r) = 0.
-1
Let h(v) be the first derivative of 3*v**5/20 - v**4 + 5*v**3/2 - 3*v**2 - 4*v + 4. Let y(g) be the first derivative of h(g). Factor y(p).
3*(p - 2)*(p - 1)**2
Let g(a) = 7*a**2 - 15*a + 45. Let f(l) = 3*l**2 - 8*l + 23. Let r(k) = 5*f(k) - 2*g(k). Factor r(p).
(p - 5)**2
Let s be ((-2)/(-6))/((-1)/(-9)). Factor -2*c**2 + c**3 - c**4 - c**2 + c**3 + c**s + c.
-c*(c - 1)**3
Let z(h) be the first derivative of h**5/20 + h**4/16 - h**3/4 - h**2/8 + h/2 - 5. Factor z(r).
(r - 1)**2*(r + 1)*(r + 2)/4
Let s = -3 + 7. Let k be s/(-14) + (-90)/(-168). Find w such that -k + 5/4*w - w**2 = 0.
1/4, 1
Suppose -4*c = -3*i - 11, 6*c = -3*i + 2*c + 29. Factor 2/5*w**4 + 0 + 0*w**2 - 1/5*w**5 - 1/5*w**i + 0*w.
-w**3*(w - 1)**2/5
Determine h so that -2 - 12*h**2 + 2*h**3 + 20*h**4 - 16*h**4 - 20*h - 6 + 2*h**3 = 0.
-1, 2
Factor 6/11 - 10/11*t + 4/11*t**2.
2*(t - 1)*(2*t - 3)/11
Let g be 4/22*11/3. Factor 3*y**4 - 2*y - 8/3*y**2 + 4/3*y**5 - 1/3 + g*y**3.
(y - 1)*(y + 1)**3*(4*y + 1)/3
Let b(p) be the third derivative of p**5/270 + p**4/54 + p**3/27 - 55*p**2. Factor b(o).
2*(o + 1)**2/9
Let f(r) be the first derivative of -r**5/35 + r**4/7 + r**3/7 - 9*r**2/7 + 19. Find h, given that f(h) = 0.
-2, 0, 3
Let v(r) be the first derivative of 1/6*r**2 + 1/3*r - 1 - 2/9*r**3. Factor v(s).
-(s - 1)*(2*s + 1)/3
Let d be 15/(-27)*10/(-25). Let x(s) be the first derivative of -8/9*s**4 - d*s**2 - 3 + 0*s + 22/27*s**3 + 14/45*s**5. Let x(l) = 0. Calculate l.
0, 2/7, 1
Let c(w) = w**3 + 4*w**2 + w + 2. Let d be c(-3). Let g be d/10*5/2. Factor -3*k + 14*k + 5 + 7*k**3 - 3 + 16*k**g.
(k + 1)**2*(7*k + 2)
Let j(o) = o**3 - 6*o**2 + 7*o + 4. Let y be j(4). Factor 2/9*h**2 + y + 2/9*h**3 + 0*h.
2*h**2*(h + 1)/9
Let h be (-30 - -27)*(-2)/9. Suppose -2*a + 0 - h*a**2 = 0. What is a?
-3, 0
Let n(c) = 4*c**3 - 31*c**2 + 43*c - 12. Let w(b) = 10*b**3 - 92*b**2 + 128*b - 35. Let k(u) = -11*n(u) + 4*w(u). Solve k(l) = 0 for l.
-8, 1/4, 1
Let v = 14 + -20. Let n be (-2)/(-12) + (-2)/v. Suppose 0 - 1/3*z**2 + 0*z - 4/3*z**4 + 7/6*z**3 + n*z**5 = 0. Calculate z.
0, 2/3, 1
Let b(v) be the second derivative of -1/2*v**5 + 3/2*v**4 - 7/3*v**3 + 0 + 1/15*v**6 + 2*v**2 - 3*v. Find h such that b(h) = 0.
1, 2
Let s be (0 - 1)/(-3) - 8/24. Let b(f) be the first derivative of 0*f**3 - 3 - 1/6*f**4 + s*f + 1/9*f**2 - 4/45*f**5. Factor b(l).
-2*l*(l + 1)**2*(2*l - 1)/9
Let k(a) be the third derivative of a**5/80 - a**4/32 - a**3/4 + a**2. Find c such that k(c) = 0.
-1, 2
Let a(p) be the third derivative of p**7/1470 + p**6/210 + p**5/105 + 12*p**2. Factor a(s).
s**2*(s + 2)**2/7
Let g be (17 - 11)/((-21)/(-2)). Factor 0*p + 0 + 2/7*p**5 + 2/7*p**3 + g*p**4 + 0*p**2.
2*p**3*(p + 1)**2/7
Let h(d) be the third derivative of -2*d**2 + 1/8*d**4 + 0*d + 1/40*d**5 + 1/3*d**3 + 0 + 1/480*d**6. Factor h(m).
(m + 2)**3/4
Let h = 2 + 2. Let g(n) be the third derivative of -5/2*n**5 + 0*n - 4/3*n**3 + 0 - 5/2*n**h - 2*n**2 - 25/24*n**6. Factor g(z).
-(5*z + 2)**3
Let a be ((-864)/20)/9 + 6. Factor 8/5*u**2 - 2/5 + a*u.
2*(u + 1)*(4*u - 1)/5
Let z = 54 - 29. Suppose -w - 5*t = z, 5*w = t - 1 + 6. Factor -1/3*l**4 + 1/3*l - 1/3*l**3 + 1/3*l**2 + w.
-l*(l - 1)*(l + 1)**2/3
Let n(f) be the second derivative of -f**9/37800 + f**4/4 + 6*f. Let w(m) be the third derivative of n(m). Factor w(t).
-2*t**4/5
Find k such that 1/10*k**2 + 2/5*k + 0 = 0.
-4, 0
Let z(m) be the third derivative of 4*m**2 + 0*m**7 + 0*m + 1/1512*m**8 + 0 + 0*m**4 + 0*m**5 - 1/540*m**6 + 0*m**3. Factor z(g).
2*g**3*(g - 1)*(g + 1)/9
Factor -1/3*g**2 + 0*g + 0.
-g**2/3
Suppose 0 = -2*s + 3*i + 43, 5*s - 36 - 9 = -5*i. Suppose -3*u + s = 4*c, 5*u - 3 = 7. Factor 0*p**c - 1/4*p**3 + 0*p + 0.
-p**3/4
Let i be -4*((-12)/(-16) + -2). Let f be i - 4 - (-2 - 0). Let 2*w + 1/2 + f*w**2 + 2*w**3 + 1/2*w**4 = 0. Calculate w.
-1
Factor -3*v + 2*v**2 + v - v - 4 + v.
2*(v - 2)*(v + 1)
Suppose -w + 2 + 2 = 0. Let o be (1/14)/(w/14). Let 3/4*v - 1/2 - o*v**2 = 0. Calculate v.
1, 2
Let k be 2/8 + 26/(-104). Find f such that 0*f - 2/5*f**3 - 2*f**4 - 4/5*f**5 + 4/5*f**2 + k = 0.
-2, -1, 0, 1/2
Let z(k) be the first derivative of -k**6/300 + k**5/75 - k**4/60 + k**2/2 + 4. Let q(n) be the second derivative of z(n). Suppose q(a) = 0. What is a?
0, 1
Factor 0*g - 1/3*g**3 + 1/3*g**5 - 1/3*g**2 + 1/3*g**4 + 0.
g**2*(g - 1)*(g + 1)**2/3
Let u(n) = 3*n**2 - n. Let q(k) = -k**2 - k. Let m(h) = q(h) - u(h). Factor m(s).
-4*s**2
Let q(p) be the first derivative of p**8/3360 - p**6/240 + p**5/120 + p**3 + 5. Let s(k) be the third derivative of q(k). Factor s(c).
c*(c - 1)**2*(c + 2)/2
Let r(i) be the third derivative of i**6/1440 + i**5/240 + i**3/6 - i**2. Let l(p) be the first derivative of r(p). Factor l(w).
w*(w + 2)/4
Let o(l) = 4*l**3 - 8*l**2 - 2*l + 4. Let t(b) = -17*b + 19*b - 3 - 1 - 5*b**3 + 9*b**2 + b**4. Let s(w) = 3*o(w) + 2*t(w). Factor s(f).
2*(f - 1)**2*(f + 1)*(f + 2)
Let j be -2 - 1/(3/(-222)). Let g be 208/j + (-1 - 1). Solve -8/3*d + g + 10/9*d**2 = 0.
2/5, 2
Let q = 113 - 111. Determine k so that 10/3*k**3 + 6*k + 4/3 + 8*k**q = 0.
-1, -2/5
Let r = -6 - -8. Solve -3*b - 7*b**5 + 5*b**3 + 5*b + 2*b**4 + 5*b**4 - 9*b**r + 2*b**4 = 0 for b.
-1, 0, 2/7, 1
Let h be 0 + 6 + -1 - 3. Solve -l + l**h + l**3 - 7 + 5 + l**2 = 0 for l.
-2, -1, 1
Suppose -12*w = -8*w - 8. Let i be 1 + (3 - 1) + w. Factor -1/2*z**i + 0*z**2 - 1/2*z + z**3 + 0 + 0*z**4.
-z*(z - 1)**2*(z + 1)**2/2
Let c = 2594/4515 - 2/645. Let g be (-8)/21 + 4/6. Factor -g*f - 2/7*f**5 - c*f**2 + 2/7*f**4 + 4/7*f**3 + 2/7.
-2*(f - 1)**3*(f + 1)**2/7
Let x(j) = j**3 - 6*j**2 + 2*j - 7. Let w(f) = f**2 + 4*f + 6. Let a be w(-4). Let c be x(a). Factor 2*g**3 - 3*g + 2*g - c*g**4 - 3*g**2 - 5*g**3 + 4*g**4.
-g*(g + 1)**3
Let p(a) be the third derivative of -a**7/5040 + a**6/1080 - a**5/720 - a**3/6 + a**2. Let l(w) be the first derivative of p(w). Factor l(b).
-b*(b - 1)**2/6
Let p = 15 + -13. Factor -4*k**p + k - 6 - 3*k + 2*k**3 + 10.
2*(k - 2)*(k - 1)*(k + 1)
Let t(j) = j**2 - 2*j - 5. Let u be t(4). Suppose 0 = 4*f - 4*v - 4, 5*f + 4*v - 24 = 8. Suppose 0*q**2 + 0*q + 2/9*q**f + 0 + 0*q**u = 0. Calculate q.
0
Let m(d) be the second derivative of d**6/15 - d**4/3 + d**2 - 3*d. Factor m(o).
2*(o - 1)**2*(o + 1)**2
Let p(v) be the second derivative of 1/30*v**5 + v + 1/2*v**2 + 0 - 2/3*v**3 + 1/12*v**4. Let j(m) be the first derivative of p(m). Solve j(a) = 0.
-2, 1
Let o = -131/2 + 66. Suppose 3*s - 9/2 - o*s**2 = 0. Calculate s.
3
Suppose y + 22 - 7 = 3*t, 135 = -5*y + 3*t. Let x = y - -30. Factor -4/5*j**4 - 2/5*j**3 + 0*j**2 + 0*j - 2/5*j**5 + x.
-2*j**3*(j + 1)**2/5
Let p be -2 - -2 - (-5 - -3). Factor 14*y**p - 8*y**3 - 4*y + 8 - 6*y**4 - 8 - 2*y**4.
-2*y*(y + 2)*(2*y - 1)**2
Let -8/7*c**2 + 2/7*c**3 + 0 + 8/7*c = 0. Calculate c.
0, 2
Suppose 10 = -2*d, -w + 2*w = 5*d + 22. Let r = w + 5. Find x, given that 5/2*x**3 - 6*x**r - 1 + 9/2*x = 0.
2/5, 1
Find y, given that 0 - 40/9*y**3 - 128/9*y - 4/9*y**4 - 128/9*y**2 = 0.
-4, -2, 0
Suppose 5*c + 36 - 56 = 0. Let w(a) be the first derivative of -1/2*a**c + 0*a**2 + 4/3*a**3 - 4 + 0*a. Determine i, given that w(i) = 0.
0, 2
Let b be 1*3/12 - 0/(-5). Let z(a) be the first derivative of -b*a**2 + 1/3*a**3 - a + 1/8*a**4 - 1. Factor z(h).
(h - 1)*(h + 1)*(h + 2)/2
Let x be ((-10)/(-8))/(1/4). Suppose 6*d - 2 = 5*d. Factor -3*s + x*s + d*s**5 - 4*s**3 + 0*s.
2*s*(s - 1)**2*(s + 1)**2
Suppose -3*o = -4*d + o + 28, -5*o = 15. Determine k, given that k**3 - 3/2*k**2 - 1/4*k**d + k - 1/4 = 0.
1
Determine w so that 0*w + 0 - 2/11*w**3 + 0*w**2 + 1/11*w**4 = 0.
0, 2
Suppose -2*h = -h. Let d(v) be the second derivative of -1/6*v**4 + 2*v + 0*v**2 + h - 1/3*v**3. Solve d(i) = 0.
-1, 0
Let y(t) = t**2 - 2*t - 4. Suppose -5*o + 2*m = -0*o - 30, m = -2*o + 3. Let j be y(o). Factor -d**j - 3*d**3 + 0*d**4 + 0*d + 3*d + 4 - d**2 - 2.
-(d - 1)*(d + 1)**2*(d + 2)
Let j(x) = -x**3 + 6*x**2 - 5*x + 2. Let c be j(5). Suppose 2*v = 2*s + 8, 0 = c*v + 2*s - 3*s - 6. Factor 1/2*f**3 + 0*f + 1/2*f**4 - 1/2*f**5 + 0 - 1/2*f**v.
-f**2*(f - 1)**2*(f + 1)/2
Let r(v) be the first derivative of 0*v**4 - 3 - 1/40*v**6 + 0*v + 1/20*v**5 + 0*v**3 + 5/2*v**2. Let l(h) be the second derivative of r(h). Factor l(p).
-3*p**2*(p - 1)
Let h be 6/15 - 14/60. Let t(a) be th