(u) + 3*o(u). Solve h(r) = 0.
-5, 8
Let k(x) be the first derivative of -21 - 5/6*x**6 - 6*x**5 - 80/3*x**3 - 45/2*x**2 - 35/2*x**4 - 10*x. Factor k(i).
-5*(i + 1)**4*(i + 2)
Let v(r) = 9*r**4 - 15*r**3 - 11*r**2 + 11*r - 22. Let b(k) = -5*k**4 + 8*k**3 + 6*k**2 - 6*k + 12. Let c(q) = -11*b(q) - 6*v(q). Factor c(g).
g**3*(g + 2)
Let l be 11 + (-790)/70 + 32/63. Factor 8/9*d**3 - 2/9*d**4 - 4/3*d**2 + 8/9*d - l.
-2*(d - 1)**4/9
Let y(d) be the second derivative of -d**5/15 - 5*d**4/3 + 22*d**3/3 - 34*d**2/3 - 90*d + 1. Factor y(x).
-4*(x - 1)**2*(x + 17)/3
Suppose -2/23*a**2 + 76/23 - 74/23*a = 0. What is a?
-38, 1
Let m = 26377 + -26375. Factor 9/2*l**3 + 14*l - 15*l**m - 4.
(l - 2)*(3*l - 2)**2/2
Let x be (17/(-510))/((-4)/50). Let c(i) be the second derivative of -1/30*i**6 - x*i**4 + 1/3*i**3 + 1/5*i**5 + 0 - 4*i + 0*i**2. Factor c(s).
-s*(s - 2)*(s - 1)**2
Let d(p) be the first derivative of -p**7/1155 - p**6/220 - p**5/165 - 17*p**2 + 18. Let z(y) be the second derivative of d(y). Solve z(b) = 0 for b.
-2, -1, 0
Let m(j) be the third derivative of -j**4 - 8/3*j**3 + 1/168*j**8 + 1/15*j**5 + 11/60*j**6 + 0*j + 12*j**2 + 2/35*j**7 + 0. Factor m(s).
2*(s - 1)*(s + 1)*(s + 2)**3
Let d(q) = 5*q**4 + 17*q**3 - 68*q**2 - 23*q + 63. Let b(n) = -5*n**4 - 16*n**3 + 69*n**2 + 24*n - 64. Let a(j) = 3*b(j) + 4*d(j). Suppose a(i) = 0. What is i?
-6, -1, 1, 2
Find s, given that 22*s + 25*s**2 + 37*s**2 - 5*s**3 + 25 - 47*s**2 + 23*s = 0.
-1, 5
Suppose -44*i - 11*i - 17*i + 84 + 9*i**2 + 3*i**3 = 0. Calculate i.
-7, 2
Let k(x) be the third derivative of x**5/60 + 5*x**4/12 - 112*x**2. Determine r, given that k(r) = 0.
-10, 0
Suppose -5*i + 15 = -5*o, 0 = -0*o - 5*o + 4*i - 12. Suppose -4*h = 4*r, o*h = -2*h - r + 5. Factor 8/7*d**h + 0 + 10/7*d**4 + 2/7*d**3 + 0*d + 0*d**2.
2*d**3*(d + 1)*(4*d + 1)/7
Let n(d) = 30*d**2 - 218*d - 42. Let l(r) = 31*r**2 - 219*r - 43. Let c(y) = 6*l(y) - 7*n(y). Determine j so that c(j) = 0.
-1/6, 9
Find q, given that -108*q - 62 + 294 - 860*q**2 + 856*q**2 = 0.
-29, 2
Let o = 229/5 - 2051/45. Let i(u) be the third derivative of 0*u + 1/18*u**4 + 0 - 1/180*u**5 - o*u**3 + 2*u**2. Solve i(k) = 0.
2
Let g(z) be the first derivative of -7*z**4/54 - 2*z**3/27 - 12*z + 1. Let d(v) be the first derivative of g(v). Determine b so that d(b) = 0.
-2/7, 0
Suppose 3*h - 2*h = -4*p - 48, 59 = -3*p + 5*h. Let a(n) = 4*n + 52. Let g be a(p). Factor -2/3*q**2 + 0*q + g + 2/3*q**3.
2*q**2*(q - 1)/3
Let y = 1033/5 + -3957/20. Factor 5/4 + 75/4*f**2 + 45/4*f**3 + y*f.
5*(f + 1)*(3*f + 1)**2/4
What is o in 5*o**2 + o**5 + 11*o**2 - o**5 + 4*o**4 - 16*o**4 - 4*o**5 = 0?
-2, 0, 1
Let d(s) be the second derivative of -8*s**6/15 + 86*s**5/5 + 45*s**4 + 137*s**3/3 + 23*s**2 - 357*s. Determine f, given that d(f) = 0.
-1/2, 23
Suppose 10*y = 6*y + 8. Let -k**2 - 122 + 123 + y*k**2 + 2*k = 0. Calculate k.
-1
Suppose -4*n + 447 = -133. Let m be (-2)/9 - n/(-45). Factor -3*q**5 + 5*q**5 + q**5 - 4*q**3 + q**m.
3*q**3*(q - 1)*(q + 1)
Let x = 251 - 247. Suppose -10 - 25 = -5*y + 5*u, 2*y = x*u + 24. Suppose -3/2*k**3 - 9/2*k - 3/2 - 9/2*k**y = 0. Calculate k.
-1
Suppose -2*x = 2*h - 4, 5*h + 4*x - 9 = -3. Let k be 3*h*(-4)/12. Factor -1 + u**k + 3/2*u**3 - 3/2*u.
(u - 1)*(u + 1)*(3*u + 2)/2
Factor 2/7*p**2 - 2*p + 24/7.
2*(p - 4)*(p - 3)/7
Let l(n) = n**3 - 10*n**2. Suppose 10*m - 140 = -4*m. Let u be l(m). Solve u + 0*w + 1/5*w**3 + 2/5*w**2 = 0.
-2, 0
Determine w so that -4/7*w**2 + 8/7*w + 13/7*w**4 - 2*w**3 - 3/7*w**5 + 0 = 0.
-2/3, 0, 1, 2
Let u(b) be the third derivative of -b**6/60 - 14*b**5/5 + 57*b**4/4 - 86*b**3/3 - 2*b**2 - 90. Factor u(h).
-2*(h - 1)**2*(h + 86)
Let l(y) be the third derivative of 125*y**8/336 + 325*y**7/42 - 29*y**6/24 - 377*y**5/12 + 5*y**4/6 + 130*y**3/3 - 29*y**2. Find v, given that l(v) = 0.
-13, -1, -2/5, 2/5, 1
Factor -2/7*q**3 - 16/7*q**2 + 62/7*q - 44/7.
-2*(q - 2)*(q - 1)*(q + 11)/7
Let h(k) = 114*k**2 + 81*k - 21. Let f(n) = 11*n**2 + 8*n - 2. Let i(p) = -21*f(p) + 2*h(p). Factor i(d).
-3*d*(d + 2)
Factor 6/5*h + 4/5 + 2/5*h**2.
2*(h + 1)*(h + 2)/5
Let q(o) be the third derivative of -7*o**6/1980 - 23*o**5/660 - o**4/22 - 3*o**3 + 6*o**2. Let m(g) be the first derivative of q(g). Factor m(w).
-2*(w + 3)*(7*w + 2)/11
Let a(h) = h**2 + h. Let k be (9*4/48)/(2/(-16)). Let n(q) = -q**4 + 3*q**3 + 17*q**2 + 19*q + 6. Let l(m) = k*a(m) + 3*n(m). What is z in l(z) = 0?
-1, 6
Suppose 6076*m - 609*m**2 - 5488 - 1/4*m**4 + 85/4*m**3 = 0. What is m?
1, 28
Let v(r) be the second derivative of r**8/2688 + r**7/504 - r**6/288 - r**5/24 - r**4 - 10*r. Let s(m) be the third derivative of v(m). Factor s(k).
5*(k - 1)*(k + 1)*(k + 2)/2
Determine s so that -43*s**3 - 33*s**4 - 16*s**3 - 3*s**5 - 39*s**3 - 48*s**2 - 10*s**3 + 192*s = 0.
-4, 0, 1
Let q(b) = -b**4 - 65*b**3 - 193*b**2 - 191*b - 66. Let o(a) = -63*a**3 - 192*a**2 - 192*a - 66. Let f(v) = 4*o(v) - 3*q(v). Factor f(d).
3*(d - 22)*(d + 1)**3
Suppose 0 = 30*q - 2408 + 2348. Determine t so that 10/9*t**q + 4*t - 16/9 = 0.
-4, 2/5
Let w(q) be the first derivative of q**4 - q**3/3 + 1. Let f be w(1). Factor 2*r - r**2 - 2*r + r - r**2 + r**f.
r*(r - 1)**2
Let z(u) be the first derivative of u**5/15 - 3*u**4/4 + 5*u**3/3 - 7*u**2/6 + 26. Factor z(g).
g*(g - 7)*(g - 1)**2/3
Let x be (75/(-5))/(-5) - -234. Suppose 4*u**2 - 237*u - 4*u**4 + x*u = 0. Calculate u.
-1, 0, 1
Suppose 2*z = -0*z - 4. Let j be (-3)/z - (-9)/6. Factor 0*b**2 - 5 + j - 9*b**2 + 8 - 3*b.
-3*(b + 1)*(3*b - 2)
Suppose 4*n + 5*b = 32, n + 5*b = -0*n + 23. Let 39*d + 153 - 5*d**n - 12*d**2 - 4*d**3 - 171 = 0. What is d?
-3, 2/3, 1
Factor -95/4*g + 45/2 + 5/4*g**2.
5*(g - 18)*(g - 1)/4
Let o(s) = 3*s**3 - s**2 + s + 3. Let t(z) = -2*z**3 - z**2. Let p(u) = 5*o(u) + 10*t(u). Factor p(q).
-5*(q - 1)*(q + 1)*(q + 3)
Solve 4/5*w**5 - 512/5*w**2 + 1024/5*w + 16/5*w**4 - 128/5*w**3 + 4096/5 = 0 for w.
-4, 4
Let i(s) be the first derivative of s**6/1440 + s**5/960 - s**4/192 - 17*s**3/3 + 6. Let y(m) be the third derivative of i(m). Factor y(c).
(c + 1)*(2*c - 1)/8
Let n(j) be the first derivative of -5*j**6/18 + 17*j**5/15 - 4*j**4/3 + 4*j**3/9 + 48. Suppose n(i) = 0. Calculate i.
0, 2/5, 1, 2
Let b(m) be the first derivative of -m**3/2 + 21*m**2/2 - 36*m + 6. Factor b(l).
-3*(l - 12)*(l - 2)/2
Suppose 0 = -7*x + 6*x + 3. Let k be (6/90)/(x/54). Factor 0 + k*n**4 + 0*n**3 - 3/5*n**5 - 6/5*n**2 + 3/5*n.
-3*n*(n - 1)**3*(n + 1)/5
Let o(g) = g**2 + g + 1. Let m(l) = -13 - 2*l**3 + 3*l**4 - 10*l**3 + 8*l - 7*l**4 + 2*l**2 + 7*l**4. Let k(y) = m(y) + 4*o(y). What is d in k(d) = 0?
-1, 1, 3
Let d be 889/980 + 3*(-12)/42. Let z(x) be the second derivative of 0*x**3 + d*x**5 + 0*x**2 + 0 + 1/6*x**4 + 3*x. Factor z(s).
s**2*(s + 2)
Let z = 8880 - 44256/5. Let l(r) be the first derivative of 56/3*r**6 + 11/4*r**4 + z*r**5 + 6 - 3/4*r**2 + r - 47/6*r**3. Suppose l(h) = 0. Calculate h.
-1, -1/2, -2/7, 1/4
Suppose 0 = -5*p + 109 - 124. Let t be p/3*-6 + 15/(-5). Factor -1/5*q**4 - 13/5*q**2 + 6/5*q**t - 4/5 + 12/5*q.
-(q - 2)**2*(q - 1)**2/5
Let c be 13 - 1 - (4 - -5). Let b = 7/24 - 1/24. Factor 1/4*z**2 + 1/4*z**c - 1/4 - b*z.
(z - 1)*(z + 1)**2/4
Factor -5*l**4 + 135*l**2 + 272*l - 104*l - 560*l**2 + 305*l**3 - 455*l**2 + 412*l.
-5*l*(l - 58)*(l - 2)*(l - 1)
Let r(o) be the third derivative of o**7/42 + o**6/4 - 11*o**5/12 - 25*o**4/2 + 250*o**3/3 - 4*o**2 - 2. What is m in r(m) = 0?
-5, 2
Let h(u) be the second derivative of u**7/126 + u**6/45 - u**4/18 - u**3/18 - 63*u. Find w, given that h(w) = 0.
-1, 0, 1
Let t(d) = 6*d**3 + 4*d**2 - 7*d. Let b(y) = -y**3 - y**2 - y. Suppose 8 = 9*l - 7*l. Let s(m) = l*t(m) - 20*b(m). Find g such that s(g) = 0.
-1, 0, 2/11
Let l(i) = 7*i**5 - 5*i**4 - 2*i**3 + 8. Let c(n) = -n**5 + n**4 - 1. Let o = -15 - -39. Let k(x) = o*c(x) + 3*l(x). Factor k(w).
-3*w**3*(w - 2)*(w - 1)
Let y be (-28)/(-10) + 40/(-50). Let v(z) be the second derivative of 3/2*z**y + 3/4*z**4 - 3/2*z**3 - 3/20*z**5 + 0 - 6*z. Factor v(o).
-3*(o - 1)**3
Let b(y) = -165*y**2 + 143*y - 6. Let z(x) = -55*x**2 + 48*x - 1. Let c(d) = 2*b(d) - 7*z(d). Factor c(q).
5*(q - 1)*(11*q + 1)
Let c(b) be the first derivative of 1/5*b**3 - 3/5*b**2 + 0*b + 10. Factor c(r).
3*r*(r - 2)/5
Let q = 9389/19761 - -1/941. Factor -q*x - 2/2