0*z**2 + 0*z + 3/2*z**4. Factor t(m).
-2*m**2*(m - 2)*(m - 1)
Factor 0 - 2/7*g**2 - 2/7*g**4 + 0*g + 4/7*g**3.
-2*g**2*(g - 1)**2/7
Let z(t) = 39*t**2 - 39*t - 207. Let p(n) = -3*n**2 + 3*n + 16. Let x(o) = -27*p(o) - 2*z(o). Find j, given that x(j) = 0.
-2, 3
Suppose -2*y = y. Let o(h) be the second derivative of -1/90*h**5 + 0 + 1/54*h**4 + y*h**2 + 1/27*h**3 - 1/135*h**6 + h. Factor o(n).
-2*n*(n - 1)*(n + 1)**2/9
Let d(u) = u**3 + 8*u**2 + 8*u + 6. Let l be d(-7). Let s be 2/(l*(-3)/2). Suppose 2/3 - s*k**2 + 0*k**3 + 2/3*k**4 + 0*k = 0. What is k?
-1, 1
Let k = -7 - -9. Let n(w) be the first derivative of 1/5*w**5 + 0*w + 1/2*w**4 + 1/3*w**3 + k + 0*w**2. Determine f so that n(f) = 0.
-1, 0
Let m(l) be the first derivative of 5*l**3/3 + 5*l**2/2 - 10*l - 8. Find u such that m(u) = 0.
-2, 1
Let m(c) be the third derivative of 0*c + 0*c**5 + 0 + 0*c**3 + 3*c**2 - 1/70*c**7 - 1/20*c**6 + 0*c**4. Find p, given that m(p) = 0.
-2, 0
Let q(f) be the first derivative of -1/10*f**5 - 1/2*f + 0*f**2 - 1 + 1/3*f**3 + 0*f**4. Factor q(c).
-(c - 1)**2*(c + 1)**2/2
Let h(k) be the third derivative of k**8/392 + 26*k**7/735 + 6*k**6/35 + 9*k**5/35 - 9*k**4/28 - 12*k**2. Let h(y) = 0. What is y?
-3, 0, 1/3
Let m = -809 + 813. Suppose 2/5*n - 2/15*n**m + 4/15 - 2/5*n**3 - 2/15*n**2 = 0. What is n?
-2, -1, 1
Let c = 1124 - 2193/2. Let g = c + -27. Factor g*b**2 + 2 - 2*b.
(b - 2)**2/2
Let s be 5/(-15) - (-17)/(-3). Let u = 11 + s. Factor 5*b**4 + 9*b**3 + 13*b + 4*b**u + b**2 + 6*b**4 - 14*b.
b*(b + 1)**3*(4*b - 1)
Factor -3*r**3 + 0*r**3 + 0*r**5 + 3*r**5 - 3*r**3 - 3*r**4.
3*r**3*(r - 2)*(r + 1)
Find w, given that 10/3*w + 2/3 - 4*w**4 + 10/3*w**2 - 10/3*w**3 = 0.
-1, -1/2, -1/3, 1
Let c be (-14 - -17)*(-3)/(-18). What is h in c*h + 1/4 + 1/4*h**2 = 0?
-1
Let a(y) = y**2 - 2*y - 2. Let b be a(-2). Find z such that 3*z**3 - 6*z - 12*z**4 + 9*z**3 + 9*z**3 - b*z**3 + 21*z**2 = 0.
-1, 0, 1/4, 2
Let g = 237 + -2131/9. Find n, given that -g*n**2 - 4/9*n - 2/9 = 0.
-1
Let q(t) = -6*t**2 + 11*t - 7. Let f = 8 + -13. Let k = f - -4. Let w(o) = o**2 - o + 1. Let d(m) = k*q(m) - 3*w(m). Find s, given that d(s) = 0.
2/3, 2
Find p such that 521*p - 4*p**2 - 2*p**3 + 2*p**4 - 521*p = 0.
-1, 0, 2
Factor -1037 + 1035 - 23*f - f - 96*f**2 - 128*f**3.
-2*(4*f + 1)**3
Let s = 2806/3 - 919. Factor 23/3*p**2 - 4/3 - 67/3*p**3 + 16/3*p - s*p**5 - 119/3*p**4.
-(p + 1)**3*(7*p - 2)**2/3
Let t be 4 - (-2 - 52/(-9)). Let u be (-3 - 1)/((-36)/4). Factor -2/9*f**3 - u*f**2 - t*f + 0.
-2*f*(f + 1)**2/9
Let k(n) be the first derivative of 1/10*n**2 - 3 - 1/15*n**3 + 1/5*n - 1/20*n**4. Factor k(h).
-(h - 1)*(h + 1)**2/5
Suppose 5*f = 2*f + 18. Let t = 1 - -1. Factor -v**3 - v**3 - f*v**2 - t*v**3 - 1 + 0*v**3 - 4*v - v**4.
-(v + 1)**4
Let o = 535 - 51359/96. Let c(s) be the third derivative of 0*s - 1/480*s**6 - 1/24*s**3 + 0 + 1/240*s**5 + o*s**4 + 3*s**2. Solve c(b) = 0 for b.
-1, 1
Determine g, given that -3/2*g**2 - 1/6*g**4 - 1/3 + 5/6*g**3 + 7/6*g = 0.
1, 2
Let w be 1 + -4 - (-2 + -1). Factor 2/7 + w*y - 2/7*y**2.
-2*(y - 1)*(y + 1)/7
Let c be (-30)/(-2 + -4)*(-4)/(-330). Let r(p) be the first derivative of -1 + 1/33*p**6 + 6/55*p**5 + c*p**3 + 0*p**2 + 3/22*p**4 + 0*p. Factor r(t).
2*t**2*(t + 1)**3/11
Factor -2/5 - 2/5*h**2 + 4/5*h**4 + 4/5*h**3 - h + 1/5*h**5.
(h - 1)*(h + 1)**3*(h + 2)/5
Let 1/6*u + 1/6*u**3 + 1/3*u**2 + 0 = 0. What is u?
-1, 0
Let o = 51 - 48. Suppose 0 - 7/3*w**5 + 2/3*w + 3*w**2 + 5/3*w**3 - o*w**4 = 0. What is w?
-1, -2/7, 0, 1
Let l(m) be the third derivative of 1/105*m**7 + 0*m**4 + 0*m**6 + 0 + 0*m + 0*m**3 - 5*m**2 - 1/30*m**5. Factor l(k).
2*k**2*(k - 1)*(k + 1)
Let k(n) be the third derivative of n**6/1980 - n**5/330 + n**4/132 + n**3/2 + n**2. Let r(o) be the first derivative of k(o). Find y such that r(y) = 0.
1
Let p = 3 + -1. Determine v, given that -p - 10*v - 16 - 3*v**2 - 9 - 8*v = 0.
-3
Let o(f) = -f**3 - 3*f**2 + 13*f + 15. Let h be o(-5). Let -2/3*b**3 + h + 4/3*b**2 - 2/3*b = 0. Calculate b.
0, 1
Let g(x) = x**3 - 5*x**2 + x + 1. Let b be g(5). Let u be ((-6)/(-16))/(9/b). What is t in 0 + 0*t - 1/4*t**3 - u*t**2 = 0?
-1, 0
Suppose 0*g + 4*g - 8 = 0. Suppose 4*b - 4 - 20 = -2*h, 5*h + 4*b - 54 = 0. Factor h*c**3 + 5 - 8*c - 2*c**4 + 5 - 12*c**g + 6.
-2*(c - 2)**3*(c + 1)
Factor 12*v**3 + 6*v**2 + 5*v**4 + 8*v - 2*v**4 - 20*v - 4 - 5.
3*(v - 1)*(v + 1)**2*(v + 3)
Let g(o) be the first derivative of -o**3/3 + 4*o - 6. Factor g(q).
-(q - 2)*(q + 2)
Let u(a) be the third derivative of a**7/1890 + a**6/135 + 4*a**5/135 - 25*a**2. Suppose u(b) = 0. What is b?
-4, 0
Let k be (-470)/(-20) + (-1)/2. Let r = k - 45/2. Factor 1/2*a**3 + a**4 - 3/2*a**2 + 1/2 - r*a.
(a - 1)*(a + 1)**2*(2*a - 1)/2
Let w be (-12)/(-16)*(4 - 0). What is i in 2*i**4 + i**w + 4 - 16*i - 6*i**2 + 18*i - 3*i**3 = 0?
-1, 1, 2
Let t = -16 + 19. Solve o**3 + t*o**3 + 9*o + 12*o**2 + o**3 + 2 = 0.
-1, -2/5
Let z(t) = 14*t**2 - 2*t + 8. Let u(g) = -5*g**2 + g - 3. Let d(l) = 8*u(l) + 3*z(l). Factor d(w).
2*w*(w + 1)
Let g = 20285/7 + -170455/63. Let q = g + -192. Factor -2/9*b + 0 - q*b**2.
-2*b*(b + 1)/9
Let l = 181 + -177. Find b such that -4/7*b + 0 - 9/7*b**5 + 6/7*b**l - 4/7*b**2 + 11/7*b**3 = 0.
-2/3, 0, 1
Factor s**2 - 1/2*s + 0 - 1/2*s**3.
-s*(s - 1)**2/2
Let r be (-4)/10 + (-4)/20. Let u = r - -1. Factor 2/5*f**2 - u - 2/5*f + 2/5*f**3.
2*(f - 1)*(f + 1)**2/5
Let p(v) = v - 2. Let y be p(4). Factor -3*q**y + 0 - q - 8*q + 1 - 7.
-3*(q + 1)*(q + 2)
Let w be (-33)/(-4) - 1/4. Suppose -3*t = -t - w. Find c such that -t*c**3 - c**5 + c**3 - 3*c**2 + 4*c**2 + 3*c**4 = 0.
0, 1
Let y be 3 - 4 - -4 - -25. Find b such that -24*b**3 - 4*b**2 + 7*b**4 - 8 + 20*b**4 + y*b - 14*b**2 - 3*b**3 = 0.
-1, 2/3
Let n(t) = -t**3 + 2*t**2 + 5*t - 2. Let o be n(3). Suppose 0 - 2/3*a**3 + 2/3*a**2 - 2/3*a**o + 2/3*a = 0. What is a?
-1, 0, 1
Suppose -m + 0*m - 3 = 0. Let r be -3*(2/m - 0). Factor -2*b**2 - b**2 + b**2 - r*b.
-2*b*(b + 1)
Solve 0*a**4 + 0 - 16/7*a**3 + 2/7*a**5 + 0*a**2 + 32/7*a = 0.
-2, 0, 2
Let i(y) be the first derivative of y**4/3 + 2*y**3 + 4*y**2 - 5*y + 7. Let m(k) be the first derivative of i(k). Factor m(r).
4*(r + 1)*(r + 2)
Let i(j) = j**2 + 6*j + 7. Let z be i(-5). Let -4*m + 8 - 5 - m**z - 1 + 3*m**2 = 0. What is m?
1
Let p(d) be the first derivative of 2*d**3 - 3/4*d**4 + 3/2*d**2 - 2 - 6*d. Factor p(c).
-3*(c - 2)*(c - 1)*(c + 1)
Let p be 0 + -8 - 1440/(-150). Determine m, given that p*m**3 + 0*m**4 - 2/5*m**5 - 4/5 + 4/5*m**2 - 6/5*m = 0.
-1, 1, 2
Suppose 4 = -3*i + 19, 4*i - 20 = -2*r. Suppose r = -s + 5*s - 8. Factor -1/2*h**3 + 0 + 1/4*h**s + 1/4*h**4 + 0*h.
h**2*(h - 1)**2/4
Suppose -3*y = -5*f - 14, 0 = 4*y - f + 4*f - 9. Factor 18*j**3 - 5*j**3 - 4*j - 12*j**y.
j*(j - 2)*(j + 2)
Let b(x) be the third derivative of x**10/680400 + x**9/272160 + x**5/15 + 4*x**2. Let j(y) be the third derivative of b(y). Factor j(g).
2*g**3*(g + 1)/9
Suppose 0 = -0*r + 2*r - 6. Let 0*s**3 - 15*s + 6 + 9*s**2 - 3*s**4 + 3*s**3 + 0*s**r = 0. What is s?
-2, 1
Suppose -45 = -3*s - 2*s. Suppose 5*l - 1 - s = 0. Factor -6*q**3 - 5*q + 6*q**4 + 3*q - l*q**5 + 2*q**2 + 2*q.
-2*q**2*(q - 1)**3
Let o be (3 + 1)/(2/32). Factor o*l + 343*l**3 - 8 - 294*l**2 + 4*l + 16*l.
(7*l - 2)**3
Let g = -4 - -10. Factor -b**2 - 2 - 2*b - b**2 + g*b.
-2*(b - 1)**2
Let z be ((-490)/4)/(-13 + 15). Let u = -61 - z. Solve u*h**2 - h + 1 = 0.
2
Let 12/5*k**4 + 18/5*k**3 + 2/5*k**5 + 0 + 0*k + 8/5*k**2 = 0. Calculate k.
-4, -1, 0
Let c(j) be the third derivative of 1/420*j**7 - 1/240*j**6 + 0*j + 0*j**3 - 1/120*j**5 + 0 - j**2 + 0*j**4 + 1/672*j**8. Factor c(m).
m**2*(m - 1)*(m + 1)**2/2
Suppose 23 = 4*a - 3*i, -3 = -0*a - 4*a - i. Determine o, given that -16*o**2 + 3 + 13*o**a + 0 = 0.
-1, 1
Let m(h) be the first derivative of -4/3*h - 6*h**2 + 3 - 9*h**3. Let m(x) = 0. What is x?
-2/9
Let n(y) be the second derivative of -y**5/60 - y**4/4 - 3*y**3/2 + 2*y**2 - 4*y. Let t(i) be the first derivative of n(i). Factor t(p).
-(p + 3)**2
Let g(q) be the first derivative of q**7/735 + q**6/140 + q**5/105 - 2*q**2 + 2. Let w(n) be the second derivative of g(n). Factor w(i).
2*i**2*(i + 1)*(i + 2)/7
Let y be 1*(-6)/(-1) + 2. Determine o, given that -6 + 3 - 1 - y*o**2 - 2*o**3 - 10*o = 0.
-2, -1
Factor -32/5