o(p) = -p**3 + p**2 + p - 6. Let w(h) = -3*h**3 - 25*h**2 + 108*h - 124. Let l(y) = 4*o(y) - w(y). What is d in l(d) = 0?
2, 25
Let z be (15 + (0 - -1))/21. Let r = z + -2/21. Factor -2/3*t**4 - 4/3*t**3 + r*t**5 + 0 + 0*t + 0*t**2.
2*t**3*(t - 2)*(t + 1)/3
Let h(t) = -109*t + 3. Let o be h(-1). Let d be o/350*(-10)/(-4). Suppose -d*v**2 + 2/5*v**3 - 2/5*v + 4/5 = 0. What is v?
-1, 1, 2
Suppose 0 = -j - 3, 4*o = -0*j - 2*j - 82. Let t = o + 21. Solve 2*w**2 + 7*w**3 + w - 2 - 4*w + t*w - 6*w**3 = 0 for w.
-2, -1, 1
Factor -4 + 9*k**3 - k**4 + k + 5*k**2 - 6*k**3 - 4*k.
-(k - 4)*(k - 1)*(k + 1)**2
Let x(r) be the second derivative of r**4/3 + 10*r**3 + 28*r**2 - 44*r - 2. Factor x(o).
4*(o + 1)*(o + 14)
Let q(y) be the third derivative of 0*y**4 + 0*y**3 + 0*y - 21*y**2 - 1/105*y**7 - 1/15*y**6 + 0 - 2/15*y**5. Determine l so that q(l) = 0.
-2, 0
Let i(s) = -s**5 - s + 1. Let x(j) = -2*j**5 - 126*j**4 + 1656*j**3 - 7152*j**2 + 12523*j - 7771. Let z(p) = 5*i(p) - x(p). Let z(w) = 0. What is w?
2, 18
Let r = 149532/523411 + 2/74773. Determine p so that 8/7*p**4 + 2/7*p + 0 - r*p**3 - 8/7*p**2 = 0.
-1, 0, 1/4, 1
Suppose -12 = -7*k + 4*k. Suppose -7*h**3 + 2*h**2 + 3*h**3 + 4*h**4 - 6*h**2 + k*h + 0*h = 0. Calculate h.
-1, 0, 1
Suppose 5*q = -3*w + q + 6, -4*q + 8 = 4*w. Let a(f) be the first derivative of w - 2/3*f**3 + 0*f**2 + 0*f - 5/4*f**4 + 3/5*f**5. Factor a(s).
s**2*(s - 2)*(3*s + 1)
Let b(p) be the second derivative of -1/16*p**3 + 1/8*p**2 + 3/160*p**5 + 0 + 6*p - 1/48*p**4. What is u in b(u) = 0?
-1, 2/3, 1
Let t(z) be the third derivative of z**8/33600 - z**7/12600 + z**4/12 + 9*z**2. Let a(y) be the second derivative of t(y). Solve a(m) = 0 for m.
0, 1
Let g(d) = 194*d + 7760. Let a be g(-40). Factor -3/4*s**2 - 3/8*s**3 + 0 + a*s.
-3*s**2*(s + 2)/8
Find o, given that 2*o**3 + 4*o**2 + 6*o**2 + o**3 - 2*o**3 + 15*o - 6*o**3 = 0.
-1, 0, 3
Let a(m) = -m**5 - 10*m**4 - 6*m**3 - m**2 + 3*m + 5. Let l(n) = n**4 + n**2 + n - 1. Let j(d) = -a(d) - 5*l(d). Factor j(z).
z*(z - 1)*(z + 2)**3
Let n(f) = 6*f**3 + 18*f**2 + 120*f - 132. Let p(k) = 9*k**3 + 35*k**2 + 241*k - 265. Let c(a) = 5*n(a) - 3*p(a). Find t, given that c(t) = 0.
-5, 1, 9
Let l(f) = -6*f**2 - 6*f - 3. Let p(r) = r**2 - r - 1. Suppose -98 = 4*w + 38. Let u = 37 + w. Let d(z) = u*p(z) + l(z). Factor d(g).
-3*(g + 1)*(g + 2)
Let x = 1534 + -1531. Suppose 6*w - 3*w = 2*f + 51, 0 = 4*w + 2*f - 54. Find j such that 3*j - 9*j**x + w*j**2 - 2*j - 3 - 4*j = 0.
-1/3, 1
Let v(f) be the second derivative of f**7/42 + 11*f**6/60 + 11*f**5/40 - 7*f**4/24 - 13*f**3/12 - f**2 + 252*f. Suppose v(r) = 0. Calculate r.
-4, -1, -1/2, 1
Let a be (-1 + (-22)/(-6))*6. Factor a*q + 2*q**3 - 6*q**3 + 4*q**2 - 4*q**2 + 32 - 8*q**2.
-4*(q - 2)*(q + 2)**2
Suppose -2475*s = -2483*s + 16. Let r(c) be the first derivative of -3/4*c**4 - 11/6*c**2 + 2/3*c + s*c**3 + 2. Factor r(b).
-(b - 1)*(3*b - 2)*(3*b - 1)/3
Suppose 32*b + 32*b = 6*b. Let l(z) be the third derivative of 3*z**2 + 0 + 0*z**3 + b*z - 1/144*z**4 + 1/180*z**5 - 1/720*z**6. Factor l(h).
-h*(h - 1)**2/6
Let p(d) be the second derivative of -d**7/84 - 4*d**6/15 - 27*d**5/20 - 19*d**4/6 - 49*d**3/12 - 3*d**2 - 2*d + 1. Let p(f) = 0. Calculate f.
-12, -1
Let u be (-440)/30 - -22 - 2. Factor -4/3*t**3 - 13/3*t - u*t**2 - 1.
-(t + 3)*(2*t + 1)**2/3
Let g(y) be the third derivative of 0*y - 21*y**2 + 1/120*y**5 + 0 - 1/12*y**4 + 1/240*y**6 - 1/3*y**3. Factor g(v).
(v - 2)*(v + 1)*(v + 2)/2
Let i(z) be the second derivative of z**6/15 - z**5/5 - 11*z**4/6 + 4*z**3 - 8*z + 3. Factor i(h).
2*h*(h - 4)*(h - 1)*(h + 3)
Find s, given that -4/5*s**3 + 12/5*s**2 + 0*s - 16/5 = 0.
-1, 2
Let s(d) = 8*d**4 - 58*d**3 + 120*d**2 - 56*d - 7. Let n(x) = x**4 + x**2 - 1. Let k(r) = 35*n(r) - 5*s(r). Factor k(t).
-5*t*(t - 56)*(t - 1)**2
Let t(p) be the first derivative of -2/15*p**3 + 4 - 4/5*p**2 - 8/5*p. Factor t(r).
-2*(r + 2)**2/5
Let r(o) be the first derivative of o**5/10 - 7*o**3/6 + 3*o**2/2 + 397. Find p, given that r(p) = 0.
-3, 0, 1, 2
Suppose 0 = -31*p + 25*p + 6. Let d(m) be the first derivative of 1/5*m**5 - 2/3*m**3 + 0*m + 0*m**2 - 1/4*m**4 - p. Factor d(z).
z**2*(z - 2)*(z + 1)
Let h(u) be the third derivative of -1/120*u**6 + 0*u**4 + 0 + 1/120*u**5 + 6*u**2 + 1/420*u**7 + 0*u**3 + 0*u. Let h(q) = 0. Calculate q.
0, 1
Suppose 4*p = 7*p - 156. Let d = -103/2 + p. Factor -11/4*z**3 + 3/4*z**4 - 9/4*z + d + 15/4*z**2.
(z - 1)**3*(3*z - 2)/4
Let z(l) = -52*l**3 + 344*l**2 - 1604*l - 16. Let f(a) = 10*a**3 - 69*a**2 + 321*a + 3. Let x(c) = 16*f(c) + 3*z(c). What is q in x(q) = 0?
0, 9
Factor 95/4*l**2 + 20 - 15/4*l**3 + 95/2*l.
-5*(l - 8)*(l + 1)*(3*l + 2)/4
Let h(q) be the second derivative of q**9/10584 + q**8/2940 - q**6/630 - q**5/420 + 25*q**3/6 - 12*q. Let x(j) be the second derivative of h(j). Factor x(u).
2*u*(u - 1)*(u + 1)**3/7
Suppose y = -4 + 12. Let -7*w + 11*w**2 + w - y*w**2 = 0. What is w?
0, 2
Suppose 0 = -2*w + 5*u - 33 + 21, 4*u - 12 = w. What is d in 0 - 2/3*d**3 + 4/9*d**2 + 0*d + 2/9*d**w = 0?
0, 1, 2
Let j(r) = -r**2 - 7*r - 7. Let x be j(-5). Suppose 22 = 7*o + 8. Factor -6*v**2 - 8*v**x + 5*v**4 - o*v**3 + 7*v**2 + 4*v**2.
5*v**2*(v - 1)**2
Let w be (4 - 3) + 3 + 3 + 0. Let z(u) be the second derivative of 0*u**6 + 1/50*u**5 - 1/210*u**w + 0*u**4 + 0*u**2 - 1/30*u**3 + 0 + 2*u. Factor z(q).
-q*(q - 1)**2*(q + 1)**2/5
Determine g so that -g + 0 + 6/5*g**2 + 4/5*g**3 - 6/5*g**4 + 1/5*g**5 = 0.
-1, 0, 1, 5
Let x(p) = -p**2 + p + 1. Suppose 5*t + 8 = t + 4*s, 0 = 3*t + 3*s + 18. Let r(o) = 9*o**2 - 9*o - 4. Let k(f) = t*x(f) - r(f). Suppose k(v) = 0. What is v?
0, 1
Let i(r) = -10*r**3 + 322*r**2 - 590*r + 314. Let h(o) = 4*o**3 - 129*o**2 + 236*o - 126. Let b(q) = -12*h(q) - 5*i(q). Factor b(c).
2*(c - 29)*(c - 1)**2
Let q = 358 - 358. Let x(d) be the first derivative of d**2 - 8 + 2/3*d**3 + q*d. Factor x(s).
2*s*(s + 1)
Suppose 5*a + 8*x = 6*x + 4, -4*x + 8 = -4*a. Let i be 3 + ((-72)/(-10))/(-3). Solve i*t**2 + a + 3/5*t = 0 for t.
-1, 0
Let u be ((-6)/5)/(-3) + 63 + -61. Solve -3/5*x**4 - 9*x**2 - 39/5*x - u - 21/5*x**3 = 0.
-4, -1
Let q = -246 - -1234/5. Factor q*m**3 + 0 + 4/5*m - 8/5*m**2.
4*m*(m - 1)**2/5
Let h(t) be the second derivative of t**4/6 - 4*t**3/3 - 12*t**2 - 82*t. What is l in h(l) = 0?
-2, 6
Let m(q) be the third derivative of q**2 + 1/12*q**4 + 2/15*q**5 + 0*q**3 + 0*q + 0. Let m(f) = 0. Calculate f.
-1/4, 0
Suppose 3*g = 2*p + 6, g - 3*p = 8 - 6. Let 40*x - 343*x**3 - 10*x**4 + 1 + 10*x**g - 1 + 5*x**5 + 298*x**3 = 0. Calculate x.
-2, -1, 0, 1, 4
Let f be ((-81)/(-18))/(3/8). Suppose f = 4*n - 4. Suppose 2*z**n + 4*z**3 - 20*z - 4*z**5 - 2*z**2 + 2*z**3 + 18*z = 0. What is z?
-1, -1/2, 0, 1
Let s be (-198)/(-180) + (0 - 1). Let k(v) be the second derivative of -s*v**6 - 5/2*v**3 + 0 + v + 3*v**2 + 3/4*v**4 + 3/20*v**5. Let k(l) = 0. Calculate l.
-2, 1
Factor -190*v + 163 - 1185*v**2 + 1642 + 1190*v**2.
5*(v - 19)**2
Suppose 55*t**2 - 1/2*t**3 + 0 + 111/2*t = 0. Calculate t.
-1, 0, 111
Find n, given that 0*n + 8/7*n**3 + 2/7*n**5 + 0*n**2 + 10/7*n**4 + 0 = 0.
-4, -1, 0
Suppose -o - 3*m + 0 = 6, 4*o - 4*m - 56 = 0. Factor o*y**3 - 3*y**2 + 585*y**4 - 588*y**4 - 3*y**2.
-3*y**2*(y - 2)*(y - 1)
Let b(z) be the third derivative of z**6/360 - z**5/90 - 55*z**4/72 + 100*z**3/9 - 7*z**2 + 39. Suppose b(v) = 0. Calculate v.
-8, 5
Let i(p) be the third derivative of -p**6/48 - 23*p**5/120 - p**4/4 - 79*p**2. Factor i(c).
-c*(c + 4)*(5*c + 3)/2
Suppose 297 = 3*q + 282. Let p(h) be the second derivative of -4*h + 0*h**2 - 1/33*h**4 + 1/33*h**3 + 0 + 1/110*h**q. Factor p(c).
2*c*(c - 1)**2/11
Let s = -43 + 73. Find n, given that -230*n**4 - 114*n**3 - 5*n - 51*n**3 - 83*n**2 + s*n**4 - 80*n**5 + 33*n**2 = 0.
-1, -1/4, 0
Factor -773*h + 4 + 10*h**2 + 4*h**2 + 755*h.
2*(h - 1)*(7*h - 2)
Suppose 20*k + 50 = 25*k. Let h be 2*(-4)/12*(-9)/k. Factor -4/5*j + 1/5*j**2 + h.
(j - 3)*(j - 1)/5
Let j(o) be the second derivative of -13*o**7/77 + 23*o**6/55 + 9*o**5/55 - 13*o**4/11 + 7*o**3/11 + 9*o**2/11 + 84*o. Let j(h) = 0. Calculate h.
-1, -3/13, 1
Let r(m) = -m**3 + 2*m**2 + m. Let p be r(2). Factor 0*y**3 - 3*y**2 + 3*y**3 + p*y**2 - 4*y**3.
-y**2*(y + 1)
Let l be (-8)/14*7/(-15). Let k(d) be the third derivative of -1/30*d