*3 - 4*k**2 - 4*k + 4. Let o(a) = 8*a**4 + 20*a**3 - 11*a**2 - 12*a + 11. Let i(p) = -11*g(p) + 4*o(p). Suppose i(f) = 0. Calculate f.
-1, 0, 2
Factor 2/15*w**5 - 4/5*w**3 - 2/5*w**4 + 4/3*w**2 + 14/5*w + 6/5.
2*(w - 3)**2*(w + 1)**3/15
Suppose y + 4 = 3*y. Let m(g) be the first derivative of 1/10*g**5 + 0*g**4 - 1/2*g**3 + y + 0*g + 1/2*g**2. Factor m(z).
z*(z - 1)**2*(z + 2)/2
Let s(a) = 1 - 4*a**2 - a**2 + 4*a**2 - a. Let z(u) = 4*u**2 + 2*u - 8. Let m = -12 - -6. Let v(b) = m*s(b) - z(b). Suppose v(q) = 0. Calculate q.
-1
Let d(n) be the third derivative of -1/105*n**7 + n**2 + 1/30*n**5 + 0*n + 1/60*n**6 - 1/12*n**4 + 0 + 0*n**3. Factor d(s).
-2*s*(s - 1)**2*(s + 1)
Suppose 16 - 40 = -4*t. Suppose -t*r = -3*r. Find d such that 1/2*d**2 + 0*d + r = 0.
0
Let w(h) = -5*h + 4. Let f(a) = a**2 - 9*a + 7. Let l = -10 + 3. Let t(x) = l*w(x) + 4*f(x). Factor t(j).
j*(4*j - 1)
Let q be 4/(-14) - (-18)/14. Let s(p) = p**2 + 2*p + 5. Let n(w) be the first derivative of -w - 18. Let i(c) = q*s(c) + 4*n(c). Let i(z) = 0. Calculate z.
-1
Factor 0*m**3 - 3*m**4 - 2*m**3 - m**3.
-3*m**3*(m + 1)
Let o(t) be the third derivative of -t**6/600 + t**5/60 - t**4/15 + 2*t**3/15 + 6*t**2. Factor o(x).
-(x - 2)**2*(x - 1)/5
Let k(d) be the third derivative of d**8/1008 + d**7/630 - d**6/180 - d**5/90 + d**4/72 + d**3/18 + 15*d**2. Determine h so that k(h) = 0.
-1, 1
Suppose n + 21 - 7 = 2*z, 0 = n - 3*z + 14. Let h = -12 - n. What is c in 0*c + 2/3*c**4 + 2/3*c**3 + 0*c**h + 0 = 0?
-1, 0
Let z(y) = 2*y + 8 + 7*y - 10*y. Let p be z(6). Factor -2 + b**2 - 3*b**p + b**3 + 2.
b**2*(b - 2)
Let c(o) be the first derivative of -o**5/15 - o**4/6 + o**2/2 + 5. Let a(q) be the second derivative of c(q). Solve a(g) = 0 for g.
-1, 0
Let w be ((-132)/20)/3*-5. Suppose 2*g + 4*y + w = 35, 4*g + y - 20 = 0. Suppose 2/3*u**5 + 5/3*u**g + 0 - 1/3*u + u**3 - 1/3*u**2 = 0. What is u?
-1, 0, 1/2
Let r be 4/7*84/36. Factor -2/3 + 4/3*a**5 - r*a + 14/3*a**4 + 16/3*a**3 + 4/3*a**2.
2*(a + 1)**4*(2*a - 1)/3
Let s(n) be the third derivative of 0 + 0*n**4 - 1/30*n**5 + 0*n**3 - 1/30*n**6 - 1/105*n**7 - 7*n**2 + 0*n. Factor s(k).
-2*k**2*(k + 1)**2
Let i(w) = -3*w**2 - 10*w - 16. Let c(q) = q**2 + q. Let r(h) = 2*c(h) + i(h). Find d, given that r(d) = 0.
-4
Let h be 1/2*(-380)/(-335). Let m = 8969/134 + h. Factor m*r**3 + 75/2*r**4 + 36*r**2 + 6*r + 0.
3*r*(r + 1)*(5*r + 2)**2/2
Let x(w) = 8*w**4 - w**3 + 7*w**2. Let s(f) = 4*f**4 - f**3 + 3*f**2. Let n(h) = -7*s(h) + 3*x(h). Find p such that n(p) = 0.
0, 1
Factor -50*g - 300 - 3*g**2 - 45*g + 35*g.
-3*(g + 10)**2
Let t be (4 + 52/(-16))*4. Factor 0*h**t + 0*h + 2/9*h**4 + 0 - 2/9*h**2.
2*h**2*(h - 1)*(h + 1)/9
Let n(v) = 8*v**2 - 10*v - 10. Let q(r) = -r**2 + r + 1. Let a(b) = -n(b) - 10*q(b). Find d such that a(d) = 0.
0
Let t = 52 - 52. Let n(u) be the third derivative of t + 0*u**6 + 1/18*u**3 + 0*u - 1/90*u**5 - 2*u**2 + 1/630*u**7 + 0*u**4. Find f such that n(f) = 0.
-1, 1
Let n(q) be the second derivative of -q**4/42 + 8*q**3/21 - q**2 - 29*q. Factor n(l).
-2*(l - 7)*(l - 1)/7
Determine c, given that 3 - 4*c**5 + 12*c**3 + 4*c**4 - 52*c - 4*c**2 + 44*c - 3 = 0.
-1, 0, 1, 2
Let x(b) = -25*b**2 + 39*b - 14. Let s(v) = -17*v**2 + 26*v - 9. Let y(u) = 8*s(u) - 5*x(u). Factor y(k).
-(k - 1)*(11*k - 2)
Let n be (-12)/3*(-3)/6. Solve -1 + 4*q**2 - 4*q**2 + 0*q**n + 2*q - q**2 = 0 for q.
1
Let p(v) be the third derivative of v**8/112 + v**7/70 - 3*v**6/40 - v**5/20 + v**4/4 - 22*v**2. Factor p(l).
3*l*(l - 1)**2*(l + 1)*(l + 2)
Let r = 7 + -4. Let h be 8/(-44) + 96/44. Let -r*z + 4*z + z**3 - h*z**3 = 0. Calculate z.
-1, 0, 1
Let l(q) be the second derivative of -1/45*q**6 + 0 + 0*q**2 - 3*q + 0*q**3 + 0*q**4 + 1/30*q**5. Find o, given that l(o) = 0.
0, 1
Solve 3/2*k**3 - 3/2*k + 3/2*k**2 - 3/2 = 0 for k.
-1, 1
Let m(q) = -q**2 - 2*q - 1. Let g be m(-1). Suppose -o + g = -5. Let 0*r**5 - r**o - 3*r**4 + 2*r**2 - 3*r**2 - 3*r**3 = 0. Calculate r.
-1, 0
Let m(g) be the third derivative of g**7/2940 + g**6/630 + g**5/420 - g**3 + 7*g**2. Let x(c) be the first derivative of m(c). Find n, given that x(n) = 0.
-1, 0
Let t(r) be the second derivative of r**6/1080 + r**5/180 + r**4/72 + r**3/2 + r. Let g(x) be the second derivative of t(x). Factor g(c).
(c + 1)**2/3
Let o be 6/(-24) + 9/4. Suppose 2*a - 5*a - 4*y - 2 = 0, 2 = o*a + y. Factor -3/2*g**a + 3/2 - 3/2*g + 3/2*g**3.
3*(g - 1)**2*(g + 1)/2
Let x(v) be the first derivative of v**4/34 - 2*v**3/51 - v**2/17 + 2*v/17 - 1. Determine w so that x(w) = 0.
-1, 1
Factor 8*z**2 - 184*z - 12*z**5 + 4*z**3 + 184*z - 16*z**4.
-4*z**2*(z + 1)**2*(3*z - 2)
Suppose -9 = -r - 4. Suppose -r = -n - 0. Solve 1/4*f**n - 1/4*f**4 - 1/4*f**3 + 1/4*f**2 + 0 + 0*f = 0.
-1, 0, 1
Let z(f) = f**5 + 8*f**3 - 3*f**2. Let n(p) = -p**5 + p**2. Let r(v) = 3*n(v) + z(v). Factor r(s).
-2*s**3*(s - 2)*(s + 2)
Let l be 3/9 + (-2)/6. Suppose -2*y - y = l. Solve 0 + y - 4*i**4 - i**3 + i + 4*i**2 = 0.
-1, -1/4, 0, 1
Let q(b) be the first derivative of 3*b**4/2 + 7*b**3 + 9*b**2/2 + 4. Factor q(r).
3*r*(r + 3)*(2*r + 1)
Let y(x) be the third derivative of -x**5/60 + x**4/6 - x**3/2 + 4*x**2. Factor y(s).
-(s - 3)*(s - 1)
Factor 48*l**2 - 71*l**4 + 95*l**4 - 17*l**3 - 4*l**5 - 16*l - 35*l**3.
-4*l*(l - 2)**2*(l - 1)**2
Let v be (12/(-6))/(1 + -2). Let b(s) be the first derivative of 2/21*s**3 - 2/7*s**v + 2/7*s - 2. Determine k, given that b(k) = 0.
1
Let v(r) be the first derivative of 1/21*r**3 - 7 - 1/7*r**2 + 0*r. Factor v(s).
s*(s - 2)/7
Let x(y) = 18*y**4 + 54*y**3 + 44*y**2 + 22*y + 2. Let s(b) = -b**3 - b. Let u(j) = -6*s(j) - x(j). Let u(z) = 0. Calculate z.
-1, -1/3
Factor 2/5*f**5 + 2*f**3 - 4/5*f**2 + 0 - 8/5*f**4 + 0*f.
2*f**2*(f - 2)*(f - 1)**2/5
Factor -2/9*u**5 + 0*u - 2/9*u**2 + 2/9*u**3 + 0 + 2/9*u**4.
-2*u**2*(u - 1)**2*(u + 1)/9
Suppose -u + 2 = -2*u. Let p(w) = -w**5 + w**4 - 2*w**3 - 2*w - 2. Let h(d) = d**5 + d**3 + d + 1. Let c(y) = u*p(y) - 4*h(y). Factor c(s).
-2*s**4*(s + 1)
Let a(b) be the second derivative of -7*b**5/40 - 23*b**4/24 - 5*b**3/3 - b**2 + b. Factor a(z).
-(z + 1)*(z + 2)*(7*z + 2)/2
Let b(a) = 239*a**4 + 211*a**3 - 210*a**2 - 200*a - 29. Let j(c) = 48*c**4 + 42*c**3 - 42*c**2 - 40*c - 6. Let g(h) = -4*b(h) + 22*j(h). Factor g(q).
4*(q - 1)*(q + 1)*(5*q + 2)**2
Let f(y) be the second derivative of -y**5/150 + y**4/30 + y**3/5 + 5*y**2/2 - 3*y. Let h(m) be the first derivative of f(m). Factor h(o).
-2*(o - 3)*(o + 1)/5
Let f(z) be the second derivative of -z**6/180 - z**5/24 - z**4/8 - 7*z**3/36 - z**2/6 + 30*z. Determine v, given that f(v) = 0.
-2, -1
Let r(y) be the first derivative of 1/2*y**4 - 5 + 3*y**2 - 2*y - 2*y**3. Determine j so that r(j) = 0.
1
Let i(a) be the second derivative of 1/147*a**7 + 1/21*a**3 - 4/105*a**6 + 3/35*a**5 + 5*a + 0 - 2/21*a**4 + 0*a**2. Factor i(t).
2*t*(t - 1)**4/7
Let r = -19 + 25. Suppose 0 = -0*f + 2*f - 3*q - r, 4*f + 4 = -2*q. Factor f*w + 1/5*w**4 + 0 + 0*w**2 + 1/5*w**3.
w**3*(w + 1)/5
Let k be 90/24*(14/(-5))/(-7). Solve 3/4*g**2 - 3/4*g - k = 0 for g.
-1, 2
Let g(b) = -b**3 + 5*b**2 + 3. Let u be g(5). Let u*n**2 - 4*n**5 - 3*n**4 + 2*n**3 + n**5 + n**3 = 0. What is n?
-1, 0, 1
Let n = -1202548/15 - -33912190/423. Let k = 2/423 + n. Let 2/5*v**3 - 12/5*v**2 + 2/5*v + k + 4/5*v**4 = 0. What is v?
-2, -1/2, 1
Factor 70*r + 2*r**2 - 58*r + 18 + 0*r**2.
2*(r + 3)**2
Let v(j) be the first derivative of -2 - 6*j**2 + 0*j - 3/4*j**4 + 4*j**3. Let v(b) = 0. Calculate b.
0, 2
Factor 0*n + 2/11 + 4/11*n**3 - 6/11*n**2.
2*(n - 1)**2*(2*n + 1)/11
Let z(c) = 6*c**5 + 3*c**4 - 9*c**3 + 15*c**2 + 21*c - 9. Let k(l) = -3*l**5 - 2*l**4 + 4*l**3 - 8*l**2 - 11*l + 5. Let n(x) = 9*k(x) + 5*z(x). Factor n(u).
3*u*(u - 2)*(u - 1)*(u + 1)**2
Let u = 71 + -71. Solve 2/9*b**5 + 0 + 0*b**2 + u*b - 4/9*b**4 + 2/9*b**3 = 0 for b.
0, 1
Suppose 11 + 11 = 3*f + n, -2*f - 4*n + 28 = 0. Suppose -4/3 + f*t + 22/3*t**2 = 0. What is t?
-1, 2/11
Let i(o) be the third derivative of -o**8/168 - 2*o**7/105 + 2*o**6/15 - o**5/15 - 7*o**4/12 + 4*o**3/3 - 28*o**2. Factor i(j).
-2*(j - 1)**3*(j + 1)*(j + 4)
Suppose -7*b = -l - 3*b + 16, -l - b = -1. Determine a so that 9*a**3 + 0 + 9/2*a**l + 3/4*a**5 + 6*a**2 + 0*a = 0.
-2, 0
Let y = -9 + -6. Let n be (-2)/y + 4/20. Factor 2/3*x - n