t b(o) be the first derivative of -o**5/45 + 23*o**4/27 + 2*o**3/27 - 46*o**2/9 - 73*o + 160. Let c(s) be the first derivative of b(s). Factor c(h).
-4*(h - 23)*(h - 1)*(h + 1)/9
Let y(l) = -16*l**4 + 102*l**3 - 1376*l**2 + 3812*l. Let m(x) = -5*x**4 + 36*x**3 - 459*x**2 + 1271*x. Let f(n) = 10*m(n) - 3*y(n). Let f(c) = 0. What is c?
0, 7, 13
Let q be 12/(-14)*(-455)/195. Let a(z) be the third derivative of -1/54*z**4 - 21*z**q + 4/135*z**5 + 0*z + 0*z**3 + 0 - 1/72*z**6. What is y in a(y) = 0?
0, 2/5, 2/3
Let u be 518/(-111) - (-3 - 3). Let b(h) be the second derivative of 0 - 30*h + 0*h**2 + 2/15*h**6 + 2/5*h**5 - u*h**3 - 1/3*h**4. Let b(t) = 0. What is t?
-2, -1, 0, 1
Suppose 2 = 4*g + 3*j, 5*j + 4 = -3*g - 0*j. Let m be 170/(-1445) - 2*(-205)/595. Factor -16/7 + 12/7*q + m*q**g.
4*(q - 1)*(q + 4)/7
Let c(b) be the first derivative of -39/2*b**2 - 231 - 66*b + 3/5*b**5 + 21*b**3 + 39/4*b**4. Find f, given that c(f) = 0.
-11, -2, -1, 1
Let g be (-4)/(-6) + 2/(42/1435). Suppose g*s**3 - 134*s**3 + 64*s**3 + 5*s + 4*s**2 = 0. Calculate s.
-1, 0, 5
Let p(h) be the first derivative of 12/5*h + 2/5*h**2 + 123 - 1/15*h**3. Let p(o) = 0. Calculate o.
-2, 6
Let l(w) = 2229*w - 17827. Let n be l(8). Suppose 0*k**3 - 8/5*k**4 + 4/5*k + 8/5*k**2 + 0 - 4/5*k**n = 0. What is k?
-1, 0, 1
What is w in 1091*w**4 + 368*w**3 + 2292*w**2 + 1099*w**4 + 484 + 2837*w - 2174*w**4 - 813*w = 0?
-11, -1/2
Suppose -83/4 + 21*k - 1/4*k**2 = 0. Calculate k.
1, 83
Suppose -138 - 244 = -191*o. Let l(i) be the first derivative of -19 - 40/3*i**o + 2/3*i**5 - 10/3*i**4 - 1/18*i**6 + 32/3*i + 80/9*i**3. What is a in l(a) = 0?
2
Suppose -475*h - 161*h + 7701 - 4236 = -7983. Factor -3/5*d**3 - 600 - h*d**2 - 180*d.
-3*(d + 10)**3/5
Let b(s) be the first derivative of 0*s**5 - 2/3*s**3 + 0*s + 6 + 0*s**2 + 1/6*s**6 - 3/4*s**4. Factor b(l).
l**2*(l - 2)*(l + 1)**2
Let o(k) be the first derivative of 98*k**5/45 + 721*k**4/9 - 2648*k**3/9 + 1912*k**2/9 - 512*k/9 + 3366. Find l such that o(l) = 0.
-32, 2/7, 2
Let m(q) = 3*q**4 + 358*q**3 - 30617*q**2 - 126736*q - 128236. Let z(n) = -n**4 - n**3 + n**2 + n + 18. Let r(p) = m(p) + 4*z(p). Factor r(g).
-(g - 179)**2*(g + 2)**2
Factor -198*h - 198*h - 240 + 108*h - 6210*h**2 + 3*h**3 + 6165*h**2.
3*(h - 20)*(h + 1)*(h + 4)
Let b = -2050/131 - -10381/655. Find x such that -b*x**5 + 0*x + 0*x**3 + 0*x**2 - 4/5*x**4 + 0 = 0.
-4, 0
Let y = 59020 + -59016. Factor -6*x**3 - 6/5 - 52/5*x**2 + 2/5*x**y + x**5 - 31/5*x.
(x - 3)*(x + 1)**3*(5*x + 2)/5
Let f(r) = -5*r**3 - 992*r**2 + 2987*r - 1984. Let t(w) = -4*w**3 - 992*w**2 + 2988*w - 1988. Let i(v) = 2*f(v) - 3*t(v). Find k such that i(k) = 0.
-499, 1, 2
Let y(p) be the second derivative of p**5/120 + 17*p**4/72 + 3*p**3/4 - 15*p**2/4 - 5*p + 113. Factor y(v).
(v - 1)*(v + 3)*(v + 15)/6
Let g(h) = 20*h**5 + 30*h**4 - 50*h**3 + 25*h**2 + 60*h + 5. Let o(q) = -q**5 - q**4 - q**2 - q - 2. Let z(i) = -g(i) - 15*o(i). Suppose z(d) = 0. What is d?
-5, -1, 1
Let a be (-1)/(-6 - 116/(-20)). Suppose 5*t + a = 47*q - 48*q, 3*q - 1 = t. Factor q - 4/7*c**3 - 8/7*c - 2*c**2 + 2/7*c**4.
2*c*(c - 4)*(c + 1)**2/7
Let t = -79 + 82. Factor 18*c**4 + 829*c - 297*c + 40*c**t - 424*c**2 - 196 + 26*c**4 + 4*c**5.
4*(c - 1)**3*(c + 7)**2
Let x be (-384)/624 + (-721)/(-728). Factor x*m**2 - 18*m + 216.
3*(m - 24)**2/8
Let m(c) be the first derivative of c**6/14 - 18*c**5/5 - 99*c**4/7 - 134*c**3/7 - 135*c**2/14 - 605. Factor m(i).
3*i*(i - 45)*(i + 1)**3/7
Let o(y) be the first derivative of -y**4/2 + 851*y**3/3 - 635*y**2 - 848*y - 510. Let o(a) = 0. Calculate a.
-1/2, 2, 424
Let w = -705683 + 705713. Suppose 5/4*z**4 + w*z**2 + 55/2*z + 25/2*z**3 + 35/4 = 0. What is z?
-7, -1
Let n(z) be the first derivative of z**4 + 56*z**3 + 922*z**2 + 1680*z + 6174. Find r such that n(r) = 0.
-21, -20, -1
Let s(h) be the third derivative of -2*h**2 - 32/3*h**4 + 32*h**3 + 0*h**6 + 8/5*h**5 - 2/105*h**7 + 76 + 0*h. Factor s(v).
-4*(v - 2)**3*(v + 6)
Suppose -70*t + 25*t = -t - 20*t - 432. Solve 0 - 33*l**2 + t*l**3 + 0*l - 3/4*l**4 = 0.
0, 2, 22
Let t(s) be the second derivative of 2*s**7/21 - 14*s**6/15 + 13*s**5/5 - s**4/3 - 28*s**3/3 + 16*s**2 - 165*s - 1. Suppose t(p) = 0. What is p?
-1, 1, 2, 4
Let g(r) be the third derivative of 3/112*r**8 + 5*r**2 + 1/30*r**6 - 3/10*r**5 - 13/24*r**4 + 0*r - 1/3*r**3 + 2/21*r**7 - 1. Let g(l) = 0. What is l?
-1, -2/9, 1
Let c be (-4)/(-18) - 2 - -2. Suppose 1074*l - 1082*l + 28 - 4 = 0. Determine m, given that 0 - c*m**4 - 2/9*m**5 + 4/9*m + 2/3*m**l + 10/9*m**2 = 0.
-1, 0, 2
Let g(m) = 6*m**2 - 69*m + 36. Let v be g(11). Let z(i) be the second derivative of -11/2*i**v + 0 - 37*i + 3*i**2 + 5/4*i**4. Factor z(j).
3*(j - 2)*(5*j - 1)
Let s(h) be the second derivative of -h**5/140 + 15*h**4/56 + 57*h**2/2 - h - 24. Let r(m) be the first derivative of s(m). Factor r(y).
-3*y*(y - 15)/7
Let g(i) be the first derivative of -1/4*i**4 + i**3 - 3*i + 1/2*i**2 + 25. Determine n, given that g(n) = 0.
-1, 1, 3
Let -26*s**4 - 14581*s**2 - 113*s + 134*s**3 + 36 + 7239*s**2 - 109*s + 7244*s**2 = 0. Calculate s.
-1, 2/13, 3
Let p(d) = d**3 - 19*d**2 - 241*d - 307. Let y be p(28). What is o in -2*o**2 - 1/2*o**3 - 5/2*o - y = 0?
-2, -1
Let f be 10/(-4)*(48/15 + -4). Factor 120 + 5100*o**f - 5*o**3 - 43*o - 5145*o**2 - 27*o.
-5*(o - 1)*(o + 4)*(o + 6)
Let -4/3*p**5 + 220/3*p**4 - 212*p**3 + 0 - 208/3*p + 628/3*p**2 = 0. What is p?
0, 1, 52
Let m(n) be the first derivative of 316 + 1/3*n**3 + 0*n + 0*n**2. Let m(k) = 0. What is k?
0
Let x(d) = -20*d**3 - 108*d**2 + 104*d. Let v(f) = -26*f**3 - 109*f**2 + 105*f. Let w(y) = -4*v(y) + 5*x(y). Factor w(a).
4*a*(a - 25)*(a - 1)
Let r(s) be the third derivative of -s**5/30 + 517*s**4/2 - 801867*s**3 - 818*s**2. Factor r(v).
-2*(v - 1551)**2
Let b = -11387 + 11392. Let m(j) be the third derivative of 0*j**3 + 1/240*j**b + 9*j**2 + 0*j + 0 - 1/48*j**4. Factor m(f).
f*(f - 2)/4
Solve 345*g + 687/2 + 3/2*g**2 = 0 for g.
-229, -1
Let a = -142877 + 142881. Determine t, given that -4*t**3 + 4*t**a + 0*t + 0 + 4/3*t**2 - 4/3*t**5 = 0.
0, 1
Let s(r) be the second derivative of -15*r**7/14 - 157*r**6/2 - 65*r**5/2 + 575*r**4 + 1220*r**3 + 1040*r**2 + 239*r. Let s(m) = 0. What is m?
-52, -1, -2/3, 2
Let l(t) be the second derivative of -2*t**2 - 3/7*t**3 + 0 + 1/70*t**5 - 108*t + 1/7*t**4. Factor l(j).
2*(j - 2)*(j + 1)*(j + 7)/7
Suppose 5*t - 100 - 184 = i, 4*t + i = 220. Factor -h - 42*h**3 - t*h**3 - 17*h - 84*h**2.
-2*h*(7*h + 3)**2
Suppose 4*i - 206 = -5*h - 167, -33 = -5*h - 3*i. Suppose 27/4*z**2 - 3/2 - 17/4*z - z**h = 0. Calculate z.
-1/4, 1, 6
Let g(m) be the third derivative of m**6/24 - 11*m**5/4 + 60*m**4 - 630*m**3 + 138*m**2 + m. Factor g(w).
5*(w - 21)*(w - 6)**2
Let a(n) = 2*n**3 + n + 1. Let j(v) = -18*v**3 - 6*v**2 - 8*v. Let c(x) = -8*a(x) - j(x). Find p such that c(p) = 0.
-2, 1
Suppose -92/7*m - 4/7*m**3 + 64/7 - 10*m**2 = 0. Calculate m.
-16, -2, 1/2
Let i be (-1323)/(-315) + 51/5. Factor 96/5*q - i + 2/5*q**3 - 26/5*q**2.
2*(q - 6)**2*(q - 1)/5
Let o(v) = 354*v**2 - 703*v - 5. Let b be o(2). Factor 0 - 1/3*d**2 + b*d.
-d*(d - 15)/3
Let g(u) be the first derivative of u**7/42 - u**6/10 + u**5/10 + 64*u + 27. Let b(y) be the first derivative of g(y). Factor b(l).
l**3*(l - 2)*(l - 1)
Find m, given that 416*m**2 + 201*m**3 + 4*m**4 + 6*m + 6*m - 117*m**3 - 12*m = 0.
-13, -8, 0
Suppose 2*h = -c - 43 + 35, 4*c - 12 = 3*h. Let g be (-176)/(-198)*(c - 500/(-16)). Factor 400/9*t + g + 32/9*t**3 + 20*t**2 + 2/9*t**4.
2*(t + 1)*(t + 5)**3/9
Let a be (2/2)/(-7*(-12)/(-588)). Let j be a + (292/18 - 9). Factor -1/9*z**3 + 1/3*z**2 + 0 - j*z.
-z*(z - 2)*(z - 1)/9
Let n(r) = r**4 + r**3 - r**2 - 2*r + 2. Let s(h) = -15*h**4 - 1341*h**3 + 399*h**2 + 1342*h - 386. Let d(l) = n(l) + s(l). Let d(j) = 0. Calculate j.
-96, -1, 2/7, 1
Let b = 225 - 221. Factor -2*n**3 + 59*n**b - 61*n**4 - 2*n**3.
-2*n**3*(n + 2)
Let s(g) be the first derivative of -g**6/840 - g**5/40 - 3*g**4/28 - 22*g**3 + 53. Let z(l) be the third derivative of s(l). Factor z(k).
-3*(k + 1)*(k + 6)/7
Let y(t) be the third derivative of 4*t**7/245 + 37*t**6/210 + 71*t**5/105 + t**4 + 3*t**2 - 30*t - 16. Solve y(m) = 0.
-3, -2, -7/6, 0
Let x = 11/4452 + 12709/4452. Suppose 1/7*b**2 - x*b + 0 = 