 z**7/4200 + z**6/1800 + 5*z**4/12 - 5*z. Let x(g) be the third derivative of m(g). Factor x(b).
b*(b - 1)**2*(b + 2)/5
Suppose 2*z - 5*w = 7*z - 15, -12 = -4*z - 3*w. Suppose -3*f**3 - f**3 - 18*f + 2*f**z - 12*f**2 + 0*f = 0. Calculate f.
-3, 0
Let h = 21 - 19. Let z(p) be the first derivative of 0*p + 0*p**5 + 1/18*p**6 + h + 0*p**3 - 1/6*p**4 + 1/6*p**2. Let z(w) = 0. What is w?
-1, 0, 1
Let h be ((252/(-8))/7 - -4)*-4. Factor 1/2*s**h - 1/2*s**4 + 1/2*s**3 - 1/2*s + 0.
-s*(s - 1)**2*(s + 1)/2
Suppose -4*b + 28 = 4*g + g, 4*g + 2*b - 20 = 0. Suppose 4*s - g*u = 0, -s = -3*s - 2*u. Find a such that -1/3*a**4 + 1/3 + 2/3*a - 2/3*a**3 + s*a**2 = 0.
-1, 1
Let k(p) be the first derivative of -7*p**6/180 - p**5/12 + p**4/6 - 4*p**3/3 - 5. Let r(v) be the third derivative of k(v). Factor r(j).
-2*(j + 1)*(7*j - 2)
Let i = 321 + -641/2. Factor -1/2*j**2 + 1/2 - i*j**3 + 1/2*j.
-(j - 1)*(j + 1)**2/2
Let w(d) be the third derivative of -d**8/336 + d**7/42 - d**6/60 - 7*d**5/30 + d**4/8 + 3*d**3/2 + 65*d**2. Factor w(b).
-(b - 3)**2*(b - 1)*(b + 1)**2
Let z(m) be the first derivative of 8*m + 14/5*m**5 + 16*m**2 + 19/2*m**4 + 1/3*m**6 + 50/3*m**3 + 1. Factor z(f).
2*(f + 1)**3*(f + 2)**2
Let a(m) be the first derivative of 2*m**3/27 - 2*m/9 - 16. Factor a(w).
2*(w - 1)*(w + 1)/9
Let r be 3 + 122/(-18) - -4. Let o = 30 + -27. What is s in -2/9*s + 0 + 4/9*s**2 - r*s**o = 0?
0, 1
Factor 4*z**2 - 27*z**2 + 15*z - 5*z**3 + 13*z**2.
-5*z*(z - 1)*(z + 3)
Let 0*f**3 + 0 - 4/3*f**4 + 4*f**2 - 8/3*f = 0. Calculate f.
-2, 0, 1
Let c(w) = 2*w**2 - 22*w + 20. Let s(l) = -8*l**2 + 88*l - 80. Let d(i) = 22*c(i) + 6*s(i). Find z, given that d(z) = 0.
1, 10
Let y(z) be the second derivative of 2*z**6/315 - 41*z**5/210 + 13*z**4/6 - 77*z**3/9 - 49*z**2/3 + z + 3. Factor y(q).
2*(q - 7)**3*(2*q + 1)/21
Let o(r) = -9*r**2 - 21*r + 21. Let f(t) = t**2 + 2*t - 2. Let a(d) = 21*f(d) + 2*o(d). Factor a(v).
3*v**2
Factor 2/7*o**2 + 4/7*o + 2/7.
2*(o + 1)**2/7
Factor 4/3*v**2 + 0*v + 0 + 9*v**4 + 9/2*v**5 + 6*v**3.
v**2*(3*v + 2)**3/6
Suppose 0 = 4*o + 4*p, -o + 3 + 5 = -p. Let l(f) be the third derivative of 1/270*f**5 + 0*f + 1/54*f**o + 1/27*f**3 - 3*f**2 + 0. Factor l(h).
2*(h + 1)**2/9
Let c(w) = -w**2 - 6*w + 16. Let k be c(-8). Suppose k = t + t. Find i such that -2/7*i**2 + 0*i + t = 0.
0
Let n = -9 + 18. Suppose 4*g + 10 = 5*m, 5*g = 4*m + 1 - n. Factor 1/5*y**5 + 0*y**2 + 0*y**3 + 0 - 1/5*y**4 + g*y.
y**4*(y - 1)/5
Suppose 9*j - 4*j = -5*h + 50, 17 = 2*h - j. Let c = h - 7. Factor -1/3*w**4 + 1/3*w**3 + 0 + 0*w**c + 0*w.
-w**3*(w - 1)/3
Solve -s**5 + 3/4*s**3 + 0 - 4*s**2 + 11/4*s**4 - s = 0.
-1, -1/4, 0, 2
Let p be (-14)/(-91) + (-4)/26. Let q(h) be the third derivative of 1/240*h**5 - 1/96*h**4 + 0 + p*h + 0*h**3 + h**2. Factor q(c).
c*(c - 1)/4
Let u(v) = 5*v**2 - 6*v + 4. Let t be (-6)/21 + 90/21. Let q(a) = -a**2 + a - 1. Let n(j) = t*q(j) + u(j). Suppose n(f) = 0. What is f?
0, 2
Let l(r) be the first derivative of -r**3 - 2*r**2 + 4*r - 7. Let l(j) = 0. Calculate j.
-2, 2/3
Let c(r) be the first derivative of -3*r**4/28 + r**3/7 + 18. Suppose c(h) = 0. Calculate h.
0, 1
Let d be (-7)/3*-1*3. Let z = d - 2. Find j, given that j**4 - 3*j**2 + j + 0*j**4 - j**z - 2*j + 2*j**3 + j**2 + 1 = 0.
-1, 1
Let y = 68 - 68. Factor 2/5*p**3 + p**4 - 7/5*p**5 + 0*p + y + 0*p**2.
-p**3*(p - 1)*(7*p + 2)/5
Let b = -10 + 21. Factor 2*l**5 + 5*l + 12*l**3 + 0*l + b*l**2 + 8*l**4 - 3*l - 3*l**2.
2*l*(l + 1)**4
Let s = -2/343 - -100/343. Determine h so that 4/7 - h + 1/7*h**3 + s*h**2 = 0.
-4, 1
Let a = -30 - -36. Let x(w) be the third derivative of 2*w**2 + 0*w**4 + 0*w**5 + 1/315*w**7 + 0*w + 0*w**3 + 0 + 0*w**a. Factor x(v).
2*v**4/3
Factor 0*g**3 + 12/5*g**4 + 0 + 0*g - 2/5*g**5 - 64/5*g**2.
-2*g**2*(g - 4)**2*(g + 2)/5
Let m = 16 + -14. Let -y - m*y**3 + 5*y + 7*y**2 - 5*y**2 = 0. What is y?
-1, 0, 2
Factor -5/8*h**5 + 3/4*h**3 + 0*h + 0*h**2 + 13/8*h**4 + 0.
-h**3*(h - 3)*(5*h + 2)/8
Let a be (-14)/3*(4 + (-60)/14). Factor -1/3*k**3 + a*k + 0 + 0*k**2.
-k*(k - 2)*(k + 2)/3
Let q = -86 - -260/3. Let m(s) be the first derivative of 1/2*s**4 + 1 + 0*s + 0*s**2 + q*s**3. Factor m(j).
2*j**2*(j + 1)
Let y = 4 + -2. Determine n so that 2*n**2 - 2*n**3 - y + 0 + 3*n - n = 0.
-1, 1
Let c = 1595 + -3189/2. Find j, given that -1/2 + c*j**2 + 0*j = 0.
-1, 1
Let u(d) = -d - 3. Let h be u(-6). Suppose -i = 0, -4*i = -l + 4*l - h. Factor -l - 23*r**2 + 5 + 19*r**3 - 8*r + 82*r**4 + 25*r**5 - 27*r**4.
(r + 1)**3*(5*r - 2)**2
Let m(t) be the first derivative of t**6/2 - 3*t**5 + 27*t**4/4 - 7*t**3 + 3*t**2 + 5. Factor m(y).
3*y*(y - 2)*(y - 1)**3
Let -4/15*y**3 + 0*y + 0 + 2/15*y**4 + 0*y**2 = 0. What is y?
0, 2
Let k be (6*5)/5 + -4. Let c(n) be the third derivative of 1/60*n**5 + 0*n + 0 - 1/6*n**3 - 3*n**k + 0*n**4. Factor c(p).
(p - 1)*(p + 1)
Let n = -6 + 6. Suppose b = -3*a + 4*a, n = 4*a + 4*b. Factor 1/3*c**4 + 1/3 + a*c + 0*c**3 - 2/3*c**2.
(c - 1)**2*(c + 1)**2/3
Let b(s) = 6*s**3 - 3*s**2 + 3*s - 6. Let f(h) = 5*h**3 - 3*h**2 + 3*h - 5. Let u(l) = -4*b(l) + 5*f(l). Find t, given that u(t) = 0.
1
Let b(y) be the first derivative of 4*y**3/27 + 4*y**2/3 + 4*y - 4. Let b(u) = 0. Calculate u.
-3
Let d be 12/(-64)*-4 - 3/12. Factor -p + 3/4*p**2 - 1 + d*p**3 - 1/4*p**4.
-(p - 2)**2*(p + 1)**2/4
Let v(z) be the first derivative of 0*z - 1 - 1/3*z**2 - 1/6*z**4 + 4/9*z**3. Determine w so that v(w) = 0.
0, 1
Let b(t) be the first derivative of -4*t**3/3 + 4*t + 1. Factor b(m).
-4*(m - 1)*(m + 1)
Suppose 0*j + 3*j - 15 = -3*u, 4*u = -j + 11. Let c(y) be the third derivative of 2/3*y**3 + 1/30*y**5 + 0 + 1/4*y**4 - u*y**2 + 0*y. Find o such that c(o) = 0.
-2, -1
Let v = 23/34 - 3/17. Factor v*l**2 + 1/2*l**5 + 3/2*l**3 + 3/2*l**4 + 0 + 0*l.
l**2*(l + 1)**3/2
Let y(o) = -o**3 - 4*o**2 - 4*o - 1. Let q be y(-3). Factor -2*j**2 + j**q + 3*j + 2*j**2 - 2*j.
j*(j + 1)
Factor 7/4*l**2 - 4*l + 1.
(l - 2)*(7*l - 2)/4
Let s = -10 + 0. Let r(k) = k + 13. Let f be r(s). Suppose 2/3*o**2 + 4/3*o**f + 0 + 2/3*o**4 + 0*o = 0. Calculate o.
-1, 0
Factor 0*w**3 - 3*w + 24*w**2 - 6 + 9*w**2 - 33*w**3 + 9*w**4.
3*(w - 2)*(w - 1)**2*(3*w + 1)
Let m = 0 - -3. Suppose -13 + m = -5*l. Factor 0 - 4 - y**l + 5*y - y.
-(y - 2)**2
Let t = -1507/4 - -383. Let f = 27/4 - t. Let f + 1/2*r**2 - r = 0. What is r?
1
Let z = 3 + -3. Let w = -1420/9 + 158. Factor z - w*o + 2/9*o**5 + 0*o**3 - 4/9*o**4 + 4/9*o**2.
2*o*(o - 1)**3*(o + 1)/9
Let o(i) = 2*i**2 + 16*i - 21. Let d(l) = -4*l**2 - 32*l + 41. Let b(v) = 3*d(v) + 5*o(v). What is m in b(m) = 0?
-9, 1
Let r(x) be the first derivative of -x**5/5 - 3*x**4/4 + 2*x**3/3 + 6*x**2 + 8*x + 19. Find p, given that r(p) = 0.
-2, -1, 2
Let f be 3/(-1) - 11/(-1). Suppose 10 = 3*o - 2*l, -l + 9 = 4*o - f. Find m such that 14*m + 4*m**o + 10*m**3 - 8*m**2 - m**4 + 26*m**2 + 4 - m**4 = 0.
-2, -1
Let a(j) be the third derivative of -j**5/210 - j**4/84 + 2*j**3/7 + 14*j**2 + 1. Factor a(f).
-2*(f - 2)*(f + 3)/7
Suppose 3*w - 21 = 4*a, -w - a + 12 = -4*a. Factor -2/3*c**w + 1/3 + 5/3*c**2 - 4/3*c.
-(c - 1)**2*(2*c - 1)/3
Let w(x) be the second derivative of -4*x - 1/30*x**6 + 0*x**3 - 1/6*x**4 + 0*x**2 + 0 - 3/20*x**5. Suppose w(f) = 0. Calculate f.
-2, -1, 0
Suppose 3*c = -7 + 19. Suppose -1/2 + d - d**3 + 0*d**2 + 1/2*d**c = 0. What is d?
-1, 1
Let y(q) be the second derivative of -q**5/60 - q**4/36 + 2*q**3/9 + 2*q**2/3 + q. Factor y(t).
-(t - 2)*(t + 1)*(t + 2)/3
Let y be (-18)/(-8) + (-3)/12. Let i = 101/4 + -25. Factor 0 + 1/4*g - i*g**y.
-g*(g - 1)/4
Let f(b) be the third derivative of 0 + 0*b**3 + 1/6*b**4 + 0*b - 1/30*b**5 + 2*b**2. Factor f(p).
-2*p*(p - 2)
Let z(s) be the second derivative of 0 + 3*s - 3/25*s**5 - 2/5*s**3 - 3/10*s**2 - 3/10*s**4 - 1/50*s**6. Factor z(i).
-3*(i + 1)**4/5
Suppose -5*o = -2*i - i - 16, 25 = 5*o. Let j(w) be the second derivative of -1/60*w**5 + 0*w**2 + 1/18*w**4 - 1/18*w**i + 2*w + 0. What is c in j(c) = 0?
0, 1
Solve -6/5*w + 6/5*w**2 + 2/5 - 2/5*w**3 = 0 for w.
1
Let h = -21/19 - -265/171. Let v(a) be the first derivative of 8/9*a - h*a**2 - 2 + 2/27*a**3. Let v(d) = 0. What is d?
2
Let s(u) = 10*u**2 - 10*u + 1. Let p(y) = y**2 + y - 1. Let m = 0 - -3. Let c be (1 - 1) + m/3. Let w(x) = c*s(x) - p(x). Let w(r) = 0. Calculate r.
2/9, 1