e of 0*q + c*q**4 - 4*q**2 + 2 + 16/3*q**3 - 2*q**5. Factor p(a).
-2*a*(a - 2)*(a + 1)*(5*a - 2)
Suppose 14*y + 8 = 18*y. Factor -m + 68*m**2 + 3*m - 67*m**y.
m*(m + 2)
Let v = 12/8183 - -8135/32732. Factor 0*h + 0*h**3 - v*h**2 + 1/4*h**4 + 0.
h**2*(h - 1)*(h + 1)/4
Let z(j) = 4*j - 3. Let d be z(3). Find r, given that -37*r - d*r**2 + 2*r**3 - 3 + 46*r + r**3 = 0.
1
Let -10*k**4 + 18560*k**3 - 18592*k**3 - 4*k**4 - 22*k**2 - 4*k = 0. What is k?
-1, -2/7, 0
Let o(r) be the second derivative of -1/330*r**6 + 0 + 2*r**2 + 1/110*r**5 + 0*r**3 + 12*r - 1/132*r**4. Let q(k) be the first derivative of o(k). Factor q(h).
-2*h*(h - 1)*(2*h - 1)/11
Suppose -5*x = -20, -3*o + 5*x - 17 = -2*o. Suppose o*k + 3 = 0, 2*v - 3*k = 55 - 2. Find q such that 10*q - 9*q**3 + 7*q - v - 21*q**2 + 22 = 0.
-3, 1/3
Let y(i) = 2*i**3 - 8*i**2 - 5*i + 4. Let v be y(6). Let 16*m + 48*m - 4*m**2 - v - 138 = 0. What is m?
8
Suppose 2*n + n = -4*p + 103, n + 2*p = 31. Let s = 45 - n. What is a in 2/5 - 4/5*a**2 + 0*a**3 + 2/5*a**s + 0*a = 0?
-1, 1
Let v = 1/285 - -63/95. Let 1/3 - 2/3*p - 1/3*p**4 + v*p**3 + 0*p**2 = 0. Calculate p.
-1, 1
Let f = -2/851 - -1720/7659. Let k(u) be the second derivative of 0 + 0*u**2 + 4/45*u**6 + 1/9*u**3 + f*u**4 + 1/5*u**5 + u + 1/63*u**7. Solve k(z) = 0 for z.
-1, 0
Let p(r) be the first derivative of -r**5/24 + 5*r**4/18 - 35*r + 42. Let z(y) be the first derivative of p(y). Determine n so that z(n) = 0.
0, 4
Let l(h) = h**2 + h - 4. Let z be l(0). Let o = 8 + z. Factor 2*a**5 + 0 + o*a**4 + 0 + 2*a**3 + 0.
2*a**3*(a + 1)**2
Determine x, given that 1/4*x**3 - 2*x**2 - 5/2 + 17/4*x = 0.
1, 2, 5
Determine q so that 0 + 2/17*q**2 - 210/17*q = 0.
0, 105
Suppose -15*q + 3*q**2 + 30*q**2 - 5*q**3 - 70 + 60*q - 3*q**2 = 0. What is q?
-2, 1, 7
Suppose 3*k - 14 = 1. What is d in -66 + k*d**2 + 51*d + 191 - d = 0?
-5
Let q(x) = -2*x - 10. Let z be q(-6). Suppose -f = -1, 5 = -2*w + 3*w + f. Factor 2*j**5 - 4*j + 11*j - 4*j**w - 7*j + z*j**3.
2*j**3*(j - 1)**2
Suppose 1/5*z**2 - 111/5*z + 22 = 0. Calculate z.
1, 110
Let p(i) = -i**3 - 7*i**2 - 12*i - 6. Let y be p(-5). Let m(w) be the second derivative of 1/4*w**y + 0 - 3*w**2 + 1/2*w**3 + 2*w. Determine j so that m(j) = 0.
-2, 1
Let h(d) be the third derivative of 8*d**2 + 0 + 1/15*d**5 + 0*d + 0*d**3 - 1/3*d**4. Factor h(t).
4*t*(t - 2)
Suppose -5*b = -2*m + 3*m - 10, 0 = 3*b. Factor -17*z**3 - 12*z + 6*z**3 - 3*z**2 + 4*z**3 + 12 + m*z**3.
3*(z - 2)*(z - 1)*(z + 2)
Let u(q) be the third derivative of 0*q**3 + 0 + 1/210*q**5 + 11/84*q**4 + 0*q + 42*q**2. Solve u(k) = 0 for k.
-11, 0
Let d(v) = v + 8. Let m(s) = s**3 + 13*s**2. Let j be m(-13). Let t be d(j). Let -3*a**2 + 9*a + 0*a**2 - t*a + 4*a**4 = 0. Calculate a.
-1, 0, 1/2
Find c, given that 8*c**2 - 106/7*c + 52/7 - 2/7*c**3 = 0.
1, 26
Factor r**2 + 661*r - 4*r**2 - 64 - 709*r - 128.
-3*(r + 8)**2
Let c be (-3)/(-3)*12/(-1). Let s = -16 - c. Let l(p) = 3*p**2 - 4*p - 7. Let m(o) = -o**2 + 1. Let g(q) = s*m(q) - l(q). Factor g(k).
(k + 1)*(k + 3)
Let s be (-8)/(8/(-3)) - (13 + 864/(-84)). Solve 0 + 8/7*f**3 + 4/7*f - 10/7*f**2 - s*f**4 = 0 for f.
0, 1, 2
Solve -119004*x - 11*x**5 - 14084*x**3 - 97336 - 137032*x + 3*x**5 - 129628*x**2 - 572*x**4 = 0.
-23, -2, -1/2
Let b = -539 - -543. Let h(n) be the first derivative of -5 + 1/9*n**3 + 1/18*n**6 - 1/15*n**5 + 0*n + 0*n**2 - 1/12*n**b. Let h(a) = 0. What is a?
-1, 0, 1
Let q be 7 + ((-828)/63)/2. What is z in 1/7*z**3 + 0 + 2/7*z - q*z**2 = 0?
0, 1, 2
Let g(x) be the second derivative of -2/27*x**3 - 1/108*x**4 + x + 0 - 5*x**2 + 1/270*x**5. Let h(t) be the first derivative of g(t). Factor h(v).
2*(v - 2)*(v + 1)/9
Let w(d) be the second derivative of -d**5/70 + 13*d**4/42 - 12*d**3/7 - 21*d + 10. Suppose w(q) = 0. What is q?
0, 4, 9
Let s(c) be the first derivative of c**4/34 - 10*c**3/51 + 8*c**2/17 - 8*c/17 - 55. Factor s(z).
2*(z - 2)**2*(z - 1)/17
Let h(r) be the second derivative of -49*r**7/18 + 245*r**6/9 - 154*r**5/5 - 716*r**4/9 - 472*r**3/9 - 16*r**2 - 7*r + 2. Find b such that h(b) = 0.
-2/7, 2, 6
Determine h, given that 2/7*h**3 + 0 + 6/7*h**2 - 36/7*h = 0.
-6, 0, 3
Let t(u) be the first derivative of u**6/450 + u**5/300 + u**3/3 - 2. Let r(l) be the third derivative of t(l). Factor r(c).
2*c*(2*c + 1)/5
Let l(o) be the first derivative of -o**5/30 - o**4/3 - 4*o**3/3 - 8*o**2/3 - 8*o/3 - 75. Factor l(h).
-(h + 2)**4/6
Suppose -3*q - 26 = 7*d - 11*d, -5*d = -q - 16. Suppose 8/19 + 0*j - 2/19*j**d = 0. Calculate j.
-2, 2
Let x(t) be the third derivative of -t**7/2520 - t**6/720 + t**5/60 - 11*t**4/24 - 24*t**2. Let f(r) be the second derivative of x(r). Factor f(q).
-(q - 1)*(q + 2)
Let n(l) be the second derivative of 0*l**4 + 0 + 1/20*l**5 + 0*l**3 - 8*l + 0*l**2 + 1/30*l**6. Solve n(v) = 0.
-1, 0
Let w(r) = 4*r**2 - 3*r - 3. Let z(d) = -3*d**2 + d + 2. Let v(t) = 2*w(t) + 3*z(t). Find i, given that v(i) = 0.
-3, 0
Let j(p) be the second derivative of 2*p**6/45 - p**5/3 + 7*p**4/9 - 2*p**3/3 + 46*p. Solve j(b) = 0 for b.
0, 1, 3
Let t(i) be the second derivative of -4*i**6/15 - 7*i**5/10 - i**4/3 + i**3/3 - 3*i - 5. Determine l, given that t(l) = 0.
-1, 0, 1/4
Let j(b) = -b. Let c be j(-3). Factor 10*n + 9*n**2 - 3*n**4 - c*n**3 + 3 - 7*n - 9.
-3*(n - 1)**2*(n + 1)*(n + 2)
Let j(g) be the third derivative of g**8/168 - 11*g**7/105 + 31*g**6/60 - 17*g**5/30 - 8*g**4/3 + 28*g**3/3 + 503*g**2. Let j(p) = 0. What is p?
-1, 1, 2, 7
Let q(h) = 3*h**2 - 3*h + 8. Let i(n) = 20*n**2 - 18*n + 41. Let t(w) = -w**2 + w. Let o(y) = i(y) + 4*t(y). Let k(b) = -2*o(b) + 11*q(b). Factor k(a).
(a - 3)*(a - 2)
Let a(l) = 2*l**3 - 4*l**2 - 3*l + 1. Let m be a(-3). Let d = 562/7 + m. Let 0 - 2/7*s**3 + 2/7*s**2 - 2/7*s**4 + 0*s + d*s**5 = 0. Calculate s.
-1, 0, 1
Let c be (37 - -7)/(34/6*-3) - -4. Determine b so that -4/17*b**3 + 30/17*b**2 - 32/17*b - c = 0.
-1/2, 2, 6
Let u be 1/(((-36)/(-16))/9). What is h in 9*h**4 - 23*h**u + 4*h**3 + 10*h**5 + 48*h - 48*h = 0?
0, 2/5, 1
Factor 9*y**2 - 13*y**2 + 23*y - 27*y - y**3 + 0*y**3.
-y*(y + 2)**2
Let c(j) = -j**4 + j + 1. Let x(v) = -2*v**5 - 4*v**4 + 12*v**3 - 28*v**2 + 28*v. Let r(t) = -6*c(t) + x(t). Factor r(a).
-2*(a - 1)**4*(a + 3)
Let j(n) be the third derivative of n**5/30 - 9*n**4/4 - 28*n**3/3 - 3*n**2 - 28*n. Determine i, given that j(i) = 0.
-1, 28
Suppose 3*y = c - 16, -32 = -c - 2*c + y. Factor 5*w**3 - 2*w**4 + 12*w**5 - c*w**5 - 13*w**3 + 8*w**2.
2*w**2*(w - 2)*(w - 1)*(w + 2)
Suppose -x - 2 = -27. Factor -28*q**2 - 3*q**3 - 5*q + 4*q - q**4 + x*q**2.
-q*(q + 1)**3
Let b = 2 + 1. Suppose 3*x = 2*x + b. Factor -25*p**4 - 4*p**2 + 14*p**3 + 4*p**5 - 2*p + 10*p**4 + p**2 + 2*p**x.
p*(p - 2)*(p - 1)**2*(4*p + 1)
Suppose -9*d + 14*d = 10. Suppose -4*v = -l + 5, 4*l - d*v = 2*l + 10. Factor 4*c**l - 2*c**5 + c**2 - 5*c**3 + 7*c**5 - 2*c**4 + 5*c**4.
c**2*(c + 1)*(3*c - 1)**2
Let j(o) = -4 - o - o**2 + 0 - 6*o. Let i be j(-6). Find b, given that -2*b**2 - 2*b**2 + 2*b**2 + 1 + b**i = 0.
-1, 1
Let u(q) be the second derivative of q**4/54 + 130*q**3/27 + 4225*q**2/9 - 3*q + 24. Factor u(t).
2*(t + 65)**2/9
Let l = -32 - -50. Factor -7*s - 3*s + 9*s**2 - 11*s - l.
3*(s - 3)*(3*s + 2)
Let r(h) be the second derivative of h**6/210 - h**5/28 - h**4/28 + 13*h**3/42 + 5*h**2/7 + 53*h. Factor r(z).
(z - 5)*(z - 2)*(z + 1)**2/7
Let d(v) = 6 - v**2 + v + v - 3*v - 9*v. Let g be d(-9). Let -2*u - 4*u**2 - g + 2*u + 19 = 0. Calculate u.
-1, 1
Let d(s) be the first derivative of s**5/15 - 5*s**4/12 + 7*s**3/9 - s**2/2 - 79. Let d(t) = 0. What is t?
0, 1, 3
Let u(c) be the first derivative of -8/7*c + 15/7*c**2 + 6 + 8/21*c**3. What is i in u(i) = 0?
-4, 1/4
Determine j, given that 118/3*j**4 - 7*j**5 + 8/3 - 235/3*j**3 - 68/3*j + 66*j**2 = 0.
2/7, 1/3, 1, 2
Let r = 5255/9233 - -3/1319. Factor 2/7*w**2 - 6/7*w + r.
2*(w - 2)*(w - 1)/7
Let p(f) be the first derivative of 0*f**2 - 4 + 1/840*f**5 - 1/84*f**4 + 0*f - 4*f**3 + 1/2520*f**6. Let m(b) be the third derivative of p(b). Factor m(g).
(g - 1)*(g + 2)/7
Let s = 23399/11 - 2127. Factor s*p**2 + 0 + 4/11*p.
2*p*(p + 2)/11
Suppose 6*y - y = -5*x + 20, 3*y - 5*x - 20 = 0. Let l(w) be the first derivative of -1/2*w + 1/24*w**4 + y - 1/12*w**2 + 1/6*w**3. Factor l(t).
(t - 1)*(t + 1)*(t + 3)/6
Suppose 16 = 