 - 8*r**2 - 12*r + 12. Let p be t(9). Let d be (-2 + 1)*42/p. Determine u so that -4/5 - d*u**2 - 18/5*u = 0.
-1, -2/7
Let d(m) be the first derivative of -2*m**5/5 + 20*m**4 - 400*m**3 + 4000*m**2 - 20000*m - 36. Factor d(f).
-2*(f - 10)**4
Suppose -4 = -4*i - 2*o, 5*o = -0*o - 20. Let r(v) be the first derivative of -2 + 0*v**2 + 1/2*v**4 - v + v**i. Factor r(w).
(w + 1)**2*(2*w - 1)
Let x(n) be the first derivative of -19*n**3/3 - 26*n**2 - 20*n - 6. Let h(i) = 13*i**2 + 35*i + 13. Let r(s) = -8*h(s) - 5*x(s). Factor r(f).
-(f + 2)*(9*f + 2)
Let c(p) be the third derivative of 0*p + 0 + 0*p**4 + 1/60*p**5 + 0*p**3 + 1/210*p**7 - 1/60*p**6 - 8*p**2. Suppose c(r) = 0. What is r?
0, 1
Let y(v) be the second derivative of 5*v**7/42 + v**6/6 - v**5/4 - 5*v**4/12 - 5*v. Factor y(q).
5*q**2*(q - 1)*(q + 1)**2
Let f(y) = y. Let v be f(3). Factor 8*l**3 + v*l**4 + 2*l**5 + 2*l**3 + 4*l**2 + 5*l**4.
2*l**2*(l + 1)**2*(l + 2)
Let a = -5 + 7. Let b(s) be the third derivative of 0*s**5 + s**a + 0 + 0*s + 0*s**7 + 1/600*s**6 + 0*s**3 - 1/1680*s**8 + 0*s**4. Suppose b(d) = 0. What is d?
-1, 0, 1
Let h be (13/(-39))/(3/((-45)/20)). Find j, given that 1/2*j**2 - 1/4*j**3 - h*j + 0 = 0.
0, 1
Let u = 15/22 - 2/11. Suppose u*m + 1/4*m**2 + 0 = 0. Calculate m.
-2, 0
Let i(w) be the first derivative of -1/20*w**5 + 1/12*w**3 + 1/16*w**4 + 4 - 1/24*w**6 + 0*w + 0*w**2. Find h such that i(h) = 0.
-1, 0, 1
Let t(q) be the first derivative of q**3/2 - 3*q**2 + 6*q + 33. Determine c, given that t(c) = 0.
2
Let x be 4/(-6) - (-8)/3. Determine r so that 16*r + 2*r**3 + 8 + 8*r**2 - 13*r**x - 12*r**3 - 9*r**2 = 0.
-2, -2/5, 1
Let q(c) be the first derivative of -c**5/10 + c**4/12 + c**3/3 - c**2/2 + 3*c + 3. Let j(l) be the first derivative of q(l). Factor j(t).
-(t - 1)*(t + 1)*(2*t - 1)
Let z(b) be the first derivative of 0*b**3 - 1/12*b**4 + 0*b - 4 + 1/6*b**2. Factor z(h).
-h*(h - 1)*(h + 1)/3
Let z(b) be the second derivative of 3*b - 1/30*b**5 + 0*b**2 + 1/36*b**4 + 0*b**3 + 1/90*b**6 + 0. Let z(f) = 0. Calculate f.
0, 1
Let x = -5 - -7. Let 2*y**4 + 0*y**4 + 3*y + 4*y**4 - 2*y**x - 4*y**2 - 3*y**5 = 0. What is y?
-1, 0, 1
Let j(l) be the third derivative of -l**8/60480 + l**5/20 - l**2. Let t(g) be the third derivative of j(g). Solve t(z) = 0 for z.
0
Let g be (-4)/26 + 264/702. Let b(x) be the first derivative of -g*x**3 + 4/3*x + 2 + 1/3*x**2. Find z, given that b(z) = 0.
-1, 2
Let l be (3 + -4)*3 + 5. Factor -2 + 4*x + 3/2*x**l - 9/2*x**3.
-(x + 1)*(3*x - 2)**2/2
Let q(l) be the first derivative of -1 + 2*l - 2*l**2 + 0*l**3 + l**4 - 2/5*l**5. Determine x so that q(x) = 0.
-1, 1
Let f = 2/419 + 3767/838. Let z = 26/3 + -95/12. Determine l so that z + 15/4*l**4 - 9/4*l**5 + 3/2*l**3 - f*l**2 + 3/4*l = 0.
-1, -1/3, 1
Solve 3/4*c**4 - 3/4*c**5 + 0 + 0*c - 3/4*c**2 + 3/4*c**3 = 0 for c.
-1, 0, 1
Let s = -110 - -112. Let q be ((-3)/2)/(1/(-2)). Let 4*b**3 - b**2 + 2*b**q - 3*b**3 + 4*b**s = 0. Calculate b.
-1, 0
Let d = 371 + -368. Let v be ((-4)/6)/(4/(-12)). Determine k, given that -2/3*k + 0 - 8/3*k**v - 2*k**d = 0.
-1, -1/3, 0
Let l(t) be the third derivative of -t**6/480 - t**5/240 + t**4/48 - 8*t**2. Factor l(m).
-m*(m - 1)*(m + 2)/4
Let d(l) = -l - 2. Let y = 13 - 18. Let s be d(y). Determine w so that w**3 - s*w**3 + 3*w**3 = 0.
0
Suppose 3*b - 21 = -2*a, 2*a + 4*b = 23 + 3. Let r(d) be the third derivative of -d**2 + 0*d**a + 0 + 0*d + 0*d**4 + 1/210*d**5 + 1/420*d**6. Factor r(s).
2*s**2*(s + 1)/7
Suppose 0 - 10*p**2 + 20*p + 5/4*p**3 = 0. What is p?
0, 4
Let k(p) be the third derivative of -p**7/70 + 7*p**6/120 + p**5/60 - 7*p**4/24 + p**3/3 + 4*p**2. Let k(r) = 0. What is r?
-1, 1/3, 1, 2
Let d be (3 - 2)/((-1)/(-2)). Let f be 8 + (-451)/55 + 7/10. Factor 1/2*m**d - 1 + f*m.
(m - 1)*(m + 2)/2
Determine x so that 0 + 2/7*x**2 + 8/7*x = 0.
-4, 0
Let a(m) be the second derivative of m**4/16 - 3*m**2/8 + 17*m. Let a(z) = 0. Calculate z.
-1, 1
Let z = -10 + 12. Suppose -9 = -2*a + 5*h - 29, 5*h = 5*a + 20. Factor 1 + 2 + 1 + a - 6*p - 10*p**z.
-2*(p + 1)*(5*p - 2)
Factor 4/3*q**2 - 2/3 - 2/3*q**4 + 0*q + 0*q**3.
-2*(q - 1)**2*(q + 1)**2/3
Let s(w) be the first derivative of 0*w + 1/240*w**5 + 0*w**4 + 0*w**2 + 1/720*w**6 - 1/3*w**3 + 1. Let f(r) be the third derivative of s(r). Factor f(q).
q*(q + 1)/2
Factor -15/8*c**3 + 27/8*c**2 + 3/4 + 3/8*c**4 - 21/8*c.
3*(c - 2)*(c - 1)**3/8
Suppose 0 = 3*o - 131 + 125. Let 1/4*m**4 - 1/2*m**3 + 1/4*m**o + 0 + 0*m = 0. What is m?
0, 1
Let x(a) be the third derivative of a**6/1260 + a**5/420 - a**3/3 - 2*a**2. Let s(u) be the first derivative of x(u). Suppose s(v) = 0. What is v?
-1, 0
Let b(h) be the second derivative of 1/2*h**2 + 0*h**3 + 0 + 1/108*h**4 + 0*h**5 - 1/540*h**6 - h. Let v(r) be the first derivative of b(r). Factor v(m).
-2*m*(m - 1)*(m + 1)/9
Suppose -2/5*w**4 + 32/5*w**3 + 80*w - 50 - 36*w**2 = 0. Calculate w.
1, 5
Let x = -9 - -11. Factor 2*y**2 + 6*y**2 - x*y - 4*y**3 - 2*y.
-4*y*(y - 1)**2
Let a be 2 - -1 - 9/6. Factor 3/4*v - a*v**2 + 3/4*v**3 + 0.
3*v*(v - 1)**2/4
Let m(j) be the first derivative of -1/2*j**2 - 1/360*j**6 - 2 + 1/90*j**5 - 1/72*j**4 + 0*j**3 + 0*j. Let h(b) be the second derivative of m(b). Factor h(s).
-s*(s - 1)**2/3
Let -13*a**3 - 3*a**3 + 5*a**2 + 4*a**4 + 11*a**2 = 0. What is a?
0, 2
What is m in -8/3*m**2 + 1/3*m**5 + 2/3*m**4 - 2/3 - 2/3*m**3 - 7/3*m = 0?
-1, 2
Let 3/4*u**3 + 3/4*u**4 + 0*u + 0 + 0*u**2 = 0. What is u?
-1, 0
Let o(g) be the second derivative of g**7/2940 - g**6/2520 + g**4/4 + 2*g. Let k(h) be the third derivative of o(h). Find j, given that k(j) = 0.
0, 1/3
Let z(x) = -x**5 - 2*x**4 + 2*x**3 - 2*x**2 + x. Let c(k) = -k**4 - k**2 + k. Let b(f) = -10*c(f) + 5*z(f). Factor b(r).
-5*r*(r - 1)**2*(r + 1)**2
Suppose 1/3*v**3 + 1/6 - 1/3*v + 0*v**2 - 1/6*v**4 = 0. Calculate v.
-1, 1
Let r(n) be the first derivative of n**5 - 5*n**4/4 - 5*n**3/3 + 5*n**2/2 + 11. Factor r(s).
5*s*(s - 1)**2*(s + 1)
Let u = -479/3 - -163. Factor -4/3*t - 4/3*t**3 + 0 - u*t**2.
-2*t*(t + 2)*(2*t + 1)/3
Let u(h) be the third derivative of -h**5/240 - h**4/32 + 4*h**2. Factor u(a).
-a*(a + 3)/4
Suppose d = 2*d - 6. Let t be 3/(d/(-4) + 3). Suppose -1/3*s + 1/3*s**t + 0 = 0. Calculate s.
0, 1
Let c = 16 - 12. Let r(f) be the third derivative of -1/24*f**3 + 0*f - 1/48*f**c + 1/240*f**6 + 0 + 2*f**2 + 1/840*f**7 + 0*f**5. Factor r(i).
(i - 1)*(i + 1)**3/4
Let n be ((-18)/8)/(3/(-8)). Suppose 0 = -2*q - 35 + 41. Solve -4*r**4 + 1/4*r + 0 - 9/4*r**2 + n*r**q = 0.
0, 1/4, 1
Let g(s) be the second derivative of -s**9/9072 + s**8/5040 + s**7/2520 - s**6/1080 + s**3/2 + 3*s. Let z(y) be the second derivative of g(y). Factor z(u).
-u**2*(u - 1)**2*(u + 1)/3
Let c(a) be the second derivative of -6*a + 0 + 2/5*a**2 + 6/5*a**3 + 37/60*a**4 + 121/150*a**6 - 99/50*a**5. Determine n so that c(n) = 0.
-2/11, 1
Let t = -4 - -7. Factor 1 + 0 + 10*f**t + 2*f + 3*f**4 + 4*f + 12*f**2.
(f + 1)**3*(3*f + 1)
Let w(n) be the first derivative of -2*n + 0*n**2 - 6 + 2/3*n**3. Factor w(h).
2*(h - 1)*(h + 1)
Let g be (-4)/22 + 13/11. Let f be (1/16)/(g/4). Factor -1/4 - f*w**2 - 1/2*w.
-(w + 1)**2/4
Let w(s) = s - 4. Let y(o) = -o + 4. Let k(n) = 5*w(n) + 6*y(n). Let t be k(4). Factor t*c + 2/9*c**2 + 0.
2*c**2/9
Factor 9*i - 8*i**2 - 19*i - 2*i**3 + 4*i.
-2*i*(i + 1)*(i + 3)
Let u(g) = -19*g**4 + 8*g**3 + 35*g**2 - 19*g - 16. Let s(y) = -10*y**4 + 4*y**3 + 18*y**2 - 10*y - 8. Let b(n) = 11*s(n) - 6*u(n). Find x, given that b(x) = 0.
-1, 1, 2
Let w(q) be the first derivative of q**4/24 - 2*q**3/9 + 5*q**2/12 - q/3 - 2. Factor w(p).
(p - 2)*(p - 1)**2/6
Let q(n) = -n**2 - 5*n - 1. Let u be q(-3). Suppose 19 = 3*t - 3*l + 2*l, 5*l = u*t - 25. Factor -t*v**3 + 3*v**3 + 2*v**3 + 2*v.
-2*v*(v - 1)*(v + 1)
Let s(l) be the third derivative of -1/3*l**4 + 0 + 7/15*l**5 + l**2 + 0*l - 2/15*l**6 - 2/3*l**3. Solve s(x) = 0.
-1/4, 1
Let u be 6*(2/(-4) + 1). Suppose u*m - 14 = -r - 2, -5*r + 92 = -m. Factor r*j**2 + 0*j**2 + 4 - 7*j - 2 - 5*j.
2*(3*j - 1)**2
Let v(i) = 3*i**2 + 56*i + 48. Let y(d) = -2*d**2 - 28*d - 24. Let g(a) = -2*v(a) - 5*y(a). Factor g(f).
4*(f + 1)*(f + 6)
Let w(a) be the first derivative of 0*a + 7/6*a**3 + 1/2*a**2 + 2. Factor w(o).
o*(7*o + 2)/2
Let d(c) be the first derivative of c**5/80 + c**4