 = -z**2 + 8*z - 4. Let p be b(7). Suppose p*y = i + 6, y - 5*i - 4 = -y. Factor 12*f - 3*f**2 + f**2 - 6*f - 4 + 0*f**y.
-2*(f - 2)*(f - 1)
Let l(u) be the third derivative of 0*u + 0 - 15*u**2 - 1/18*u**4 + 0*u**3 + 1/45*u**5. Determine w so that l(w) = 0.
0, 1
Let s(i) be the second derivative of 3*i**7/28 + 9*i**6/20 + 11*i**5/40 - 23*i**4/24 - 5*i**3/3 - i**2 - 3*i - 13. Find d, given that s(d) = 0.
-2, -1, -2/3, -1/3, 1
Solve -3 - 1/3*g**3 - 11/3*g**2 - 19/3*g = 0 for g.
-9, -1
Let n(s) be the second derivative of 1/10*s**5 - 1/15*s**6 + 0*s**2 + 0*s**3 + 1/6*s**4 - 33*s + 0 - 1/21*s**7. Determine r so that n(r) = 0.
-1, 0, 1
Let p(r) be the first derivative of -5/2*r**2 - 5*r**4 - 40 - 25/3*r**3 + 0*r. Let p(o) = 0. What is o?
-1, -1/4, 0
Factor -248/5*n + 7688/5 + 2/5*n**2.
2*(n - 62)**2/5
Let d(m) = 32*m**3 + 43*m**2 - 53*m - 20. Let u(r) = -33*r**3 - 45*r**2 + 54*r + 21. Let j(z) = -3*d(z) - 2*u(z). Find k, given that j(k) = 0.
-2, -3/10, 1
Let f(a) be the first derivative of 55*a**4/4 + 340*a**3/3 + 30*a**2 - 335. Determine j, given that f(j) = 0.
-6, -2/11, 0
Let k be (-21)/14*(-8)/3. Suppose 3 + 4*o**k - o**3 + 1 + 37*o**2 + 20*o + 31*o**3 + 5*o**4 = 0. What is o?
-1, -2/3
Let o(j) be the third derivative of j**8/1344 + j**7/105 + 17*j**6/480 + j**5/24 - 7*j**2 - 6*j. Factor o(i).
i**2*(i + 1)*(i + 2)*(i + 5)/4
Let d(n) = -n**3 - 5*n**2 - 15*n - 11. Let m(k) = -k**3 - 6*k**2 - 15*k - 10. Let g(c) = -3*d(c) + 4*m(c). Factor g(x).
-(x + 1)**2*(x + 7)
Suppose 5*j + l - 22 = 22, -j = -l - 4. Suppose -4*g**5 + 4*g**2 + 4*g**2 + 6*g**3 - 12*g - j + 10*g**3 = 0. What is g?
-1, 1, 2
Let w(b) be the first derivative of -b**4/18 + 2*b**3/9 - 4*b + 12. Let g(u) be the first derivative of w(u). What is v in g(v) = 0?
0, 2
Let h(r) be the second derivative of -1/150*r**6 + 0*r**3 + 4*r + 0 - 3/100*r**5 - 1/30*r**4 + 0*r**2. Let h(m) = 0. What is m?
-2, -1, 0
Factor 1/2*v**2 - 4*v + 7/2.
(v - 7)*(v - 1)/2
Let d be (-8)/(-10)*(175/(-10))/(-7). Suppose 3*q**d - q - 2*q**2 - 7*q + q**3 + 4*q - 4 = 0. Calculate q.
-2, -1, 2
Let x(o) be the first derivative of -o**6/3 - 12*o**5/5 + 3*o**4/2 + 40*o**3/3 + 12*o**2 + 300. Suppose x(m) = 0. What is m?
-6, -1, 0, 2
Let p(l) be the first derivative of -l**4/126 - l**3/63 + 2*l**2/21 - 4*l + 1. Let j(u) be the first derivative of p(u). Determine r so that j(r) = 0.
-2, 1
Factor -64/5 + 72*z - 44/5*z**2.
-4*(z - 8)*(11*z - 2)/5
Let d(u) = u**2 + u - 1. Let x(c) = -6*c**2 - 12*c + 3. Suppose -f - 36 = 3*f + 5*j, 0 = 4*j. Let z(q) = f*d(q) - x(q). Suppose z(h) = 0. Calculate h.
-1, 2
Let x(i) be the third derivative of i**5/180 + 29*i**4/24 - 44*i**3/9 + i**2 + 7*i. Factor x(m).
(m - 1)*(m + 88)/3
Let q be 5986/438 - (14 + -1). Find a, given that -2*a + 0 + q*a**2 = 0.
0, 3
Let y(x) be the third derivative of 0 + 1/84*x**4 + 1/420*x**6 + 0*x - 1/105*x**5 + 9*x**2 + 0*x**3. Let y(w) = 0. Calculate w.
0, 1
Let b be (42/8 + -3)*240/900. Let -3/5*m**2 - 3/5*m + b*m**3 + 0 + 3/5*m**4 = 0. Calculate m.
-1, 0, 1
Let d be ((-44)/33)/((-4)/15). Factor 4 - 2*k - 28*k**4 - 8*k**2 - 8*k + 32*k**3 - d*k + 7*k + 8*k**5.
4*(k - 1)**4*(2*k + 1)
Let q(b) be the second derivative of -3/2*b**3 - 3*b**2 - 10*b + 0 - 1/4*b**4. Find s, given that q(s) = 0.
-2, -1
Solve -100/3*q - 2500/3 - 1/3*q**2 = 0 for q.
-50
Let 21/2*c + 19/2*c**2 + 1 = 0. What is c?
-1, -2/19
Let s(x) = -16*x**3 - 12*x**2 + 44*x + 32. Let l be -5 + -2 + 3/1. Let w(q) = q**3 + q**2 + q. Let d(t) = l*w(t) - s(t). Factor d(r).
4*(r - 2)*(r + 2)*(3*r + 2)
Let r = -245/172 - -72/43. Solve 1/8*u**2 - 1/8*u - r = 0.
-1, 2
Let h(g) = g**2 + 35*g - 1. Let v be h(-11). Let s = v + 3447/13. Factor 2/13*a**4 - 4/13*a**2 + s - 4/13*a**3 + 2/13*a + 2/13*a**5.
2*(a - 1)**2*(a + 1)**3/13
Suppose -8/9*c**2 + 46/9*c - 20/9*c**4 - 44/9*c**3 + 28/9 - 2/9*c**5 = 0. What is c?
-7, -2, -1, 1
Let w(k) be the first derivative of -k**6/1140 + k**5/570 + 4*k**2 + 4. Let b(p) be the second derivative of w(p). Find d, given that b(d) = 0.
0, 1
Let i(g) = 147*g**4 - 768*g**3 + 4191*g**2 - 9249*g + 6846. Let o(h) = 9*h**4 - 48*h**3 + 262*h**2 - 578*h + 428. Let q(t) = -2*i(t) + 33*o(t). Factor q(j).
3*(j - 6)**2*(j - 2)**2
Let a(f) be the second derivative of 0*f**4 - 1/90*f**5 + 0 + 1/9*f**3 - 7*f + 2/9*f**2. Factor a(q).
-2*(q - 2)*(q + 1)**2/9
Let h be (-45)/18 + 6 - 12/8. Find r such that 12/5 - 22/5*r + 2/5*r**3 + 8/5*r**h = 0.
-6, 1
Suppose 2/13*k**4 - 18/13*k**3 + 0 - 42/13*k**2 - 22/13*k = 0. Calculate k.
-1, 0, 11
Let f(j) = -51*j**2 - 181*j - 51. Let p(k) = -10*k**2 - 36*k - 10. Let g be (-20)/(-90) + (-194)/(-18). Let b(i) = g*p(i) - 2*f(i). What is o in b(o) = 0?
-4, -1/4
Let m(y) be the second derivative of y**4/96 + 139*y**3/24 + 19321*y**2/16 + 5*y + 50. Suppose m(v) = 0. Calculate v.
-139
Let l(m) be the third derivative of -1/175*m**7 + 0*m**3 - 1/560*m**8 + 0 + 0*m + 1/50*m**5 + 13*m**2 + 0*m**6 + 1/40*m**4. Factor l(w).
-3*w*(w - 1)*(w + 1)**3/5
Let t be (1 - (4 - 4)) + -1. Suppose t = w + w - 6*w. Factor -1/6*n**2 - 1/6*n**3 + w + 1/6*n**4 + 1/6*n.
n*(n - 1)**2*(n + 1)/6
Factor 7*m + 175*m**3 + 190*m**3 - 4*m + 12*m**4 - 386*m**3 - 5*m**2 + 11*m**2.
3*m*(m - 1)**2*(4*m + 1)
Let r(n) be the second derivative of n**4/12 + 2*n**3/3 - 3*n**2/2 + 9*n. Let a be r(-5). What is x in 12 - 12 + 9*x**a + 2*x = 0?
-2/9, 0
Let o be -369*((-2)/(-14))/1. Let i = o - -53. Factor i*d**2 - 4/7*d**3 + 2/7*d**4 + 0*d + 0.
2*d**2*(d - 1)**2/7
Let o(x) be the third derivative of 9*x**2 + 0 - 1/120*x**5 + 0*x**3 + 0*x - 1/72*x**4 + 1/420*x**7 + 1/360*x**6. Find p such that o(p) = 0.
-1, -2/3, 0, 1
Let m = 29/9 - -5/18. Let t = 88 - 88. Factor -m*d**3 + 6*d**4 + t + 1/2*d**2 + 0*d.
d**2*(3*d - 1)*(4*d - 1)/2
Let o(h) be the third derivative of 0*h**3 - 1/90*h**5 - 1/360*h**6 + 0*h + 0 - 8*h**2 + 1/630*h**7 + 0*h**4. Factor o(v).
v**2*(v - 2)*(v + 1)/3
Let p(f) = -f**2 - f - 4. Let s(j) = -14*j**2 - 6*j - 40. Let u(t) = -10*p(t) + s(t). Factor u(c).
-4*c*(c - 1)
Let b(z) be the second derivative of -z**4/66 - 7*z**3/33 + 4*z**2 + 223*z. Solve b(q) = 0.
-11, 4
Suppose -576/5 + 108/5*g**2 - 6*g**3 + 2/5*g**4 + 64/5*g = 0. What is g?
-2, 4, 9
Let i(s) = s + 2. Let a(n) = -n**3 - 7*n**2 - 7*n - 8. Let u be a(-6). Let q be i(u). Determine p, given that 0*p + 0*p**3 - p**3 + p + q*p**3 = 0.
-1, 0, 1
Let h = 40864/7 + -5830. Factor -27/7*w**3 + h + 3/7*w**4 - 117/7*w + 87/7*w**2.
3*(w - 3)**2*(w - 2)*(w - 1)/7
Let y(g) be the second derivative of 0 + 1/2*g**3 - 3/20*g**5 - 1/2*g**4 + 3*g**2 + 36*g. Factor y(n).
-3*(n - 1)*(n + 1)*(n + 2)
Let y(j) be the first derivative of -98*j**2 + 1372/3*j - 3 - 1/3*j**4 + 28/3*j**3. Find l, given that y(l) = 0.
7
Let p(d) be the second derivative of d - 5/3*d**3 + 1/6*d**4 - 6*d**2 + 0. Factor p(o).
2*(o - 6)*(o + 1)
Let r(j) be the second derivative of -1/42*j**4 + 21*j + 0 + 0*j**2 - 4/21*j**3. Factor r(g).
-2*g*(g + 4)/7
Factor 12*c**3 + 0 + 3/4*c**4 + 147/2*c + 231/4*c**2.
3*c*(c + 2)*(c + 7)**2/4
Factor 3*d**3 - 306*d**2 + 10404*d - 17755 - 65561 - 34596.
3*(d - 34)**3
Let h = -162 - -233. Let -3*b**5 - 27 + 34*b - 46*b**3 + 18*b**2 - 23*b**4 - 23*b - b + h*b = 0. Calculate b.
-3, 1/3, 1
Let l(w) be the second derivative of -5/6*w**3 + 0 + 5/12*w**4 - 15*w**2 + 20*w. Determine n so that l(n) = 0.
-2, 3
Let z be 6/(-18) - 47/3. Let i = 24 + z. Factor i*q - 8 - 2*q**2 - 3 + 3.
-2*(q - 2)**2
Suppose -46*u + 192347 = -165349. Solve 6/5*q**5 - 36*q**4 - 46656/5 + u*q + 432*q**3 - 2592*q**2 = 0 for q.
6
Solve -1/8*g**3 + 1/2 + 1/8*g - 1/2*g**2 = 0.
-4, -1, 1
What is k in 0 + 1/7*k - 2/7*k**2 + 1/7*k**3 = 0?
0, 1
Let v(x) = -1. Let i(t) = t**3 - 39*t**2 + 507*t - 39. Let b(q) = -i(q) + 6*v(q). Let c(w) be the first derivative of b(w). Factor c(n).
-3*(n - 13)**2
Let x be 1/3*12/12. Let w(q) be the second derivative of -q**2 - 1/20*q**5 - 5/6*q**3 + 0 - 3*q - x*q**4. Factor w(a).
-(a + 1)**2*(a + 2)
Let w(u) be the second derivative of 3*u**5/20 + u**4/2 - 119*u. Factor w(i).
3*i**2*(i + 2)
Let d = -48 - -54. Suppose d = -b + 10. Factor 3/4*y**2 - 1/4*y**b + 0*y**3 + 0 - 1/2*y.
-y*(y - 1)**2*(y + 2)/4
Let j(h) = -h**3 + 10*h**2 + 22*h + 4. Let p be j(12). Let n be (-345)/p + (-6 - 6/(-2)). Factor -21/4*r**5 + 3/4*r**2 + 3/2*r - 45/4*r**3 + n*r**4 + 0.
-3*r*(r - 