1. Let x(d) be the third derivative of r(d). Factor x(k).
k*(k - 1)**2*(k + 1)**2
Let f(n) = 3*n - 81. Let x be f(28). Let s be (-9)/(-18) - (1 - (-1)/(-2)). Determine q so that 1/4*q + 1/4*q**x - 1/2*q**2 + s = 0.
0, 1
What is s in -22499 + 22518 - 127*s**2 - s**3 + 144*s**2 + 37*s = 0?
-1, 19
Let h be 5 - 1 - 10/((-70)/(-7)). Let b(n) be the second derivative of 0 + 0*n**2 + 3/20*n**5 + 1/20*n**6 + 1/8*n**4 + 11*n + 0*n**h. Let b(v) = 0. What is v?
-1, 0
Let m(g) = 5*g**2 + 33*g + 20. Let o be m(-6). Let s(i) be the first derivative of 5/2*i**o - 18 + 10*i - 5/3*i**3. Let s(p) = 0. Calculate p.
-1, 2
Suppose -s - 74*k = -69*k + 37, -4*s = -4*k - 44. Suppose 4/9 - 4/9*n**5 - 2/9*n**2 - 10/9*n + 14/9*n**s - 2/9*n**4 = 0. What is n?
-2, -1, 1/2, 1
Determine w, given that 40*w**3 + 120*w - 86084*w**4 - 81*w**2 + 43039*w**4 - 43*w**2 + 43041*w**4 = 0.
0, 2, 3, 5
Let v = 1376860/7 + -196690. Factor 27/7*m + 3/7*m**2 - v.
3*(m - 1)*(m + 10)/7
Let i(h) be the third derivative of 5/144*h**4 + 11*h**2 + 0*h + 0 - 2*h**3 - 1/1080*h**6 + 1/80*h**5. Let y(m) be the first derivative of i(m). Factor y(l).
-(l - 5)*(2*l + 1)/6
Let -27075 - 1/3*o**2 - 190*o = 0. What is o?
-285
Let g(z) be the second derivative of z**5/50 - 11*z**4/15 - 79*z**3/15 + 20*z**2 + 4279*z. Factor g(o).
2*(o - 25)*(o - 1)*(o + 4)/5
Suppose -4*d + 24 = 2*d. Let k(x) = 7*x - 26. Let v be k(d). Factor 8*q - q**3 - 3*q**3 + 8*q**v + 6*q**3.
2*q*(q + 2)**2
Let k = 370 - 753. Let f = k + 385. Let 0 + 8/9*w**3 + 0*w + 2/9*w**4 + 8/9*w**f = 0. Calculate w.
-2, 0
Let v = 338 + -344. Let k be ((-108)/1449)/(v/63). Factor -2/23*t**3 - 30/23*t - 14/23*t**2 - k.
-2*(t + 1)*(t + 3)**2/23
Let w(b) be the third derivative of 67*b**2 + 0*b**6 + 0 - 1/192*b**4 + 1/840*b**7 + 0*b**3 - 1/240*b**5 + 1/2688*b**8 - 2*b. Factor w(y).
y*(y - 1)*(y + 1)**3/8
Let q be (-38)/(-19) + 27/((-1080)/50). Solve -1/4*l**2 + 0 - q*l**4 - 5/4*l**3 + 1/4*l = 0.
-1, 0, 1/3
Let u be (-336)/(-4368) + 844/182. Suppose u*m - 9/7*m**3 + 3/7*m**4 - 9/7*m**2 - 18/7 = 0. What is m?
-2, 1, 3
Let d = 133 + -131. Find p such that 5 - 1 + 5 - 3*p - 3*p - 3*p**d = 0.
-3, 1
Suppose -3*v = -5*l + 2334, -4*l + 1075 = v - 782. Let b = 469 - l. Let -87/7*s**3 - 3*s**5 + 66/7*s**2 - 90/7*s**b + 108/7*s + 24/7 = 0. Calculate s.
-2, -1, -2/7, 1
Suppose 2 = -5*i + 6*i. Suppose 0 = -5*t - 8 + 63. Determine p, given that t*p + 93*p**3 + 0*p**i - 92*p**3 - 7*p**2 - 5 = 0.
1, 5
Suppose -92*f - 16 = -100*f. Let q(u) be the second derivative of -1/20*u**5 - 7*u + 1/6*u**3 + 0*u**4 + 1/60*u**6 - 1/4*u**f + 0. Factor q(m).
(m - 1)**3*(m + 1)/2
Let q(i) be the third derivative of 0 - 1/60*i**5 + 0*i**3 - 34*i**2 - 2*i - 1/1680*i**7 + 1/48*i**4 + 1/192*i**6. Find d, given that q(d) = 0.
0, 1, 2
Let w(d) be the second derivative of d**4/48 + 21*d**3/2 + 3969*d**2/2 + d - 80. Factor w(u).
(u + 126)**2/4
Suppose 6*q + 135 - 177 = 0. Let a(r) be the first derivative of -q + 0*r + 10/3*r**3 + 5/2*r**2. Factor a(h).
5*h*(2*h + 1)
Let m(h) be the second derivative of h**5/4 - 80*h**4/3 + 625*h**3/6 - 155*h**2 - 1203*h. Find q such that m(q) = 0.
1, 62
Let c(m) be the second derivative of 3*m**7/28 + 61*m**6/20 + 17*m**5/20 - 137*m**4/6 - 142*m**3/3 - 40*m**2 + 3357*m. Suppose c(g) = 0. What is g?
-20, -1, -2/3, 2
Let x(w) = -657*w**2 - 10519*w - 110. Let z be x(-16). Factor 4/5 + 6/5*s + 2/5*s**z.
2*(s + 1)*(s + 2)/5
Factor -61/2 + 29/3*m + 1/6*m**2.
(m - 3)*(m + 61)/6
Let f(s) be the third derivative of 0*s + 1/1155*s**7 + 0*s**3 + 1/165*s**6 + 1/66*s**4 + 0 - 71*s**2 + 1/66*s**5. Factor f(a).
2*a*(a + 1)**2*(a + 2)/11
Let n = -5 - -5. Suppose -14 = -4*z - 2*b, -4*z - 5*b + 2*b + 17 = n. Factor 6*o**3 + 6*o**z - 4*o**2 - 4*o**3.
2*o**2*(o + 1)
Let z(y) = -10*y**2 + 32*y + 1405 - 1425 + 46*y. Let p(h) = 9*h**2 - 79*h + 20. Let s(n) = 4*p(n) + 5*z(n). Factor s(g).
-2*(g - 5)*(7*g - 2)
Let s(v) be the first derivative of 4*v**3/21 + 27*v**2/2 + 185*v/7 + 69. Suppose s(j) = 0. What is j?
-185/4, -1
Let o(m) be the second derivative of m**6/8 - 591*m**5/40 - 21*m**4/4 + 197*m**3/4 + 237*m**2/8 - m - 3209. Find r such that o(r) = 0.
-1, -1/5, 1, 79
Suppose 63404 = 41*j + 3011. Let z = j + -1471. Factor -1 - 13/2*n**2 + 11/2*n + z*n**3.
(n - 2)*(n - 1)*(4*n - 1)/2
Let l(s) be the first derivative of s**4/126 - s**3/63 - 98*s + 253. Let u(q) be the first derivative of l(q). Solve u(f) = 0 for f.
0, 1
Let n(k) = -k**2 - 4 - k**2 - 4*k + 14*k. Let j be n(4). Let -10*y**3 + 5*y**2 + 5*y**j + 28 - 56 + 28 = 0. Calculate y.
0, 1
Suppose 2233 + 1706 = 1313*n. Determine f, given that 0 + 2*f**n - 1/4*f**4 - 36*f + 3*f**2 = 0.
-4, 0, 6
Let y(a) be the first derivative of 0*a**4 - 3/5*a**5 + 71 - 3*a + 0*a**2 + 2*a**3. Let y(m) = 0. Calculate m.
-1, 1
Suppose 4*v = -2*j + 234, 0 = -18*v + 14*v + 4. Let 60*a - 5*a**5 - 38790 + 38790 - 15*a**4 + j*a**2 + 45*a**3 = 0. Calculate a.
-4, -1, 0, 3
Let o(y) = -41*y + 2. Let f be o(2). Let u = -76 - f. Determine g, given that 0*g**u + 28*g**3 - 15*g**3 - 2*g**4 + 6*g**2 - 17*g**3 = 0.
-3, 0, 1
Let q(s) be the second derivative of -s**5/270 + 19*s**4/108 - 139*s**2/2 + 16*s - 1. Let w(g) be the first derivative of q(g). Factor w(l).
-2*l*(l - 19)/9
Let y(g) be the third derivative of -1/10*g**4 - 51*g**2 + 1/50*g**6 + 0*g + 0*g**3 - 1/150*g**5 + 0 + 1/525*g**7. Factor y(i).
2*i*(i - 1)*(i + 1)*(i + 6)/5
Let s(k) = 9*k**3 - 271*k**2 - 334*k + 1684. Let n(j) = -55*j**3 + 1625*j**2 + 2010*j - 10105. Let m(v) = -4*n(v) - 25*s(v). What is w in m(w) = 0?
-3, 2, 56
Let r(o) be the first derivative of -7*o**4/6 - 52*o**3/9 - 13*o**2/3 + 4*o - 4329. Factor r(l).
-2*(l + 1)*(l + 3)*(7*l - 2)/3
Let x = 6354 - 6348. Factor 2/3*d**4 + 10/3*d + 0 - x*d**2 + 2*d**3.
2*d*(d - 1)**2*(d + 5)/3
Solve 135 + 62537*r**3 + 1161*r + 682*r**2 - 40*r**2 - 62585*r**3 = 0.
-3/2, -1/8, 15
Determine y so that 237*y**3 + 25783*y**2 - 973*y - 108*y**4 + 512 + 349*y + 391*y**3 - 4*y**5 - 26187*y**2 = 0.
-32, -1, 1, 4
Let j(g) = 3*g**5 + 8*g**4 + 11*g**3 - 8*g**2 - 12*g. Let k(a) = 7*a**5 + 17*a**4 + 23*a**3 - 18*a**2 - 24*a. Let u(s) = 5*j(s) - 2*k(s). Factor u(w).
w*(w - 1)*(w + 2)**2*(w + 3)
Let z(f) = -f**3 - 2*f**2 + 2*f - 6. Let s be z(-3). Let q be ((-5)/(-3) - -2) + s. Determine k so that 0 - q*k**2 + 0*k - 2/3*k**5 + 2/3*k**4 + 2/3*k**3 = 0.
-1, 0, 1
Let r(d) = d**3 + 2*d**2 + 4*d. Let y(q) = -18*q**3 + 1461*q**2 - 1830*q + 408. Let s(w) = -3*r(w) + y(w). Let s(g) = 0. Calculate g.
2/7, 1, 68
Suppose -60*r - 6*r = -264. Let t(q) be the first derivative of -5/2*q**2 + 5*q**3 + q**5 + 0*q + 15 - 15/4*q**r. Factor t(a).
5*a*(a - 1)**3
Suppose -189 = -21*p + 84. Suppose -2*t = 4*b - 6, p*t = -5*b + 12*t + 9. Suppose 0 + 3/2*d + 3/2*d**4 - 3/2*d**b - 3/2*d**3 = 0. What is d?
-1, 0, 1
Let j = -71/11527 - -11740/34581. Factor -j*p**2 - 17/3*p - 10.
-(p + 2)*(p + 15)/3
Let k = 34365/6242 + -17/3121. Factor 0 + 1/2*q + k*q**2.
q*(11*q + 1)/2
Let r(f) be the third derivative of f**7/140 + 5*f**6/48 + f**5/15 - 4*f**2 + 106. Solve r(u) = 0.
-8, -1/3, 0
Suppose 4*n + 220 = 50*h - 52*h, 3*h = -n - 60. Let l be ((-42)/315)/(12/n). Let -11/5*g + l*g**2 - 1/5*g**4 + 3/5*g**3 + 6/5 = 0. Calculate g.
-2, 1, 3
Factor 72*c**2 - 32*c**2 - 20*c**2 - 25*c**2 + 1285 - 1280*c.
-5*(c - 1)*(c + 257)
Let v(q) = -36*q**2 + 69*q. Let r(b) = b**2 - b - 1. Let f be (8/(-12))/(-4*(-1)/(-6)). Let z(s) = f*v(s) + 6*r(s). Let z(h) = 0. What is h?
1/10, 2
Determine k so that 11*k**3 + 213*k**2 + 75*k**2 - 26*k**3 + 13*k**3 + 1782*k + 2700 = 0.
-3, 150
Let y be -35*24/(-84) - (-396)/(-77). Determine d, given that -2/7*d**2 + 76/7 + y*d = 0.
-2, 19
Factor 4738 - 85*x - 1258 + 5*x**2 + 467*x + 793*x.
5*(x + 3)*(x + 232)
Let x(n) be the second derivative of n**4/30 - 214*n**3/15 + 11449*n**2/5 + 683*n. Factor x(o).
2*(o - 107)**2/5
Suppose -4550*p = -4586*p + 72. Let f = -2 - -2. Find n such that 4/3*n**3 + 8/3*n**p + f + 4/3*n = 0.
-1, 0
Let w(g) = 27*g**2 + g - 381 + 381. Let d be w(-1). Determine l so that -d*l**2 + 2*l - 2*l**5 + 30*l**2 + 0*l - 4*l**4 = 0.
-1, 0, 1
Let l(u) be the first derivative of 3*u**4/4 - 19*u**3 - 123*u**2/2 - 63*u - 6734. Factor l(w).
3*(w - 21)*(w + 1)**2
Factor -58824*k**2 + 7808*k + 117732*k**2 + 1712*k - 43*k**3 - 58840*k**2 + 9408 + k**4.
(k - 28)**2*(k + 1)*