 8*h**5/5 + 8*h**3/3 - 2*h**2 + 2244. Determine a, given that b(a) = 0.
-1, 0, 1
Let v(m) = -25*m**4 - 47*m**3 - 1753*m**2 - 1633*m - 49. Let c(d) = 3*d**4 + 6*d**3 + 219*d**2 + 204*d + 6. Let f(x) = -49*c(x) - 6*v(x). Solve f(j) = 0 for j.
-6, -1, 0, 11
Solve -10*d**2 - 3*d**4 + 3*d**4 + 5403*d**3 - d**4 - 10825*d**3 + 5411*d**3 = 0 for d.
-10, -1, 0
Let -408 + 559*y + 482*y + 7*y**2 - 1566*y + 874*y = 0. What is y?
-51, 8/7
Suppose q + 4*w = 14 - 12, -2*q + 4 = -4*w. Factor 3*z**4 + z**4 - z - 9*z**3 + 10*z**2 + 20*z**q - 24*z**2.
z*(z - 1)**2*(4*z - 1)
Let n(t) = 105*t**3 - 2310*t**2 + 9324*t - 9368. Let m(w) = 59*w**3 - 1320*w**2 + 5328*w - 5353. Let k(u) = 16*m(u) - 9*n(u). Factor k(p).
-(p - 2)**2*(p + 334)
Suppose 0 = v - 5, -8*g = -12*g - 3*v + 27. Let i(y) be the first derivative of -1/36*y**6 + 0*y - g + 0*y**5 + 0*y**2 + 0*y**3 + 1/24*y**4. Factor i(p).
-p**3*(p - 1)*(p + 1)/6
Suppose 4*c - 44 = -3*t, 54*t + 2*c - 22 = 13*t. Solve -2/13*d**4 + t + 2/13*d**2 + 4/13*d - 4/13*d**3 = 0.
-2, -1, 0, 1
Let m(u) be the third derivative of -4/15*u**4 - 38*u**2 + 1/300*u**5 + u + 128/15*u**3 + 0. Factor m(z).
(z - 16)**2/5
Let t(y) = 935*y + 65453. Let b be t(-70). Find s, given that 20/11*s + 18/11 - 20/11*s**b - 2/11*s**4 - 16/11*s**2 = 0.
-9, -1, 1
Find z, given that -39*z**2 - 48*z**4 + 8*z**3 + 6*z - 43*z**4 + 6 + 7 + 103*z**4 = 0.
-13/6, -1/2, 1
Suppose 3*x - 2*x = 48. Suppose -2*z - 2*z + x = 0. Factor z*p - 34*p**2 + 6*p**2 + 20*p**3 - 2*p**4 - p**4 - p**4.
-4*p*(p - 3)*(p - 1)**2
Let 947 + 74*u + 9*u - 15*u - 507 - 6*u**2 + 2*u**2 = 0. What is u?
-5, 22
Factor 2/3*x**2 + 200*x + 0.
2*x*(x + 300)/3
Suppose 150 = 17*r - 11*r. Suppose 6*u - 11*u = -r. Find q, given that -5*q - 15 + 17*q - u*q**2 + 8*q = 0.
1, 3
Factor -167281/3*k**2 - 3272*k - 48.
-(409*k + 12)**2/3
Suppose 767*u - 783*u = 128. Let a be u/(-1) + -10 + 5. Factor -1/4*s**a - 1 - 5/4*s**2 - 2*s.
-(s + 1)*(s + 2)**2/4
Find r such that -1/10*r**3 - 882/5 - 37/10*r**2 + 276/5*r = 0.
-49, 6
Let p = -28241/2 + 14127. Let r be ((-12)/10)/((-24)/60). Factor 11/2*v**2 + 5/2*v - 3 - p*v**r + 3/2*v**4.
(v - 3)*(v - 1)**2*(3*v + 2)/2
Let y(c) = -18*c**3 - 6*c**2 - 144*c - 121. Let m(o) = -16*o**3 - 12*o**2 - 144*o - 122. Let d(w) = -7*m(w) + 6*y(w). Suppose d(b) = 0. What is b?
-8, -2
Suppose -21*v - 4 = -22*v. Suppose 65 = v*q - 19. Find g such that -9*g**2 + 3*g**2 + 6*g - 27*g**4 + 33*g**2 - q*g**5 + 15*g**3 = 0.
-1, -2/7, 0, 1
Let l(y) be the second derivative of -y**4/4 - 17*y**3 - 99*y**2/2 - 44*y. Determine t, given that l(t) = 0.
-33, -1
Let a(w) be the third derivative of w**7/840 - 7*w**6/160 - 41*w**5/80 - 179*w**4/96 - 13*w**3/4 - 2*w**2 - 130*w - 2. Determine z, given that a(z) = 0.
-3, -1, 26
Suppose -3*c + u = 4, -5*c - 4*u + 7 = -9. Factor -74*k**2 - 617*k + 4 + c + 547*k.
-2*(k + 1)*(37*k - 2)
Let y(g) be the third derivative of 1/48*g**8 - 13/42*g**7 + g**2 + 0 - 35/12*g**5 - 2*g**3 + 11/8*g**6 + 10/3*g**4 - 18*g. Factor y(i).
(i - 6)*(i - 1)**3*(7*i - 2)
Let i be (-43)/(-2) - 11/22. Determine d so that -46*d**2 + 70 - 2*d**5 - i + 14*d**4 - 17 + 16*d - 9*d**3 - 5*d**3 = 0.
-1, 1, 4
Let d be -8 + 390/45 - 1/3. Let a(i) be the second derivative of -d*i**4 - 16/3*i**3 - 32*i**2 - 10*i + 0. Factor a(w).
-4*(w + 4)**2
Let w(p) = p**4 - 2*p**3 - p**2 + p - 1. Let a(q) = 6*q**5 + 78*q**4 + 290*q**3 + 14*q**2 - 834*q + 450. Let u(s) = a(s) + 2*w(s). Let u(j) = 0. Calculate j.
-7, -4, 2/3, 1
Let g(j) = -2*j**2 - 3*j. Let u(i) = -6*i**2 + 1122*i - 159048. Let f(q) = -4*g(q) + 2*u(q). Factor f(z).
-4*(z - 282)**2
Let g(s) = -s + 28. Let u be g(25). Factor -24*v + 4*v - 383 - 16*v**2 + 383 + 4*v**u.
4*v*(v - 5)*(v + 1)
Suppose -3/2*n**3 - 3510*n - 126*n**2 - 32448 = 0. Calculate n.
-32, -26
Let r be (112/20)/((-2)/(-5)). Let f be 2975/170*16/r. Solve -f*m - 25/3*m**2 - 12 = 0 for m.
-6/5
Find j, given that -33/4*j**4 - 12 + 36*j**2 + 5/4*j**5 - j**3 - 16*j = 0.
-2, -2/5, 1, 2, 6
Factor 2/11*n**3 + 218/11*n**2 + 2070/11 - 1362/11*n.
2*(n - 3)**2*(n + 115)/11
Factor -118/11*k + 186/11 - 6*k**2 - 2/11*k**3.
-2*(k - 1)*(k + 3)*(k + 31)/11
Suppose -21*l - 26*l + 282 = 0. Suppose -12 = -3*n + 2*v - l, 0 = -4*n - v + 8. Solve 0 + 4/3*i - 10/3*i**3 + n*i**2 = 0.
-2/5, 0, 1
Determine w, given that -600/7 - 342/7*w**3 - 2046/7*w**2 - 16/7*w**4 - 2320/7*w = 0.
-10, -1, -3/8
Let s(o) be the third derivative of o**8/6720 + o**7/84 + 19*o**6/240 - o**5/30 + o**3 - 43*o**2 - 2. Let h(r) be the third derivative of s(r). Factor h(y).
3*(y + 1)*(y + 19)
Suppose 5*k - 6 = -4*b, 0*k - 5*k - 3*b + 7 = 0. Factor -561*r**4 - 5*r**5 + 567*r**4 + k*r**5 - 3*r**3.
-3*r**3*(r - 1)**2
Solve -1351 + 445*k + 412*k**2 + 151*k - 401 - 416*k**2 = 0 for k.
3, 146
Factor 0 - 72*p**2 + 0*p + 1/2*p**3.
p**2*(p - 144)/2
Let i be ((-1)/(-3)*14)/(18 + 1064/(-84)). Let w(z) be the second derivative of 0*z**2 + z**3 - 13*z - i*z**4 + 3/20*z**5 + 0 + 1/20*z**6. Factor w(v).
3*v*(v - 1)**2*(v + 4)/2
Let w(o) = 6*o**3 + 204*o**2 - 414*o - 2600. Let v(p) = 7*p**3 + 254*p**2 - 414*p - 2602. Let s(m) = -4*v(m) + 5*w(m). Suppose s(k) = 0. Calculate k.
-9, 16
Let k be (-5)/(-7) + 1/(-7). Let x(y) be the first derivative of -1/7*y**2 - 28 - 2/21*y**3 + k*y. Suppose x(b) = 0. What is b?
-2, 1
Let f(s) be the third derivative of 0*s**3 - 1/20*s**6 + 0*s**4 + 1/70*s**7 + 2*s - 4*s**2 + 1/20*s**5 + 0. Let f(w) = 0. Calculate w.
0, 1
Suppose -732 = 37*o + 267. Let d = -77/3 - o. Factor 8/3 - 4/3*i - d*i**2.
-4*(i - 1)*(i + 2)/3
Suppose 238 = 1001*q + 66 - 1830. Factor -1/3*r**q - 11/3 - 4*r.
-(r + 1)*(r + 11)/3
Factor -2/5*n**2 + 0 + 78/5*n.
-2*n*(n - 39)/5
Factor 252 - k**4 - 45*k**3 + 140*k**3 + 441*k**2 + 52*k**2 + 48 + 697*k.
-(k - 100)*(k + 1)**2*(k + 3)
Let x(r) be the first derivative of r**4/12 - 2*r**3 - 13*r**2/2 + 278*r - 20. Let v(s) be the first derivative of x(s). Factor v(f).
(f - 13)*(f + 1)
Let f = -559 + 570. Suppose 1953 = f*q + 1920. Find k, given that 27/5*k - 3/5*k**4 - q*k**3 - 9/5*k**2 + 0 = 0.
-3, 0, 1
Let 24/23*c**2 - 164/23 - 1966/23*c = 0. What is c?
-1/12, 82
Let v = 473/61 - 85079/10980. Let r(t) be the third derivative of -v*t**5 + 0*t - 2/3*t**3 + 7/72*t**4 + 0 + 22*t**2. Factor r(n).
-(n - 4)*(n - 3)/3
Let y(j) be the second derivative of -1/4*j**4 + 114*j - 51*j**2 - 2 - 35/2*j**3. Factor y(u).
-3*(u + 1)*(u + 34)
Let h(s) = 10*s**2 - 48*s - 136. Let u(c) = 22*c**2 - 94*c - 285. Let d(f) = -13*h(f) + 6*u(f). Factor d(k).
2*(k + 1)*(k + 29)
Suppose 0 = 661*i + 269*i - 2790. Determine p so that 3/7*p + 6/7 + 3/7*p**4 - 9/7*p**2 - 3/7*p**i = 0.
-1, 1, 2
Let r(x) be the second derivative of -x**4/33 + x**3/11 + 277*x. Factor r(d).
-2*d*(2*d - 3)/11
What is t in 516*t**3 - 66 - 106 - 80 - 2443*t**2 + 1019*t**3 - 257*t**4 + 1464*t - 7*t**5 - 40*t**3 = 0?
-42, 2/7, 1, 3
Factor 20 + 28/3*n**2 + 86/3*n + 2/3*n**3.
2*(n + 1)*(n + 3)*(n + 10)/3
Let x(u) be the first derivative of u**5/10 + 45*u**4/8 - 314*u**3/3 - 168*u**2 + 3959. Determine g so that x(g) = 0.
-56, -1, 0, 12
Let l be (-4)/14 - (24 + (-6780)/210). Suppose -1 + 3 = i. Suppose 144*u**2 + 18*u**i - 26*u - 46*u + l = 0. Calculate u.
2/9
Let f = -964 - -962. Let x be (-7 + -21)/7 - f*2. Factor 0 + 2/13*u**4 + x*u + 4/13*u**2 - 6/13*u**3.
2*u**2*(u - 2)*(u - 1)/13
What is w in 218/11*w**4 + 24/11*w + 0 - 188/11*w**3 - 52/11*w**5 - 2/11*w**2 = 0?
-4/13, 0, 1/2, 1, 3
Factor -68/9*o + 176/3 + 1/9*o**3 - 20/9*o**2.
(o - 22)*(o - 4)*(o + 6)/9
Let u be ((-11)/(-2))/(2/4). Suppose -2*a - 99 = -u*a. Factor -11*f + a*f + 8*f - 4*f**2.
-4*f*(f - 2)
Let b(r) be the third derivative of r**7/945 - 7*r**6/135 + 5*r**5/54 + r**4/2 - 157*r**2 - 7*r. What is g in b(g) = 0?
-1, 0, 2, 27
Factor 270 - 468*w - 64/3*w**4 + 16*w**3 + 216*w**2.
-2*(2*w - 3)**3*(4*w + 15)/3
Let z = 5965 - 47713/8. Let d(j) be the first derivative of 1/2*j**3 + 7/10*j**5 + 19 - z*j**2 + 25/16*j**4 - 1/2*j. Find s such that d(s) = 0.
-1, -2/7, 1/2
Suppose -41*o + 41/4*o**3 - 78 + 37/2*o**2 + 1/4*o**4 = 0. Calculate o.
-39, -2, 2
Suppose -3*y + 2*o + 9 = 0, 135*y - 126*y + 2*o - 27 = 0. Determine p so that 0*p + 1/8*p**4 + 17/8*p**2 + 0 + 9/4*p**y = 0.
-17, -1, 0
Let v(h) be the second derivative of -h**4/48 + 5*h**3/4 - 13*h**2 - 377*h. Factor v(z).
-(z - 26)*(z - 4)/4
Suppose 0 = -4*w -