i.
-4*i*(i + 2)**3
Let n be 4 - 8/(-5 + 13). Let i(o) be the third derivative of 3*o**2 + 0*o**n - 1/48*o**4 + 0*o + 1/120*o**5 + 0. Factor i(z).
z*(z - 1)/2
Let 15*d**2 + 85*d - 65*d**2 - 16*d**2 - 14*d**2 - 5 = 0. Calculate d.
1/16, 1
Find f such that -486/11 + 2052/11*f - 438/11*f**2 + 24/11*f**3 = 0.
1/4, 9
Let h = -4943 - -9889/2. Determine m so that -7/4*m - 1/4*m**2 - h = 0.
-6, -1
Let q = -24 - -32. Determine f so that -5*f**3 - 4*f**3 - q*f**4 + 8*f**2 + 2*f**3 + 4*f**5 + 3*f**3 = 0.
-1, 0, 1, 2
Let q(c) be the third derivative of -6*c**2 + 0 + 1/24*c**6 - 11/4*c**5 + 0*c + 425/8*c**4 + 1445/6*c**3. Factor q(k).
5*(k - 17)**2*(k + 1)
Let t(h) be the third derivative of 28*h**2 + 0*h**3 + 0*h - 1/160*h**5 + 0*h**4 + 0. Factor t(x).
-3*x**2/8
Let r be 25/15*((-1782)/(-570) - 3). Find y, given that -18/19*y - 4/19*y**2 + 18/19*y**3 + r = 0.
-1, 2/9, 1
Let m = 3/2581 + 23214/12905. Factor -6/5*c - 21/5*c**2 + 0 - 24/5*c**3 - m*c**4.
-3*c*(c + 1)**2*(3*c + 2)/5
Let i(s) be the first derivative of -s**6/60 + s**5/50 + 3*s**4/40 - s**3/30 - s**2/10 + 82. Determine n, given that i(n) = 0.
-1, 0, 1, 2
Let k be 6/(2 - 15/12). Suppose 3*t = 20 - k. Factor 3*o**2 - 8 + t*o**2 - o**2 - 2*o**2 - 4*o.
4*(o - 2)*(o + 1)
Let i(b) be the first derivative of -b**8/1680 - b**7/525 - b**6/600 + 57*b**2/2 - 49. Let v(a) be the second derivative of i(a). Factor v(k).
-k**3*(k + 1)**2/5
Let h(k) be the second derivative of -k**4/4 + 54*k**3 - 4374*k**2 - 2*k + 96. Factor h(v).
-3*(v - 54)**2
Suppose -3*d = -3*v - 0 - 3, -5*v + 4*d = 0. Find z, given that 2*z**2 - z**3 + 6*z**2 - 3*z**v - 6*z**2 = 0.
-1, 0, 2/3
Factor 2/5*g**3 - 12/5 + 2/5*g + 8/5*g**2.
2*(g - 1)*(g + 2)*(g + 3)/5
Factor -21/2*p + 81/8 + 3/8*p**2.
3*(p - 27)*(p - 1)/8
Let t(f) be the third derivative of f**7/1260 - f**6/240 - f**5/24 + 19*f**4/144 + 5*f**3/6 - 228*f**2. Find q, given that t(q) = 0.
-3, -1, 2, 5
Let n = 12897/25802 - -2/12901. Factor -1/2*a - 1/2*a**4 + a**2 - 1/2*a**5 - n + a**3.
-(a - 1)**2*(a + 1)**3/2
Let z(s) = -4*s + 28. Let w be z(6). Let l(n) be the third derivative of 8*n**2 + 4/15*n**3 + 7/15*n**w + 49/150*n**5 + 0 + 0*n. Find t such that l(t) = 0.
-2/7
Let v(a) be the first derivative of a**5/110 + a**4/132 - 17*a**2/2 - 3. Let w(c) be the second derivative of v(c). Let w(u) = 0. What is u?
-1/3, 0
Let c(w) = 41*w - 41. Let z(i) = -19*i + 20. Let h(s) = 6*c(s) + 13*z(s). Let p be h(11). Factor -1/4*y - 1/4*y**2 + 1/4*y**4 + 0 + 1/4*y**p.
y*(y - 1)*(y + 1)**2/4
Suppose -68/7*l**2 - 240/7*l**3 - l**4 + 0 + 0*l = 0. Calculate l.
-34, -2/7, 0
Let w be (224/168)/(3/18). Suppose -4*g = 4*j - 452, g + 450 = 5*g + 2*j. Suppose -w*a**3 - g + 4*a**2 + 112 + 4*a**4 = 0. Calculate a.
0, 1
Let t(y) be the third derivative of y**6/5 - 3*y**5/20 - y**2 - 90. Factor t(s).
3*s**2*(8*s - 3)
Let m(s) be the third derivative of 9*s**6/70 + 8*s**5/35 - s**4/6 - 8*s**3/21 + 6*s**2 + s. Find l such that m(l) = 0.
-1, -1/3, 4/9
Let w(g) be the first derivative of -3*g**5/5 - 6*g**4 + g**3 + 12*g**2 - 167. Let w(j) = 0. Calculate j.
-8, -1, 0, 1
Let v = 18 + -24. Let c be (7/3)/(-7) - 2/v. Solve -2/9*f**3 + 4/9*f**2 + c - 2/9*f = 0 for f.
0, 1
Let k(w) be the first derivative of -9/20*w**2 - 1/5*w**3 + 0*w + 42 - 1/40*w**4. What is p in k(p) = 0?
-3, 0
Let -11/3*c**2 + 2*c + 4/3*c**3 + 0 + 1/3*c**4 = 0. What is c?
-6, 0, 1
Suppose 2*p + 8 = -4*u, -4*p - 2*u - u = 1. Let z(x) be the second derivative of 0*x**2 - p*x - 1/15*x**6 + 0 - 1/3*x**3 - 3/10*x**5 - 1/2*x**4. Factor z(w).
-2*w*(w + 1)**3
Let d(r) be the first derivative of -r**6/40 + 3*r**5/80 + r**4/4 - r**3/2 - 5*r + 1. Let n(b) be the first derivative of d(b). Factor n(j).
-3*j*(j - 2)*(j - 1)*(j + 2)/4
Let w = -26 + 73. Let n = w - 42. Factor 21/4*c**n + 0 