 - a. Suppose 3*n - 3*n - n**2 + n**4 - n**r + n**3 + 0*n = 0. Calculate n.
-1, 0, 1
Let r = -52 + 58. Let c(j) be the first derivative of 0*j + 8/27*j**3 + 1 + 1/27*j**r + 8/45*j**5 + 1/9*j**2 + 1/3*j**4. Solve c(g) = 0 for g.
-1, 0
Let l(k) = 3*k**4 + 9*k**3 + 6*k**2 - 3*k + 3. Let x(t) be the first derivative of t**4/4 + t**3/3 - t**2/2 + t + 3. Let m(p) = l(p) - 3*x(p). Factor m(f).
3*f**2*(f + 1)**2
Let 2*h**4 + 0*h + 4/3*h**3 - 2/3*h**2 + 0 = 0. What is h?
-1, 0, 1/3
Let y(w) be the first derivative of 2*w**5/5 + w**4/2 - 2*w**3/3 - w**2 - 14. Factor y(m).
2*m*(m - 1)*(m + 1)**2
Let s be (-3)/1 - (-255)/145. Let t = s - -440/261. Solve -t*j + 2/9 + 2/9*j**2 = 0.
1
Let r = 111/4 + -27. Suppose r*t**2 + 3/4*t**3 + 0*t + 0 = 0. What is t?
-1, 0
Let x = 133 + -130. Let b(c) be the third derivative of 0 + 0*c**x + 0*c + 4*c**2 - 1/60*c**5 + 1/24*c**4. Factor b(y).
-y*(y - 1)
Let x(q) = -q**3 + 3*q**2 - 1. Let t be x(2). Factor 3*w**2 - 4*w - t*w + w.
3*w*(w - 2)
Let k(w) be the second derivative of -w**4/4 - w**3/6 + w**2 - 19*w. Find i, given that k(i) = 0.
-1, 2/3
Suppose -f + i + 2*i + 1 = 0, 0 = i - 1. Let y = 35 + -35. Factor 0*c**2 + 0*c**f - 1/3*c**5 + 0 + y*c + 0*c**3.
-c**5/3
Let z = -13 + 21. Suppose -2*c + z = -0. Factor 0*p + 1/2*p**3 + 0*p**c - 1/2*p**5 + 0*p**2 + 0.
-p**3*(p - 1)*(p + 1)/2
Let m(v) be the second derivative of -v**6/2 + 17*v**5/4 - 85*v**4/6 + 70*v**3/3 - 20*v**2 + 27*v. Let m(o) = 0. Calculate o.
2/3, 1, 2
Let h(f) be the second derivative of -f**6/75 - f**5/50 + f**4/30 + f**3/15 + 17*f. Factor h(k).
-2*k*(k - 1)*(k + 1)**2/5
Let s(n) be the first derivative of 3 + 0*n**2 - n + 1/3*n**3. Determine m so that s(m) = 0.
-1, 1
Let a(j) be the first derivative of -30*j**2 + 27*j**2 - 2*j**4 + 2*j + 4*j**4 + 2. Solve a(t) = 0.
-1, 1/2
Determine b, given that -14/3*b**3 - 8/3*b**4 + 2/3*b - 4/3*b**2 + 0 = 0.
-1, 0, 1/4
Factor 31*y + 33*y - y**2 - 38*y - 169.
-(y - 13)**2
Suppose 2/7*f**3 - 2/7*f**2 + 2/7 - 2/7*f = 0. What is f?
-1, 1
Suppose 0 = -0*z - z + 2. Let p be -4 - -6 - (-10)/z. Let f(j) = -j**2 + 3*j + 2. Let c(g) = -4*g**2 + 10*g + 7. Let i(x) = p*f(x) - 2*c(x). Factor i(b).
b*(b + 1)
Let y be (8/1)/(4/2). Suppose y*o - o = 6. Solve -4*d**o + 2*d**3 + 5*d**4 - 4*d**4 + 5*d**2 = 0.
-1, 0
Let q(w) = -6*w**3 - 12*w**2 - 12*w - 9. Let t(h) = 13*h**3 + 24*h**2 + 23*h + 19. Let y(c) = -7*q(c) - 3*t(c). Factor y(v).
3*(v + 1)**2*(v + 2)
Let g be 0/(2 - (-2)/(-2)). Factor -6*p + g*p**2 + p**2 + 0*p**2 - 3 - 4*p**2.
-3*(p + 1)**2
Suppose -3 + 15/4*g - 3/4*g**2 = 0. Calculate g.
1, 4
Let d(c) be the second derivative of 7*c**5/40 + c**4/12 - 7*c**3/3 - 2*c**2 + 17*c. Solve d(y) = 0.
-2, -2/7, 2
Let i = 123/110 + -7/22. Let 0*y + 4/5*y**3 + 0 - 1/5*y**4 - i*y**2 = 0. Calculate y.
0, 2
Let z = -1057/2 + 529. Let -1/2*h**2 - z*h + 0 = 0. What is h?
-1, 0
Let o(m) be the second derivative of 3*m**5/8 + 5*m**4/12 - 5*m**3 - 10*m**2 + 12*m. Factor o(g).
5*(g - 2)*(g + 2)*(3*g + 2)/2
Let l(q) be the first derivative of -q**3/18 + q**2/6 + q/2 + 4. Factor l(d).
-(d - 3)*(d + 1)/6
Let a(l) be the third derivative of l**2 + 0 + 0*l**3 + 1/240*l**6 + 0*l - 1/48*l**4 + 0*l**5. Solve a(p) = 0 for p.
-1, 0, 1
Determine q so that -q - 1/2*q**2 - 1/2 = 0.
-1
Let o(b) be the second derivative of b + 2/15*b**3 + 0 - 1/5*b**2 - 1/30*b**4. Let o(v) = 0. What is v?
1
Solve 2*a**4 + 6/5*a**3 + 0 - 18/5*a**2 + 2/5*a**5 + 0*a = 0 for a.
-3, 0, 1
Let w(h) be the third derivative of -h**6/90 - h**5/45 + h**4/9 - 7*h**2. Determine t, given that w(t) = 0.
-2, 0, 1
Let -4*s**2 + 0 + 0*s + 4 - 4*s + 4*s**3 + 0 = 0. What is s?
-1, 1
Let j = 405 + -403. Let -4/7*v**3 - 48/7*v - 32/7 - 24/7*v**j = 0. Calculate v.
-2
Let l(n) = -5*n**4 - 18*n**3 + 28*n**2 + 15*n - 17. Let h(t) = -10*t**4 - 35*t**3 + 55*t**2 + 30*t - 35. Let d(p) = 3*h(p) - 5*l(p). Solve d(f) = 0.
-4, -1, 1
Let q be (-4 + 1 - -3)/(-2). Find f, given that q + 0*f - f**5 - 1/3*f**4 + 2/3*f**3 + 0*f**2 = 0.
-1, 0, 2/3
Let c(m) = -3*m**3 - 29*m**2 - 81*m - 83. Let d = 17 - 8. Let a(f) = 12*f**3 + 117*f**2 + 324*f + 333. Let v(i) = d*c(i) + 2*a(i). Factor v(r).
-3*(r + 3)**3
Let m(f) = -f**2 - 6*f + 9. Let z be m(-7). Let t(n) be the third derivative of -1/36*n**4 + 0*n**3 - 1/90*n**5 + n**z + 0 + 0*n. Factor t(r).
-2*r*(r + 1)/3
Let o = -22 + 24. Factor -2/5*m + 1/5 + 1/5*m**o.
(m - 1)**2/5
Suppose 8/3 + 10/3*c + 2/3*c**2 = 0. Calculate c.
-4, -1
Let o(b) be the second derivative of -8/11*b**2 + 17/110*b**5 + 1/15*b**6 - 20/33*b**3 + 4*b + 0 - 1/33*b**4 + 2/231*b**7. Suppose o(k) = 0. Calculate k.
-2, -1/2, 1
Let w(b) = b**3 - b**2 - b - 1. Let y(g) = 16*g**3 + 42*g**2 + 20*g + 14. Let u(r) = 7*r - 7. Let k be u(5). Let j(o) = k*w(o) + 2*y(o). Factor j(z).
4*z*(3*z + 1)*(5*z + 3)
Let c(p) be the second derivative of 3*p**5/160 + p**4/8 + p**3/4 + 16*p. Factor c(t).
3*t*(t + 2)**2/8
Suppose -5*y - 35 = 5*x, 3*y + 5*x - x = -18. Let f = 12 + y. Suppose 2/5 - 2/5*z**f + 0*z = 0. What is z?
-1, 1
Let w(l) be the second derivative of -l**6/420 - l**5/105 - l**4/84 - l**2 + l. Let d(x) be the first derivative of w(x). Factor d(s).
-2*s*(s + 1)**2/7
Suppose 8 = -z - z. Let w = -2 - z. Factor 2*p**5 - 5*p**5 - w*p**4 + 5*p**5.
2*p**4*(p - 1)
Factor 0*n**2 + 0 + 2/13*n**4 + 0*n - 2/13*n**3.
2*n**3*(n - 1)/13
Let o(g) = -11*g**2 - 36*g + 42. Let m(i) = -5*i**2 - 18*i + 21. Let r(d) = -5*m(d) + 2*o(d). Factor r(x).
3*(x - 1)*(x + 7)
Let k(d) be the first derivative of 0*d**5 + 1 + 1/420*d**7 + 0*d**4 + 0*d - 2/3*d**3 + 0*d**6 + 0*d**2. Let j(q) be the third derivative of k(q). Factor j(b).
2*b**3
Let a(j) = 30*j**3 - 42*j**2 + 6*j + 3. Let w(s) = 29*s**3 - 43*s**2 + 6*s + 4. Let z(h) = 4*a(h) - 3*w(h). Factor z(f).
3*f*(f - 1)*(11*f - 2)
Let b(f) be the second derivative of 5/16*f**5 + f**3 + 4*f - 15/16*f**4 - 1/2*f**2 + 0. Factor b(y).
(y - 1)*(5*y - 2)**2/4
Let u(z) be the third derivative of -z**6/40 + 27*z**5/20 - 243*z**4/8 + 729*z**3/2 + 21*z**2. Suppose u(t) = 0. Calculate t.
9
Let p = 0 + 5. Suppose 0 = -p*d + 10 + 5. Find n, given that -5*n**2 + 3*n**4 + 0 + d - n**2 = 0.
-1, 1
Let g(z) be the third derivative of -1/540*z**6 - 1/27*z**3 + 0 + z**2 + 1/108*z**4 + 0*z + 1/270*z**5. Factor g(m).
-2*(m - 1)**2*(m + 1)/9
Let m(r) be the second derivative of -r**5/80 + 7*r**4/48 + r**3/24 - 7*r**2/8 - 14*r. What is j in m(j) = 0?
-1, 1, 7
Let g = -4 - -8. Factor g*m**2 + 2*m**2 - 5*m**2.
m**2
Let q be 8/(-144)*(-2)/12. Let r(z) be the third derivative of 1/270*z**5 - z**2 + 0 + 0*z**3 + q*z**4 + 0*z. Determine p, given that r(p) = 0.
-1, 0
Let i = -198/91 - -32/13. What is o in 2/7*o - 4/7*o**2 + i*o**3 + 0 = 0?
0, 1
Let p be ((-4)/(-10))/(9 - 5). Let w(l) be the second derivative of 2*l + 5/9*l**4 + 0 + p*l**5 + 2/3*l**2 + l**3. Factor w(d).
2*(d + 1)*(d + 2)*(3*d + 1)/3
Suppose 15 = 4*w - 1. Let s be 2/w*(-12)/(-3). Solve -6*j**s + 31*j**4 + j**3 + 4*j**4 + 2*j**2 - 5*j**3 = 0 for j.
-2/7, 0, 2/5
Suppose 7 = -2*q - r, 0 = 3*q + 4*r - 0*r + 23. Let b = 5 + q. Factor -13*y**2 + 15*y**2 + 4*y**3 + 5*y**b + 3*y**3.
y**2*(y + 1)*(5*y + 2)
Let x = 139/845 - -6/169. Determine v, given that -x*v**3 + 0 + 2/5*v**2 + 0*v - 1/5*v**4 = 0.
-2, 0, 1
Factor 11*t - 3 - 2*t + 7 - 16*t**2 + t**3 + 22*t**2.
(t + 1)**2*(t + 4)
Let b(m) be the first derivative of -m**4/14 - 10*m**3/21 - 8*m**2/7 - 8*m/7 - 15. What is y in b(y) = 0?
-2, -1
Let y(f) be the first derivative of 6*f**3 + 6*f**2 + 2*f - 14. Determine q, given that y(q) = 0.
-1/3
Suppose -l + 1 = 5*i, -2*i - 3*l = -5*i - 3. Suppose -a + 2*a - 3 = i. Factor -f**2 + 2 + f - f**a + f**4 - 2.
f*(f - 1)**2*(f + 1)
Let r = -4 + 9. Suppose -3*k - 17 = -5*v, 3*k = 4*v + r*k - 18. Let y**3 + 0*y**3 - 2*y**v + y**2 - y + y**4 = 0. Calculate y.
-1, 0, 1
Find c, given that -4*c**2 + 20/3*c**4 - 8/3 - 28/3*c**3 + 28/3*c = 0.
-1, 2/5, 1
Let w = 28513/1326 + -2/663. Let h = -21 + w. Factor h*o**3 - 3/2*o - 1 + 0*o**2.
(o - 2)*(o + 1)**2/2
Let v(r) be the first derivative of 0*r**2 - 2*r**3 + 3 - 2/5*r**5 - 2*r**4 + 0*r. Factor v(g).
-2*g**2*(g + 1)*(g + 3)
Let n(s) be the first derivative of s**5/15 - s**4/6 - s**3/9 + s**2/3 - 22. Solve n(y) = 0.
-1, 0, 1, 2
Let o(g) be the third derivative of g**6/540 - g**5/90 - g**3/3 - 3*g**2. Let r(x) be the first derivative 