2*(b + 2)*(b + 5)
Let u = -470844 + 470847. Factor -6/11*z**2 + 4/11*z + 0 + 2/11*z**u.
2*z*(z - 2)*(z - 1)/11
Suppose 275 = 5*a - 5*t, -2*a + 61 + 44 = 3*t. Factor a*m**4 - 64*m**4 + 13*m**4 - 12*m**2.
3*m**2*(m - 2)*(m + 2)
Let l be -3 + 1 - -7*(-5)/(-15). Let y be 30*15/90 - 18/4. Determine j so that l + 1/6*j**2 + y*j = 0.
-2, -1
Let v(y) be the third derivative of -15*y**2 + 1/20*y**6 - 1/8*y**4 - 1/112*y**8 + 1/280*y**7 - 1/40*y**5 + 1 + 0*y + 1/8*y**3. Find p, given that v(p) = 0.
-1, 1/4, 1
Let j(c) be the third derivative of c**6/320 + c**5/10 + 73*c**4/64 + 45*c**3/8 + 1046*c**2. Factor j(p).
3*(p + 2)*(p + 5)*(p + 9)/8
Determine f so that 0 - f**4 + 19/3*f**3 + 0*f + 50/3*f**2 = 0.
-2, 0, 25/3
Let v(r) = -r**2 + r + 5. Let p be v(0). Suppose 0 = -0*a - 5*a - p*a. Let 0*u**2 + 1/9*u**3 - 1/9*u + a = 0. What is u?
-1, 0, 1
Let v(a) = -2*a**3 + 39*a**2 - 16*a - 49. Let y be v(18). Let r = y + -1898/3. Factor 2*h + 0 - 13/3*h**2 - 26/3*h**3 - r*h**4.
-h*(h + 1)*(h + 3)*(7*h - 2)/3
Let u = 4149 + -4144. Let i(v) be the second derivative of -12*v - 3/2*v**2 + 1/4*v**4 + 0 - 1/8*v**u + 5/12*v**3. Find m such that i(m) = 0.
-1, 1, 6/5
Factor -768800*g - 1/6*g**3 - 953312000/3 - 620*g**2.
-(g + 1240)**3/6
Let m be 8*(18 + (-3444)/192). Let h(z) be the second derivative of 27/40*z**5 - 42*z + 0 + 0*z**2 + 7/8*z**4 - m*z**3. Solve h(u) = 0.
-1, 0, 2/9
Let q = 9641 - 9638. Determine d so that 4/3*d**q - 1/3 + 7/3*d**2 + 2/3*d = 0.
-1, 1/4
Let w be (145/30 - 5)/(6/(-16)). Let l be (1088/(-36))/4 - (1 + -9)*1. Let w*c**2 - l + 2*c**3 - 2*c = 0. Calculate c.
-1, -2/9, 1
Suppose -6*i = 5*i + 121. Let c(q) = q**3 + 9*q**2 - 19*q + 33. Let o be c(i). What is h in 44/9*h**4 + 16/9*h**5 + 2*h**3 - 4/9*h - 14/9*h**2 + o = 0?
-2, -1, -1/4, 0, 1/2
Let h be (-5)/13*16/160*-10. Let p(j) be the first derivative of 2/39*j**3 - h*j**2 - 19 + 0*j. Factor p(b).
2*b*(b - 5)/13
Let k = 947/32 - 2809/96. Let 14*v - 147 - k*v**2 = 0. Calculate v.
21
Let x(m) be the second derivative of -m**4/12 - 7*m**3/6 - 5*m**2 + 9*m. Let i be x(-4). Factor -2*p**2 - i*p + 4*p**2 - 115 + 111.
2*(p - 2)*(p + 1)
Let v be (-3 + (-110)/(-32))*((-58)/(-609) + (-64)/(-336)). Factor v*c - 1/8*c**3 + 0*c**2 + 0.
-c*(c - 1)*(c + 1)/8
Let q(p) be the first derivative of -4*p**5/5 - 27*p**4 + 132*p**3 + 550*p**2 + 600*p - 3278. Solve q(k) = 0 for k.
-30, -1, 5
Let x(z) be the first derivative of -z**3/18 - 136*z**2/3 + 545*z/6 - 7122. What is y in x(y) = 0?
-545, 1
Let n = 100897/5658 + -107/6. Let k = 152752/19803 - n. What is f in -18/7*f**2 - 54/7*f - k - 2/7*f**3 = 0?
-3
Suppose -1 = 4*m + 2*g - 7, 4*g + 20 = 0. Suppose 4*k**2 - 61*k + 5*k**5 - 60*k - 15*k**3 + 125*k + 2*k**m = 0. Calculate k.
-2, -2/5, 0, 1
Let v(h) be the first derivative of -h**4/2 - 514*h**3/3 - 254*h**2 + 1024*h - 5477. Factor v(q).
-2*(q - 1)*(q + 2)*(q + 256)
Let 21*c**2 - 903*c + 247*c - 25*c**2 = 0. Calculate c.
-164, 0
Let w(i) = -i**4 + i**3 - 4*i - 5. Let d(l) = -8*l**4 + 13*l**3 + 20*l**2 - 52*l - 99. Let n(v) = 3*d(v) - 21*w(v). Find x, given that n(x) = 0.
-2, 2, 8
Let l = -35 - -38. Factor -20*c - 10*c**4 + 80*c**2 - 5*c**4 + 5*c**l - 5*c**4.
-5*c*(c - 2)*(c + 2)*(4*c - 1)
Let t = 71 + -71. Suppose -2*w = -0*w - 4. Factor w*q**2 - 2*q + t*q**2 + 2*q**2 - 2*q**2.
2*q*(q - 1)
Factor 32/7*z - 1/7*z**2 - 16.
-(z - 28)*(z - 4)/7
Let t be (1 - (-5)/(-2))*4. Let w(l) = -3*l**2 + 548*l + 6*l**2 - 545*l. Let z(h) = -9*h**2 - 10*h - 1. Let d(o) = t*z(o) - 17*w(o). Factor d(k).
3*(k + 1)*(k + 2)
Let s(w) = -14*w + 680. Let d be s(47). Suppose 0 = -0*u + d*u. Factor -3/7*z**2 + 3/7*z**4 - 6/7*z + 6/7*z**3 + u.
3*z*(z - 1)*(z + 1)*(z + 2)/7
Factor 178/9*g + 20/3 - 2/3*g**2.
-2*(g - 30)*(3*g + 1)/9
Suppose 51*n + 107 = 184*n - 159. Factor n + 10*w + 23/2*w**2 + 7/2*w**3.
(w + 1)*(w + 2)*(7*w + 2)/2
Solve 1833*x - 230*x**3 - 3960*x - 25*x**4 - 635*x**2 + 1447*x - 240 + 10*x**3 = 0.
-4, -3, -1, -4/5
Solve 5*m**2 - 1/4 - 19/4*m = 0.
-1/20, 1
Let z = 57 + 79. Factor -21*w**3 + z*w**2 - 3*w**5 - 292*w**2 - 15*w**4 + 147*w**2.
-3*w**2*(w + 1)**2*(w + 3)
Let d(z) be the first derivative of -2/3*z**3 - 93 + 1/9*z**6 + 1/6*z**4 + 2/5*z**5 - 2/3*z**2 + 0*z. Find h such that d(h) = 0.
-2, -1, 0, 1
Let i be (-4)/(-4) - -4*1. Suppose -7*l + 4*l = i*c + 6, 0 = -l - c. Factor -17*d**3 + 2*d**4 - 2*d**3 + l*d**3 + 12*d**2 + 50 + 80*d.
2*(d - 5)**2*(d + 1)**2
Suppose -18 = 56*u - 18. Let o(g) be the first derivative of 0*g + 0*g**4 + 5 + 0*g**3 + 0*g**5 - 1/24*g**6 + u*g**2. Determine n, given that o(n) = 0.
0
Let l(z) be the third derivative of -z**5/480 + 5*z**4/12 - 116*z**2 + 5*z. Find b such that l(b) = 0.
0, 80
Suppose -14*h + 12*h + 118 = 3*g, -2*g + 57 = -3*h. Let r be (-15)/(-24)*-4*g/(-20). Factor 3/4*o**2 - 21/4 - r*o.
3*(o - 7)*(o + 1)/4
Let v(c) be the second derivative of -5/12*c**4 + 0 + 140*c - 25/6*c**3 + 35*c**2. Factor v(o).
-5*(o - 2)*(o + 7)
Suppose 54 = -1253*m + 1259*m. Let n be (-96)/180*m/(-24)*14. Factor 0*q + 2/5*q**5 + n*q**3 + 0 + 6/5*q**2 + 2*q**4.
2*q**2*(q + 1)**2*(q + 3)/5
Let a(c) be the second derivative of -1/66*c**4 - 118/33*c**3 + 5 - 3481/11*c**2 - 25*c. Solve a(r) = 0.
-59
Solve 9/5*l**4 + 75*l**3 + 0 + 468/5*l + 948/5*l**2 = 0.
-39, -2, -2/3, 0
Let o = 197 - 157. Factor 6*k - 51*k**2 - o*k**2 + 86*k**2.
-k*(5*k - 6)
Let h(s) = s**3 - 35*s**2 - 449*s + 16422. Let b be h(34). Let i = -4 - -9. Factor 0 + b*m + 0*m**3 + 3/8*m**i + 3/2*m**2 - 9/8*m**4.
3*m**2*(m - 2)**2*(m + 1)/8
Let u(p) = 14*p**2 - 249*p - 54. Let v be u(18). Factor 0*f + v - 5/3*f**2 + 1/3*f**3.
f**2*(f - 5)/3
Let m(g) be the third derivative of -g**8/24 - 8*g**7/175 + 941*g**6/300 + 423*g**5/25 + 117*g**4/5 + 72*g**3/5 - 3*g**2 + 420*g. Find w such that m(w) = 0.
-3, -2/5, -2/7, 6
Let s = -165771/2 + 82887. Factor -3*j - 45/2 + s*j**2.
3*(j - 5)*(j + 3)/2
Suppose 3*g - 6*n = 48, -3*g = 18417*n - 18418*n - 8. Factor 0*j + 0 + g*j**2 - 5/3*j**4 - 1/3*j**5 - 4/3*j**3.
-j**3*(j + 1)*(j + 4)/3
Suppose -830 = -4*v - l, -v + l - 6*l + 217 = 0. Let j = 208 - v. Factor m**4 - 4*m**2 - m**3 - j + 1/2*m**5 - 7/2*m.
(m - 2)*(m + 1)**4/2
Let y(v) = -219*v**2 + 2*v - 8. Let m be y(2). Let o = m - -882. Suppose 3/4 + 1/8*k**o + 5/8*k = 0. What is k?
-3, -2
Let s(x) be the second derivative of x**6/45 + 191*x**5/30 + 63*x**4/2 + 565*x**3/9 + 188*x**2/3 + 1410*x + 1. Factor s(v).
2*(v + 1)**3*(v + 188)/3
Let m = -4645 + 4645. Let o(w) be the third derivative of 0 - 1/12*w**5 + 0*w**4 + m*w + 1/42*w**7 + 0*w**3 + 1/24*w**6 + 22*w**2 - 5/336*w**8. Factor o(q).
-5*q**2*(q - 1)**2*(q + 1)
Let s = 209002/21 + -69658/7. Suppose -112/3 - 36*o + s*o**2 = 0. Calculate o.
-1, 28
Let x(a) be the first derivative of -10*a**3/3 - 8*a**2 - 6*a - 1594. Solve x(m) = 0.
-1, -3/5
Suppose r + 20 = 6*r. Let v(x) = 2*x**3 + 119*x**2 + 53*x - 351. Let m be v(-59). Let f**5 - 4*f**4 + 2*f**r - 2*f**3 + 9*f**m - 6*f**3 = 0. What is f?
0, 1
Let r be (-24 - -22)/((-6)/51 + 0). Suppose 8*p - r = 7. Factor -1/7*d**4 - 8/7*d**2 - 6/7*d**p + 9/7 + 6/7*d.
-(d - 1)*(d + 1)*(d + 3)**2/7
Let n(r) be the third derivative of r**8/110880 - 5*r**5/6 + r**4/24 - 24*r**2 - 1. Let f(b) be the third derivative of n(b). Factor f(i).
2*i**2/11
Let f(b) = 5*b**3 + b**2 + 8*b - 10. Let r be f(1). Determine m so that r + 66*m**4 + 94*m**2 + 68 - 26*m**4 + 178*m**2 - 4*m**5 - 152*m**3 - 228*m = 0.
1, 2, 3
Let u(i) = i**2 + 36*i - 1441. Let d(k) = k**2 + 36*k - 1420. Let y(a) = -4*d(a) + 3*u(a). Find x such that y(x) = 0.
-59, 23
Let a = -39 - -49. Factor 30*b - 30*b**3 - 5*b**4 - 19 - 10*b**2 + 44 - a*b**2.
-5*(b - 1)*(b + 1)**2*(b + 5)
Let v(t) be the third derivative of -1/5*t**5 + 10*t - t**2 + 0*t**3 - 1/30*t**6 - 1/3*t**4 + 0. Factor v(g).
-4*g*(g + 1)*(g + 2)
Let v(k) be the third derivative of -171*k**2 + 0*k**3 + 0*k + 0 - 1/12*k**4 + 1/30*k**5. Factor v(h).
2*h*(h - 1)
Let k(r) = -r**2 + 18*r + 15. Let y be k(17). Factor 3920 - 280*u - y*u**2 + 65*u**2 - 28*u**2.
5*(u - 28)**2
Let 95/2*n**3 + 9025/4*n + 4375/4 - 41/4*n**4 + 2441/2*n**2 + 1/4*n**5 = 0. What is n?
-7, -1, 25
Let y(d) be the third derivative of d**7/350 - 27*d**6/100 - 11*d**5/20 + 2*d**2 - 380. Solve y(m) = 0.
-1, 0, 55
Let d(a) be the first derivative of a**5 + 20*a**4 + 440*a**3/3 + 480*a**2 + 720*a - 411. Suppo