. Let q(n) be the second derivative of t(n). Factor q(i).
(i + 2)*(i + 5)/7
Let m(h) be the first derivative of h**3/2 + 51*h**2/2 - 105*h/2 + 210. Determine z, given that m(z) = 0.
-35, 1
Let -4*x**4 - 981*x**2 + x**4 + 837*x**2 + 42*x**3 = 0. What is x?
0, 6, 8
Factor -v**2 + 0*v + 0 - 1/3*v**4 + 1/3*v**5 - 5/3*v**3.
v**2*(v - 3)*(v + 1)**2/3
Factor 90*d**2 - 21*d**4 + 27*d**3 + 20*d**4 + 4*d**4 + 72 + 132*d.
3*(d + 2)**3*(d + 3)
Let t(h) be the first derivative of h**6/6 + 4*h**5/5 - h**4/2 - 8*h**3/3 + h**2/2 + 4*h - 699. What is a in t(a) = 0?
-4, -1, 1
Let h(w) be the second derivative of -1/90*w**6 + 0*w**3 - 1/18*w**4 + 1/20*w**5 + 0 - 10*w + 0*w**2. Factor h(d).
-d**2*(d - 2)*(d - 1)/3
Suppose -2*j = r + 2, -19*r - 5*j - 18 = -23*r. Let t(u) be the third derivative of -1/96*u**4 + 0 + 1/120*u**5 + 0*u - 1/480*u**6 + 0*u**3 - u**r. Factor t(a).
-a*(a - 1)**2/4
Suppose 41 = 5*p + 5*c + 6, -2*p + 17 = 3*c. Suppose f**2 + f - 4 + 6 - p = 0. Calculate f.
-2, 1
Let w(m) be the second derivative of 3/140*m**5 - 2/35*m**6 + 0*m**3 - 6*m + 1/14*m**4 - 3/98*m**7 + 0*m**2 + 0. Factor w(r).
-3*r**2*(r + 1)**2*(3*r - 2)/7
Let o = 1353 - 10821/8. Let m(n) be the second derivative of 9*n + 1/16*n**3 - 3/160*n**5 + 0 + o*n**2 - 1/16*n**4. Solve m(f) = 0.
-2, -1, 1
Factor 0 - 15/7*h - 27/7*h**2 - 12/7*h**3.
-3*h*(h + 1)*(4*h + 5)/7
Let y(m) = -m**3 - 5*m**2 - 2*m - 3. Let u be y(-5). Let s be -2 - u/((-105)/54). Factor -1/5*g**3 + 6/5*g**2 - 12/5*g + s.
-(g - 2)**3/5
Let v(p) be the third derivative of 17*p**6/40 - 13*p**5/12 + 13*p**4/24 + p**3/6 - 44*p**2. Factor v(o).
(o - 1)*(3*o - 1)*(17*o + 1)
Let d = -1 - -21. Solve -54*y**3 + 0*y**2 - d*y**2 + 49*y**3 - 20*y = 0 for y.
-2, 0
Let k(x) = -127*x**2 - 207*x - 38. Let v(z) = 42*z**2 + 67*z + 13. Let i(s) = -2*k(s) - 7*v(s). Suppose i(d) = 0. Calculate d.
-1, -3/8
Let b(m) be the first derivative of 3*m**3/4 + 5*m**2/4 - 183. Factor b(k).
k*(9*k + 10)/4
Factor 1/4*p**2 + 9/2 - 9/4*p.
(p - 6)*(p - 3)/4
Let b(r) be the first derivative of 2*r**5/5 + 4*r**4 - 20*r**3/3 - 8*r**2 + 18*r - 588. Find l such that b(l) = 0.
-9, -1, 1
Let z(r) be the first derivative of -r**4/18 + 14*r**3/9 - 540. Factor z(y).
-2*y**2*(y - 21)/9
Let f(y) = -15*y**2 + 25*y + 10. Let o(k) be the first derivative of -k**3/3 + k - 46. Let n(d) = -f(d) + 10*o(d). Factor n(b).
5*b*(b - 5)
Suppose 9 = 2*d - 5*d - 3*v, -8 = 2*v. Let b be (-2)/(d/((-356)/8)). What is g in 89*g + 6*g**2 - 2*g**3 - 8 - b*g = 0?
-1, 2
Suppose 0 = 4*g + 20, 57 - 26 = -3*y - 5*g. Let p be (4/(-85 - -5))/(y/8). Solve 2/5*k - p - 1/5*k**2 = 0 for k.
1
Let x(t) be the second derivative of 21*t - 5*t**3 + 0 + 5/12*t**4 + 25/2*t**2. Let x(w) = 0. Calculate w.
1, 5
Let u(w) be the first derivative of 6*w + 1/2*w**5 + 2/15*w**6 - 2 + 1/2*w**4 - 1/3*w**3 - w**2. Let b(h) be the first derivative of u(h). Factor b(o).
2*(o + 1)**3*(2*o - 1)
Let r be (-60 - (3 - 0))*(-8)/(-8). Let i be 0 + (-8)/28 + (-32)/r. Find b such that 8/9*b - i - 8/9*b**3 + 2/9*b**2 = 0.
-1, 1/4, 1
Let g(p) be the first derivative of -2*p**6/135 - 2*p**5/45 + p**4/27 + 4*p**3/27 - 9*p + 4. Let h(i) be the first derivative of g(i). Factor h(m).
-4*m*(m - 1)*(m + 1)*(m + 2)/9
Let r = 3 - 1. Let n = -797 + 8769/11. Factor 8/11*d**4 + 4/11*d**r + 0*d + 0 + 10/11*d**3 + n*d**5.
2*d**2*(d + 1)**2*(d + 2)/11
Let h = 37 - 25. Factor -2*r**3 + 31*r - 19*r + 7*r**4 - 3*r**5 - h*r.
-r**3*(r - 2)*(3*r - 1)
Suppose -5*w + 23 + 7 = 0. Let s be w - (0 + 6)/3. Factor 2*z**4 + 6*z**s + 4*z**5 - 2*z**2 - 2*z**4.
2*z**2*(z + 1)**2*(2*z - 1)
Let q be (-4)/(-18) - (-120)/(-54). Let x = 3 - q. Find z, given that z + 15*z**3 - x*z**2 - 6*z**5 + z**5 - 11*z + 5*z**4 = 0.
-1, 0, 1, 2
Let g(z) = -7*z**2 + 8*z + 6. Let y(f) = -7*f**2 + 7*f + 5. Let v be 4/10*60/(-4). Let p be (-1)/1 - -6 - 0. Let c(o) = p*g(o) + v*y(o). Factor c(k).
k*(7*k - 2)
What is u in 4/13*u**5 + 140/13*u**2 - 64/13 + 10/13*u**3 - 2*u**4 - 64/13*u = 0?
-2, -1/2, 1, 4
Let y = -99 + 99. Let p(j) = -j**2 + 5*j - 4. Let i be p(3). Factor 4/11*g**i + y + 2/11*g.
2*g*(2*g + 1)/11
Let c be 26/(-78) - ((-42)/(-9))/(-2). Let l(a) be the second derivative of 4*a**c + 1/3*a**4 - 2*a**3 + 0 - 12*a. Suppose l(j) = 0. What is j?
1, 2
Let j(w) be the second derivative of 0 + 0*w**2 - 1/5*w**5 - 12*w + 2/3*w**3 + 0*w**4. Factor j(g).
-4*g*(g - 1)*(g + 1)
Let v(i) be the second derivative of 0*i**4 + 0*i**3 + 2/7*i**7 + 0*i**2 - 3/20*i**5 + 3/10*i**6 - 11*i + 0. Factor v(x).
3*x**3*(x + 1)*(4*x - 1)
Let h = 94 + -48. Suppose 89 = 5*y - h. Find u, given that 12*u**5 + 17 - 6*u + y*u**2 - 27*u**4 - 6*u**3 - 17 = 0.
-1, 0, 1/4, 1, 2
Determine s, given that -46*s - 30*s + 76*s - 3*s**2 - 1 + 4*s**2 = 0.
-1, 1
Let m(c) = c**3 + 46*c**2 + c + 48. Let n be m(-46). Let q be -2 + 51/21 + 0. Determine g so that -q*g - 1/7*g**3 - 3/7*g**n - 1/7 = 0.
-1
Let v(g) = 7*g - 205. Let p be v(30). Let d(n) be the first derivative of 1/3*n**6 - n**4 + n**2 + 0*n + 7 + 0*n**p + 0*n**3. Factor d(f).
2*f*(f - 1)**2*(f + 1)**2
Let r = -73 + 512/7. Let v = 448 + -3120/7. Suppose r*c**2 - 8/7*c + v = 0. Calculate c.
4
Suppose -37 + 7 = -5*d. Suppose 0*s - d = -2*s. Factor -4*t**3 - 8*t - 12*t**2 - 4*t**3 + 8*t**s - 4*t**3.
-4*t*(t + 1)*(t + 2)
Suppose 5*y - 8 = -2*i, -2*i + 3*y - 16 = -24. Find x such that -1/2*x**i + 1/2*x**2 - 1/2*x + 0 + 1/2*x**3 = 0.
-1, 0, 1
Let w(l) be the second derivative of -l**5/20 - l**4/2 + 16*l**2 - 12*l + 3. Factor w(o).
-(o - 2)*(o + 4)**2
Let i = 16973/45 - 377. Let f(b) be the first derivative of 8/27*b**3 + 3 + i*b**5 - 1/9*b**2 - 1/3*b**4 - 1/27*b**6 + 0*b. Suppose f(g) = 0. Calculate g.
0, 1
Factor 2/5*d**2 + 0*d + 0 - 2/5*d**3.
-2*d**2*(d - 1)/5
Let -75485*s**2 - 11*s**4 + 25600 - 31573*s**2 - 76160*s - 2572*s**3 + s**4 - 6*s**4 + 2742*s**2 = 0. Calculate s.
-80, -1, 1/4
Let o be 22 + -27 + (-350)/2. Let k = -532/3 - o. Find i, given that 26/3*i**3 + 0 + k*i + 28/3*i**2 - 3*i**5 - i**4 = 0.
-1, -2/3, 0, 2
Suppose 4*c - 24 + 16 = 0. Factor -29*v**3 - 5*v**4 - 39*v**2 - 11*v**3 - 41*v**2 + 0*v**c.
-5*v**2*(v + 4)**2
Let l(f) be the second derivative of f**4/36 + f**3/9 - 35*f**2/6 - 175*f. Suppose l(d) = 0. Calculate d.
-7, 5
Suppose -793*w + 2328 = -211*w. Find c, given that 4/5 + 16/5*c**3 + 2/5*c**5 - 32/15*c**w - 22/15*c - 4/5*c**2 = 0.
-2/3, 1, 3
Suppose -8*h + 12 = -4. Suppose -4*f = -h - 14. Factor 0*b - 5/3*b**3 - b**5 + 0 + 7/3*b**f + 1/3*b**2.
-b**2*(b - 1)**2*(3*b - 1)/3
Let h(f) be the second derivative of 0 + 0*f**4 + 0*f**2 - 10*f - 1/35*f**5 + 1/35*f**6 - 1/147*f**7 + 0*f**3. Let h(v) = 0. What is v?
0, 1, 2
Let v(t) be the first derivative of 0*t + 15 - 5*t**5 + 4*t**2 - 44/3*t**3 + 35/2*t**4. Find k such that v(k) = 0.
0, 2/5, 2
Let v(t) be the second derivative of -36/7*t**2 - 4/7*t**3 + 4*t + 0 - 1/42*t**4. What is r in v(r) = 0?
-6
Let h(t) be the second derivative of -t**6/135 + 43*t**5/45 + 569*t. Factor h(g).
-2*g**3*(g - 86)/9
Let m = -14809 - -14812. Factor 0*a + 0 + 6/11*a**2 - 1/11*a**m - 1/11*a**4.
-a**2*(a - 2)*(a + 3)/11
Let w = 67 - 65. Let q = 4 - w. Factor -4/5 + 2/5*g**3 - 8/5*g**2 + q*g.
2*(g - 2)*(g - 1)**2/5
Let f(r) be the second derivative of -r**5/20 - r**4/3 - r**3/6 + 3*r**2 + 16*r + 1. Factor f(l).
-(l - 1)*(l + 2)*(l + 3)
Let s = -20 + 15. Let w be (s/10 - -1) + 2/(-20). Factor w*i**3 + 0 + 1/5*i**2 - 1/5*i**4 - 2/5*i.
-i*(i - 2)*(i - 1)*(i + 1)/5
Factor 165*y - 252 + 16 - 25 - 5*y**2 - 3 - 186.
-5*(y - 30)*(y - 3)
Let r(d) = d**3 - 3*d**2 - 4*d + 2. Let z be r(4). Let v be 0/(-2*(-3)/(-6)). Factor v*k - 12*k**z + 12*k**4 + k - 4*k**3 + 4*k - k.
4*k*(k - 1)*(k + 1)*(3*k - 1)
Find y, given that 136/9*y + 92/9 + 43/9*y**2 - 1/9*y**3 = 0.
-2, -1, 46
Let y(i) be the second derivative of 2/3*i**2 + 0 + 29/36*i**4 - 25*i - 3/20*i**5 - 4/3*i**3. Determine u so that y(u) = 0.
2/9, 1, 2
Let c(l) be the third derivative of -l**8/1176 + 2*l**7/245 - 13*l**6/420 + 2*l**5/35 - l**4/21 - 190*l**2 + 2*l. Factor c(z).
-2*z*(z - 2)**2*(z - 1)**2/7
Let i be 22/(33*(8/66)/((-184)/(-276))). Factor -i*x + 2 + x**2.
(x - 3)*(3*x - 2)/3
Suppose 0 + 0 = 33*i. Suppose 4/7*w**4 + i*w**3 + 0*w - 8/7*w**2 + 4/7 = 0. What is w?
-1, 1
Let s(x) = -x**4 + x**3 - 1. Let z(q) = 4*q**5 + 10*q**4 - 10*q**3 - 4*q**2 + 6. Let c be (48/32 - (-2