4
Let l(a) be the second derivative of a**5/10 - 29*a**4/9 - 119*a**3/27 - 20*a**2/9 + 514*a. Solve l(i) = 0 for i.
-1/3, 20
Suppose -5*h + 6*c + 864 = 2*c, 2*c = 8. Let v be (h/32)/((-2)/(-4)). What is m in 9*m + 13*m - 6*m - 6 - 21*m**2 + v*m = 0?
2/7, 1
Let s(v) be the second derivative of 0*v**2 + 0 - 146*v - 1/32*v**4 - 69/16*v**3. Suppose s(c) = 0. Calculate c.
-69, 0
Let r(w) be the second derivative of -w**4/3 - 56*w**3/3 - 11*w + 20. Suppose r(h) = 0. Calculate h.
-28, 0
Let p be -4*(-5 + 8)/(1 - 4). Factor 4*b**5 - 16*b**4 + 4*b**p - 2*b**3 + 18*b**3 - 4*b**4.
4*b**3*(b - 2)**2
Let h(x) = x**2 + 520*x - 37374. Let j be h(64). Factor 22/9*o - 8/3*o**j + 0 + 2/9*o**3.
2*o*(o - 11)*(o - 1)/9
Let n(t) be the first derivative of 0*t**2 - 3/8*t**4 - 1/8*t**6 + 9/20*t**5 + 0*t**3 + 0*t - 159. Factor n(u).
-3*u**3*(u - 2)*(u - 1)/4
Let s(i) = 37*i**4 - 450*i**3 + 1939*i**2 - 3098*i + 1500. Let q(m) = -75*m**4 + 900*m**3 - 3880*m**2 + 6195*m - 3000. Let d(p) = 2*q(p) + 5*s(p). Factor d(n).
5*(n - 5)**2*(n - 2)*(7*n - 6)
Let z(x) = -14*x + 101. Let u be z(7). What is v in 137*v - 72*v + 5*v**u + 5*v**2 - 75*v = 0?
-2, 0, 1
Let v(f) = 8*f - 318. Let p be v(39). Let o be ((1/p)/((-2)/4))/1. Factor -1/3*j**2 + o*j + 2.
-(j - 3)*(j + 2)/3
Suppose 10 - 17 - 37 = -11*i. Let o(r) be the second derivative of -3*r - 3/7*r**2 - 1/42*r**i + 4/21*r**3 + 0. Factor o(m).
-2*(m - 3)*(m - 1)/7
Let n = -1581 - -1581. Let o(s) be the first derivative of -3/16*s**2 + 1/6*s**3 + n*s - 1/32*s**4 + 2. Solve o(z) = 0.
0, 1, 3
Let u(q) be the first derivative of 83521*q**5 + 1295*q**3 + 97*q + 10265*q**3 - 176 + 49130*q**4 - 17*q + 1360*q**2. Factor u(p).
5*(17*p + 2)**4
Let y(v) be the second derivative of -2/21*v**7 + 0 - 7/5*v**5 + 0*v**2 + 0*v**3 - v**4 - 2/3*v**6 + 89*v. Find h, given that y(h) = 0.
-3, -1, 0
Find j, given that -2*j**3 + 751978*j + 4694048 - 2345163*j + 2*j**3 + 6130*j**2 - 2*j**3 - 3106991*j = 0.
1, 1532
Let f = 24470 + -24470. Determine z so that -3/4*z**2 + f + 21/4*z = 0.
0, 7
Let w(i) be the second derivative of -743*i**4/9 - 2974*i**3/9 - 4*i**2/3 - 7364*i. Factor w(m).
-4*(m + 2)*(743*m + 1)/3
Factor 2853571*j**2 + 35 - 179 - 2853573*j**2 + 34*j.
-2*(j - 9)*(j - 8)
Suppose -3*f + 0*x + x = -7, 0 = -3*x + 15. Factor -b**3 + 12 - 5*b**4 + f*b**3 + 4*b**4 + 31*b**2 - 22*b**2 - 23*b.
-(b - 4)*(b - 1)**2*(b + 3)
Suppose -5*b + 2*g + 11 = 0, -4*b + 5*g + 17 = -2*b. Let m be -1*(b/6)/((-28)/42). Factor -3/4*z - m*z**2 - 1/2.
-(z + 1)*(z + 2)/4
Let h(w) = -w**3 - w**2 - 7*w - 2. Let u(a) = 218*a**3 - 2167*a**2 + 1186*a - 194. Let b(d) = -7*h(d) + u(d). Factor b(z).
5*(z - 9)*(3*z - 1)*(15*z - 4)
Suppose 0 = -8*s + 2 + 14. Suppose 1626 + 7*p**2 - 18 - 180*p - 4*p**s + 1092 = 0. What is p?
30
Let x(o) be the second derivative of 7/3*o**3 + 1/3*o**4 - 163*o - 1/10*o**5 + 0 + 4*o**2. Factor x(k).
-2*(k - 4)*(k + 1)**2
Let r = 3079 - 1155. Factor 16*n**2 - 48 + 20*n**2 + 1716*n - r*n.
4*(n - 6)*(9*n + 2)
Let g = 13 - 10. Find w, given that 4 + 8*w + w + 4*w**g + 10*w**4 + 4*w**5 - 14*w**2 - 6*w**3 - 11*w = 0.
-2, -1, 1/2, 1
Let n(b) be the second derivative of b**7/70 + b**6/20 + b**5/20 - 69*b**2/2 + 10*b. Let x(d) be the first derivative of n(d). Factor x(y).
3*y**2*(y + 1)**2
Let n = -1/9274 + 23221/333864. Let b(p) be the second derivative of -5/36*p**3 - 5/6*p**2 + n*p**4 + 12*p + 0. Determine y so that b(y) = 0.
-1, 2
Let j(x) be the first derivative of 23 - 60*x**2 - 115*x - 5/3*x**3. Let j(k) = 0. Calculate k.
-23, -1
Let s(h) be the second derivative of -h**7/315 - h**6/45 - h**5/18 - h**4/18 + 19*h**2/2 - 6*h - 3. Let v(o) be the first derivative of s(o). Factor v(l).
-2*l*(l + 1)**2*(l + 2)/3
Find n such that -91/6*n**2 - 89/6*n**3 + 89/6*n + 15 + 1/6*n**4 = 0.
-1, 1, 90
Let m(x) be the first derivative of -1/15*x**3 - 81 - 1/5*x**2 + 0*x. Factor m(n).
-n*(n + 2)/5
Let z be (164/6 + 0)/((-27)/(-162)). Suppose 3*v - 2*w = 8*v - 820, z = v - 2*w. Factor -v*q**4 + 40*q + 159*q**4 + 11*q**2 + 19*q**2 + 15.
-5*(q - 3)*(q + 1)**3
Let a(z) be the first derivative of 5*z**3/3 - 235*z**2/2 + 8987. Factor a(n).
5*n*(n - 47)
Let a(x) = 14*x**2 + 14*x - 10. Let z be a(7). Let b = z - 771. Determine f so that -3*f**2 - 1/2*f**b - 9/2*f - 2 = 0.
-4, -1
Let r(i) be the first derivative of -18*i**5/35 + 11*i**4/2 - 394*i**3/21 + 199*i**2/7 - 20*i + 4562. Solve r(s) = 0 for s.
1, 14/9, 5
Let g be (-142)/(-497) + 2/14*-2. Let l(z) be the third derivative of 0*z + 6/25*z**5 + g + 1/30*z**6 - 4*z**2 + 7/30*z**4 - 4/5*z**3. Factor l(b).
4*(b + 1)*(b + 3)*(5*b - 2)/5
Let p(x) be the third derivative of -x**6/60 + x**5/15 + 49*x**4/12 - 98*x**3/3 + 2447*x**2. Factor p(f).
-2*(f - 7)*(f - 2)*(f + 7)
Let o(j) = -161580*j**2 + 6436*j - 56. Let v(b) = -6*b**2 - b - 2. Let g(u) = o(u) + 4*v(u). Find q, given that g(q) = 0.
4/201
Let l(o) be the third derivative of 7*o**8/96 - 13*o**7/14 + 29*o**6/6 - 38*o**5/3 + 15*o**4 + 8*o**3/3 + 362*o**2 + 2*o + 8. Factor l(v).
(v - 2)**4*(49*v + 2)/2
Factor -53725 - 53864 - 189436 + 1065*j**2 + 5*j**3 + 53955*j.
5*(j - 5)*(j + 109)**2
Let l(i) = -5*i**4 + 6*i**3 - 12*i**2 - 4*i. Let x(g) = g**4 - g**3 - 2*g. Suppose -4*c = 2*d - 10, 7 = c - 3*d + 15. Let r(q) = c*l(q) + 6*x(q). Factor r(j).
j*(j - 4)*(j + 2)**2
Let h(m) be the second derivative of 3*m**5/100 + 5*m**4 + 1144*m**3/5 - 16224*m**2/5 + m - 288. Find d such that h(d) = 0.
-52, 4
Let o = -801911/7 - -114775. Let k = o + -215. Factor k*f**2 - 6/7*f**3 + 1/7*f**4 + 0 + 0*f.
f**2*(f - 3)**2/7
Let m(r) be the first derivative of r**4/32 - 27*r**2/16 - 66*r + 51. Let t(z) be the first derivative of m(z). Determine x so that t(x) = 0.
-3, 3
Let s be (96/(-9) + 12)*(-423)/(-2). Suppose -72 = 246*k - s*k. Suppose -15/4*g**3 - 165/4*g - 45/4 - 95/4*g**k = 0. What is g?
-3, -1/3
Suppose -468*k = -465*k - 12. Let 138 - 2*r - 2*r**3 - 138 + k*r**2 = 0. Calculate r.
0, 1
Let y(f) be the second derivative of f**6/50 - 63*f**5/20 + 23*f. Solve y(k) = 0 for k.
0, 105
Let x be ((25/(-7))/(-5))/((-1441)/77 + 19). Factor -x*t + 1/4*t**2 - 11/4.
(t - 11)*(t + 1)/4
Let r(y) = -3*y**2 - 620*y + 543. Let n(w) = -23*w + 3. Let v(t) = 4*n(t) - r(t). Factor v(d).
3*(d - 1)*(d + 177)
Let h(f) = 7*f - 47. Let b be h(7). Let -36*o**2 - 2*o**5 + 15*o**4 + 8*o**5 + 44*o**b - 23*o**2 - 6*o = 0. What is o?
-2, -1, -1/2, 0, 1
Let l(o) = 3*o**2 - 5*o - 44. Let q be l(-4). Let i(g) be the first derivative of -64*g + q*g**2 - 4*g**3 + 1/4*g**4 + 9. Let i(h) = 0. What is h?
4
Let o(u) be the second derivative of -u**6/60 + 359*u**5/20 - 128881*u**4/24 + 133*u - 1. Factor o(k).
-k**2*(k - 359)**2/2
Let r = -2244 + 31419/14. Let z(w) be the first derivative of r*w**4 + 15 - 3/7*w**2 + 0*w**3 + 3/35*w**5 - 3/7*w. Solve z(n) = 0 for n.
-1, 1
Let h(g) = 3*g + 21. Let m be h(-11). Let z be (-15)/28*16/m. What is p in z*p + 2/7 - p**2 = 0?
-2/7, 1
Let a(v) = 6*v**5 + 2*v**4 - 31*v**3 + 16*v**2 - 56*v + 7. Let x(b) = b**5 - b**4 - b**3 - 8*b + 1. Let i(r) = -5*a(r) + 35*x(r). Factor i(l).
5*l**2*(l - 4)**2*(l - 1)
What is u in -128/3 - 290/3*u**2 - 302/9*u**3 - 2/9*u**5 - 992/9*u - 14/3*u**4 = 0?
-8, -3, -1
Let q(g) = 27375*g**2 - 537*g - 1. Let t(n) = 191624*n**2 - 3782*n - 8. Let m(p) = -44*q(p) + 6*t(p). Factor m(j).
-4*(117*j - 1)**2
Factor 5/3*j**3 - 50/3*j - 40/3 - 5/3*j**2.
5*(j - 4)*(j + 1)*(j + 2)/3
Let t be (-39)/45 - (-31 - (-1408)/48). Factor -8/5*h - t - 4/5*h**2.
-4*(h + 1)**2/5
Let k(p) be the second derivative of 13/18*p**3 + 0 - 76*p - 2*p**2 - 1/36*p**4. Factor k(c).
-(c - 12)*(c - 1)/3
Let z = -6 - -33. Suppose 15*w - 18*w = -z. Factor -5*y**2 - 20*y - w*y**2 + 24 + 3*y**2 + 7*y**2.
-4*(y - 1)*(y + 6)
Let n(p) be the first derivative of -p**6/1800 + p**5/600 - p**3/3 - 83*p**2/2 + 136. Let c(r) be the third derivative of n(r). Factor c(x).
-x*(x - 1)/5
Let f be (-9)/(-56) - (73 - (-25740)/(-352)). Factor 0 - 12/7*q - f*q**2.
-2*q*(q + 6)/7
Let i(g) be the first derivative of g**7/70 + 3*g**6/40 - g**5/5 - 21*g**2 - 26. Let f(t) be the second derivative of i(t). What is n in f(n) = 0?
-4, 0, 1
Suppose -64 = 16*s - 20*s. Let x = -13 + s. Factor 14 + 508*r**2 + 204*r - 1430*r**4 + 1029*r**5 - 483*r**x + 254*r**4 - 106*r**2 + 10.
3*(r - 1)**2*(7*r + 2)**3
Let a(t) = t**3 - 16*t**2 + 30*t - 25. L