i(h) be the first derivative of 39*h**5/5 + 43*h**4/4 + h**3/3 - 3*h**2/2 + 3655. Factor i(k).
k*(k + 1)*(3*k + 1)*(13*k - 3)
Let t(g) be the first derivative of 2/3*g**2 + 8*g - 4/9*g**3 + 22. Determine d, given that t(d) = 0.
-2, 3
Let v(x) be the third derivative of x**7/70 - 5*x**6/8 + 183*x**5/20 - 275*x**4/8 - 242*x**3 + 658*x**2 - 2. Let v(t) = 0. What is t?
-1, 4, 11
Let x(z) = -z**3 + z**2 - z. Let k(l) = 6*l**4 - 18*l**3 - 23*l**2 + 36*l - 6. Let u(c) = -k(c) + 5*x(c). Determine q so that u(q) = 0.
-2, 1/6, 1, 3
Let r = 7195257/7 + -1027893. Factor -18/7*y**3 - 3/7*y**4 - r*y**2 + 9/7 + 15/7*y + 3/7*y**5.
3*(y - 3)*(y - 1)*(y + 1)**3/7
Suppose -5*y + 54*s = 50*s + 17, -s - 1 = 4*y. Let o be (64/288)/(y/(-6)). Factor o - 2/9*q - 2/9*q**2.
-2*(q - 2)*(q + 3)/9
Let c be (-135648)/(-256) - 2/(-16). Let z be (-1)/6 + c/300. Find n, given that z - 2*n**5 - 24/5*n + 34/5*n**3 - 6/5*n**4 - 2/5*n**2 = 0.
-2, -1, 2/5, 1
Let z(m) = 11*m**3 - 15*m**2 + 40*m + 12. Let n(a) = 2*a**3 + a**2 + 3*a + 2. Let q(o) = 6*n(o) - z(o). Factor q(r).
r*(r - 1)*(r + 22)
Let d(w) be the third derivative of -w**6/720 - w**5/20 - 5*w**4/16 + 49*w**2 + 5*w - 1. Solve d(u) = 0 for u.
-15, -3, 0
Let m(f) be the second derivative of f**5/390 + f**4/156 - 2*f**3/39 - 15*f**2 - 69*f. Let d(i) be the first derivative of m(i). Factor d(b).
2*(b - 1)*(b + 2)/13
Let b = 48 + -37. Suppose 3 + b = 7*g. Suppose 84 + 6*v**2 - v**2 + 28*v**g - 50*v - 46*v - 3*v**3 = 0. Calculate v.
2, 7
Let r = -4395 - -4397. Let h(t) be the third derivative of 0*t**3 + 0 - 1/24*t**4 + 0*t + 10*t**r + 3/40*t**5. Determine l, given that h(l) = 0.
0, 2/9
Let j be 14 + -13 + -3 + 7. Let w(f) be the third derivative of 1/15*f**j - 7/6*f**4 + 0*f + 0*f**3 + 28*f**2 + 0. Factor w(v).
4*v*(v - 7)
Let l(z) be the third derivative of z**7/630 - 13*z**6/360 - 241*z**5/60 + 1169*z**4/8 + 1323*z**3 - z**2 - 1286. Let l(h) = 0. Calculate h.
-27, -2, 21
Factor -2/3*f**3 + 2/9*f**5 - 10/9*f**2 + 0 - 4/9*f + 2/9*f**4.
2*f*(f - 2)*(f + 1)**3/9
Suppose 146*l - t = 143*l + 10, 0 = 5*l - 10*t. Let s(d) be the third derivative of 5/6*d**l + 0*d + 0 - 10/3*d**3 - 25*d**2 - 1/12*d**5. Solve s(h) = 0 for h.
2
Let c(y) be the second derivative of -y**6/45 + y**5/20 + y**4/18 - y**3/6 + 1077*y. Suppose c(v) = 0. What is v?
-1, 0, 1, 3/2
Suppose -12 = -4*j - 0. Suppose j*z = 3*f - 12, 0*f - 19 = -5*f + 4*z. Factor 16*v**2 + 8*v**f - 8*v - 7 - 5*v**4 - 5 - 3*v**4 + 4*v**4.
-4*(v - 3)*(v - 1)*(v + 1)**2
Let f = 105 - 97. Let p(o) = 8*o**2 - 5*o - 3. Let r(d) = -22*d**2 + 14*d + 8. Let m(w) = f*p(w) + 3*r(w). Factor m(l).
-2*l*(l - 1)
Let q(p) be the second derivative of p**8/2016 + 39*p**2 - 73*p. Let w(k) be the first derivative of q(k). Factor w(x).
x**5/6
Let u = -371111/5 + 74224. Factor -7/5*b - b**3 + 1/5*b**4 + u*b**2 + 2/5.
(b - 2)*(b - 1)**3/5
Let i(x) = -x**2 - 30*x + 16. Let l be i(-23). Let n be -4 + l/21 + (-8)/(-14). Let -48*q**4 - 2*q**2 - 58*q**4 + 118*q**4 - 7*q**n - 3*q**3 = 0. Calculate q.
-2/7, 0, 1
Let u(p) = 3*p**2 + 5*p - 8. Let t(c) = 8*c**2 + 14*c - 23. Let x(d) = -6*t(d) + 17*u(d). Let a(v) = -4 + 0 + 4 + 1. Let k(q) = -12*a(q) + 3*x(q). Factor k(h).
3*(h + 1)*(3*h - 2)
What is x in 954*x**3 + 288 + 2347*x**2 + 663*x**2 - 46*x**4 + 65*x**5 + 1580*x - 79*x**5 - 732*x**2 = 0?
-9, -1, -2/7, 8
Let s be (9/120)/(-7*18/(-168)). Let k(b) be the second derivative of 0*b**3 + s*b**2 + 1/150*b**6 - b + 0*b**5 + 0 - 1/30*b**4. Let k(w) = 0. Calculate w.
-1, 1
Let h(f) be the third derivative of -13/7*f**6 - f**2 - 30/49*f**7 - 26/21*f**4 - 8/21*f**3 - f - 229/105*f**5 + 0. Factor h(t).
-4*(3*t + 2)**2*(5*t + 1)**2/7
Let f(u) be the first derivative of -u**5/220 + 2*u**4/33 - 13*u**3/66 + 3*u**2/11 + 19*u + 99. Let b(q) be the first derivative of f(q). Factor b(n).
-(n - 6)*(n - 1)**2/11
Factor -27/2*h**2 + 504*h - 3/2*h**3 + 5586.
-3*(h - 19)*(h + 14)**2/2
Determine y, given that -336*y - 2923*y**2 - 128342*y**3 + y**5 - 128427*y**3 + 257104*y**3 + 43*y**4 + 2880 = 0.
-24, -1, 1, 5
Let s = 88181/100 - 22014/25. Find p such that s*p**2 + 1/4 + 3/8*p**3 + 9/8*p = 0.
-2, -1, -1/3
Let f(k) be the first derivative of -21 + 16/3*k**3 + 8*k**2 - 5*k**4 - 12/5*k**5 + 0*k. Factor f(s).
-4*s*(s - 1)*(s + 2)*(3*s + 2)
Let m(t) be the second derivative of -t**7/63 - 26*t**6/45 + 17*t**5/6 - 29*t**4/9 - 162*t. Let m(o) = 0. Calculate o.
-29, 0, 1, 2
Let q(f) = -f**3 - 2*f. Let x(a) = -a**4 - 10*a**3 + 43*a**2 + 13*a - 42. Let p(c) = 2*q(c) + 2*x(c). Let p(h) = 0. Calculate h.
-14, -1, 1, 3
Let o(m) be the third derivative of m**6/160 + 23*m**5/80 - 25*m**4/16 - 336*m**2. Factor o(d).
3*d*(d - 2)*(d + 25)/4
Let z(m) be the second derivative of -178*m**6/105 - 36*m**5/7 + 619*m**4/21 - 228*m**3/7 - 16*m**2/7 + 104*m - 1. Suppose z(d) = 0. What is d?
-4, -2/89, 1
Suppose -z = -2*g - 49, 4*z + 79 = 194*g - 197*g. Let m be 85/g + (-7 - -4) + 10. Suppose -12/5*p + m + 2/5*p**2 = 0. Calculate p.
3
Let h(w) = 3*w**3 - 5*w**2 + w + 5. Let g be h(4). Solve -c**3 - g*c - 3*c**3 + 89*c - 20*c**2 - 16 = 0 for c.
-2, -1
Let d(p) = -p**3 + 2*p**2 + 15997. Let l be d(0). Let 186*b**2 + 15949 + 4*b**3 + 146*b - l - 12*b**3 = 0. What is b?
-1, 1/4, 24
Let z be 1/((-3)/60*5). Let r be -4 + (-231)/(-44) + (-3)/z. Factor 50/3 + 2/3*n**r - 20/3*n.
2*(n - 5)**2/3
Suppose -4*u + 4 + 140 = q, q - 142 = -2*u. Let z be (32/q)/((-20)/(-50)). Determine j so that -1/7*j**5 + 0*j - 4/7*j**3 + z*j**4 + 0 + 0*j**2 = 0.
0, 2
Let p = 28 - 83/3. Let k = -58076/3 + 19359. Factor -l**2 - p*l**3 - k - l.
-(l + 1)**3/3
Let f(d) be the third derivative of -179*d**5/510 - 535*d**4/204 + 2*d**3/17 + 8*d**2 - 54*d. Factor f(v).
-2*(v + 3)*(179*v - 2)/17
Let w = -42/2209 - -2419/11045. Factor 2/5 + 1/5*a - 6/5*a**2 + 2/5*a**4 + w*a**3.
(a - 1)**2*(a + 2)*(2*a + 1)/5
Let d be 9/6 + (21/6 - 3). Factor -11*x**d - x**2 - 150*x + 4*x**2 + 3*x**2.
-5*x*(x + 30)
Let a be (2580/(-552))/43*-28. Factor -98/23 + 26/23*b**2 - 2/23*b**3 - a*b.
-2*(b - 7)**2*(b + 1)/23
Factor 47*t**3 - 594*t**2 - 8576*t - 9*t**4 + 2048 - 210*t**3 - 123*t**3 - 2222*t**2.
-(t + 8)**2*(t + 16)*(9*t - 2)
Let k be (-1029)/(-1029) - 2/6. Factor -150 - k*h**2 + 20*h.
-2*(h - 15)**2/3
Let d(g) = 12 + 14*g**3 + 27*g**2 + g**3 + 22*g - 23 + 14*g**2. Let l(z) = 5*z**3 + 14*z**2 + 8*z - 4. Let n(u) = -4*d(u) + 11*l(u). Factor n(o).
-5*o**2*(o + 2)
Suppose 6*x = 57 + 765. Determine o so that -83*o - 75*o + 3*o**2 + 30 + x*o = 0.
2, 5
Let x(z) be the third derivative of 0*z**3 - 37/245*z**7 + 1/14*z**4 + 17/35*z**5 + 0*z - 2*z**2 - 23/56*z**6 - 23. Let x(k) = 0. What is k?
-2, -2/37, 0, 1/2
Let y be (1*-3 - (-3480)/(-1800))/((-24)/(-1404)*-1). Factor 15*x**2 + 1369/5 - 1/5*x**3 - y*x.
-(x - 37)**2*(x - 1)/5
Determine n, given that -809*n**5 + 395*n**5 - 16*n**3 - 4256*n**2 + 416*n**5 + 8512 + 32*n + 532*n**4 = 0.
-266, -2, 2
Let r be ((-16)/7 + 2)/(6/(-18) - 772/(-4053)). Find p such that -363/2 + 3/2*p**3 + 429/2*p - 69/2*p**r = 0.
1, 11
Suppose 5*d = -2*p - p + 17, -4*d + 10 = 2*p. Let o be p/6 - (-441)/18. Factor -14*k - 5*k**2 + o - 6 - k.
-5*(k - 1)*(k + 4)
Let v = -89 + 122. Suppose -159*o - 17 + v*o**2 - 4 - 9 = 0. Calculate o.
-2/11, 5
Find w such that 89787/2 + 173*w + 1/6*w**2 = 0.
-519
Suppose 28747 = 35*q + 28677. Factor -1/5*n**3 + 11/5*n**q + 13/5 + 5*n.
-(n - 13)*(n + 1)**2/5
Let n = 239 + -236. Find w such that -2234*w - 45*w**2 - 5*w**n - 2255*w + 4369*w - 80 = 0.
-4, -1
Let m = -1663589/21 - -237665/3. Solve 2/7*y**2 - 24/7 + m*y = 0.
-12, 1
Let o(g) = -2*g**2 - 18*g - 16. Let n be o(-7). Determine s so that 10 - n*s + 8 - 18 + 8 + 4*s**3 = 0.
-2, 1
Let m(i) be the first derivative of 1568/5*i - 1/10*i**4 + 38/5*i**3 - 168*i**2 - 125. Find x, given that m(x) = 0.
1, 28
Let c be ((44/9)/11)/(2/((-32)/(-8))). Find s such that 2*s - 4/3*s**2 + 2/9*s**3 - c = 0.
1, 4
Let i(q) be the first derivative of q**2 - 1/4*q**3 - q + 1/20*q**5 - 1/8*q**4 + 92. Solve i(j) = 0.
-2, 1, 2
Let i(q) = -100*q**2 - 35*q - 9. Let m(a) = -104*a + 190*a - 50*a**2 - 103*a - 5. Let f(z) = 3*i(z) - 5*m(z). Determine k, given that f(k) = 0.
-1/5
Suppose 45*p**2 + 0 + 0*p**4 - 57/2*p**3 + 0*p + 3/2*p**5 = 0. What is p?
-5, 0, 2, 3
Let z be (9/(-6))/((-63)/(-42)). Let m be (6 - (z - 1)) + -6. Factor 2/9*p + 4/9 - 2/9