-5*k**5 + 12*k**3 - 2*k**2 - 3*k - 2. Let q(d) = -3*c(d) - 2*o(d). Determine b, given that q(b) = 0.
-1, 0, 1
Let d(z) be the third derivative of z**5/30 + 5*z**4/12 + 8*z**2. Factor d(g).
2*g*(g + 5)
Factor 19*c**3 + 10*c**2 + 17*c**3 - c**3 + 15*c**5 + 40*c**4.
5*c**2*(c + 1)**2*(3*c + 2)
Let r(c) be the first derivative of 2/11*c**2 - 1 - 2/11*c - 2/33*c**3. Suppose r(v) = 0. Calculate v.
1
Let r(z) = 44*z**3 - 120*z**2 + 44*z - 32. Let k(g) = 4*g**3 - 11*g**2 + 4*g - 3. Let s(l) = -32*k(l) + 3*r(l). Factor s(o).
4*o*(o - 1)**2
Let l(o) = o - 5. Let r be l(8). Let f(p) be the second derivative of -1/6*p**4 - 2/3*p**r - 2*p - p**2 + 0. Factor f(g).
-2*(g + 1)**2
Factor 0 + 3/2*r**3 - 2*r + 2*r**2.
r*(r + 2)*(3*r - 2)/2
Let s be (-2 + 2)/((-2)/(-1 - 0)). What is u in 4/11*u**2 - 2/11*u**4 - 2/11*u**3 + 0 + s*u = 0?
-2, 0, 1
Let u be (-3)/(-15)*-6*5. Let m(y) = -8*y**4 - 10*y**3 - 2*y**2 - 6*y - 6. Let o(g) = -g - 1. Let s(j) = u*o(j) + m(j). Suppose s(d) = 0. What is d?
-1, -1/4, 0
Let q = 0 + 0. Let i(w) = -w**2 + 9*w - 3. Let z be i(8). Let -6*a**3 + 19*a**4 + q*a**5 + 0*a**z + 2*a**2 - 2*a**5 - 13*a**4 = 0. Calculate a.
0, 1
Let -1/3*x**2 + 1/3 + 0*x = 0. Calculate x.
-1, 1
Let b be ((-3)/(-156)*-46)/(-1). Let f = b - 5/13. Solve -1/4*o**2 - 1/4 + f*o = 0 for o.
1
Suppose -f + 22 = 5*c - 3*f, -5*c + 24 = -4*f. Suppose 112/3*n**2 + 512/3*n**c + 1/3 - 256/3*n**5 - 17/3*n - 352/3*n**3 = 0. Calculate n.
1/4, 1
Let y be (3 - 1)*3/6. Suppose p - y - 1 = 0. Factor 0*z**2 - 7*z**2 + 6*z**2 + 3 - p.
-(z - 1)*(z + 1)
Suppose -2*b + 6*b = 76. Let c = 35 - b. Factor 2*i + 16 + 2*i**4 - c - 2*i**3 - 2*i**2.
2*i*(i - 1)**2*(i + 1)
Let b(n) be the second derivative of n**7/105 - 2*n**6/25 + 6*n**5/25 - 4*n**4/15 - 5*n. Factor b(w).
2*w**2*(w - 2)**3/5
Let y(p) be the third derivative of 1/180*p**6 - 1/630*p**7 + 0 + 1/60*p**5 + p**2 + 0*p - 1/18*p**4 - 2/9*p**3. Factor y(t).
-(t - 2)**2*(t + 1)**2/3
Let v(m) be the third derivative of -3*m**6/40 + m**5/4 - m**4/4 - 9*m**2. Suppose v(z) = 0. What is z?
0, 2/3, 1
Suppose -3*g + 6 = -0*g. Let f be 0 + -2 + g + 2. Suppose 2*w - w**4 - 5*w**4 + 4*w**f + 2*w**4 - 2*w**5 = 0. What is w?
-1, 0, 1
Let f(i) be the second derivative of -i**5/50 - i**4/10 + 6*i. Factor f(z).
-2*z**2*(z + 3)/5
Factor 3 - 5*j**4 - 429*j + 1 - 8*j**3 + 437*j + j**4.
-4*(j - 1)*(j + 1)**3
Let s(r) = -r**2 + 16*r - 61. Let c be s(8). Find q such that -1/2*q**4 + 1/4*q**5 + q**2 + 1/4*q - 1/2 - 1/2*q**c = 0.
-1, 1, 2
Let v = 623/95 + 35/19. Suppose 4*f - 4*b = 32, 2*b - b = -5*f + 10. Factor 22/5*s - 4/5 + 34/5*s**f - v*s**2 - 2*s**4.
-2*(s - 1)**3*(5*s - 2)/5
Let n(k) = k**2 + 2*k - 3. Let w be n(-3). Let g(t) be the first derivative of 1/5*t**2 + 0*t**3 - 1/5*t**6 + 1 - 16/25*t**5 - 3/5*t**4 + w*t. Factor g(j).
-2*j*(j + 1)**3*(3*j - 1)/5
Let l(s) = 3*s - 8. Let f be l(4). Suppose -12 = -3*n - r - 3, f*n = 2*r + 2. Let 1/2*w**3 - 2 + 3/2*w**n + 0*w = 0. Calculate w.
-2, 1
Let b = 13 + -11. Suppose 3*s**3 - 6*s**b - 5 - 4*s**3 + 3 + 7*s + 2*s**4 = 0. Calculate s.
-2, 1/2, 1
Let q = -16/3 - -6. Let n(x) = -x**2 + 6*x - 2. Let s be n(5). Let 0 + 1/3*o**s - 1/3*o**4 + 0*o + q*o**2 = 0. Calculate o.
-1, 0, 2
Factor 2*s + 7 - 3*s**2 - 7.
-s*(3*s - 2)
Factor -3*h**3 + 0*h**3 - 6 + 6*h**2 + 3*h + 5*h**2 - 5*h**2.
-3*(h - 2)*(h - 1)*(h + 1)
Let f = 99/235 - 1/47. Factor -f*n + 4/5*n**2 - 2/5*n**3 + 0.
-2*n*(n - 1)**2/5
Let g(n) be the second derivative of -n**4/20 + 4*n**3/5 + 27*n**2/10 + 25*n. Determine r, given that g(r) = 0.
-1, 9
Let r = 491/170 + -3/34. Factor -3/5*m**4 - 8/5*m + 0 - 4*m**2 - r*m**3.
-m*(m + 2)**2*(3*m + 2)/5
Let n be ((-2)/(-12) - (-2)/(-3))*-1. Let d(j) be the third derivative of 0*j - 4*j**2 + 1/180*j**5 + 1/12*j**4 + n*j**3 + 0. Factor d(c).
(c + 3)**2/3
Let x(c) be the first derivative of -8 + 4*c + 4/3*c**3 - 4*c**2. Factor x(j).
4*(j - 1)**2
Suppose -n - k = -4, 4*n - 5*k + 4 = -7. Let h(l) be the first derivative of 1/3*l**2 + 2/9*l**3 + n + 0*l. Factor h(w).
2*w*(w + 1)/3
Suppose -5*k + 2 + 8 = 0. Let a be (4 - (2 + 1))/k. Find b, given that -1/4*b**2 + 0 + a*b = 0.
0, 2
Let k = 10 + -8. Suppose c**2 - k*c**3 + 6*c - 2*c - 6*c**4 + 5*c**2 - 2*c**5 = 0. Calculate c.
-2, -1, 0, 1
Let m(b) be the second derivative of b**4/3 + 4*b**3/3 + 2*b**2 - 38*b - 2. Factor m(z).
4*(z + 1)**2
Factor -4/9 - 22/9*o - 32/9*o**2 - 14/9*o**3.
-2*(o + 1)**2*(7*o + 2)/9
Let -2*c**2 - 2/5 + 12/5*c - 24/5*c**3 = 0. What is c?
-1, 1/4, 1/3
Let k(n) be the second derivative of 0*n**5 + 0 + 0*n**2 - 1/24*n**4 + 1/60*n**6 + 4*n - 1/168*n**7 + 1/24*n**3. Factor k(z).
-z*(z - 1)**3*(z + 1)/4
Let l(m) be the second derivative of m**7/3780 + m**6/1620 + m**3/3 - 2*m. Let u(h) be the second derivative of l(h). Factor u(q).
2*q**2*(q + 1)/9
Let d = -9 + 13. Suppose -4*k - 2*h + 3*h = -18, -12 = -5*k - d*h. Let k*g**3 - 5*g**2 + 4*g**2 - 3*g**3 = 0. Calculate g.
0, 1
Suppose 0 = -k + 4 - 0. Solve -k*i**2 + 4*i**4 - 75*i**5 - 7*i**3 + 3*i**3 + 79*i**5 = 0.
-1, 0, 1
Let 3*n**3 + 10*n**2 + 34*n**2 - 11*n**2 = 0. Calculate n.
-11, 0
Let l(w) be the third derivative of -w**7/315 - w**6/120 + w**5/180 + w**4/24 + w**3/18 - 16*w**2. Suppose l(u) = 0. What is u?
-1, -1/2, 1
Let p(x) be the third derivative of -2*x**2 + 0 + 0*x + 0*x**3 - 1/60*x**5 + 0*x**4. Determine l, given that p(l) = 0.
0
Let f(k) = 9*k**3 + 5*k - 34. Let l(r) = -4*r**3 - 2*r + 17. Let t(b) = 3*f(b) + 7*l(b). Let y be t(0). Solve -z**2 + 11*z + y*z**2 - 5*z**3 + 2 + 12*z**3 = 0.
-1, -2/7
Find x such that 6/7*x - 3/7*x**2 + 8/7 - 1/7*x**3 = 0.
-4, -1, 2
Let g = 37723/20 + -1887. Let c = 5/4 + g. Factor 0*s - c + 2/5*s**2.
2*(s - 1)*(s + 1)/5
Suppose 0*y - y = -4*d - 13, -2*y - 4*d + 2 = 0. Let v = 10 - y. Factor -2*z**2 + 4*z**2 - 4*z - 5*z**v - 4*z**4 - 3*z**3 + 9*z**5 + 5*z.
z*(z - 1)**2*(2*z + 1)**2
Let j(u) be the first derivative of 5*u**6/6 + 2*u**5 - 35*u**4/4 + 20*u**3/3 + 31. Let j(k) = 0. Calculate k.
-4, 0, 1
Let q(u) be the third derivative of -u**7/105 + u**6/6 - 5*u**5/6 + 8*u**2. Factor q(f).
-2*f**2*(f - 5)**2
Factor -h**3 + 6*h**2 - 2*h**2 - 8*h**2 + 2*h**2.
-h**2*(h + 2)
Let b = -9 - -12. Let p(y) be the first derivative of y**b - 3 - 1/4*y**4 - 3/2*y**2 + y. Factor p(i).
-(i - 1)**3
Let q(z) be the second derivative of 5*z - 7/18*z**3 - 1/3*z**2 + 0 - 1/12*z**4. Factor q(o).
-(o + 2)*(3*o + 1)/3
Let h = 103 + -52. Let v be 3/(-1) + h/15. Find w, given that 0 + 2/5*w + 2/5*w**2 - 2/5*w**3 - v*w**4 = 0.
-1, 0, 1
Let c be (2/(-72)*3)/(-3). Let h(x) be the third derivative of 0*x + 1/18*x**3 + 0 + 1/180*x**5 - x**2 + c*x**4. Factor h(n).
(n + 1)**2/3
Suppose 0 = -8*z + 5*z - 36. Let p = z + 12. Find u, given that p - 2/3*u**2 + 4/3*u = 0.
0, 2
Let r(s) be the second derivative of 0*s**2 - 1/63*s**7 - 2/45*s**6 + 0*s**3 + 1/9*s**4 + 7*s + 0 + 1/30*s**5. Determine m so that r(m) = 0.
-2, -1, 0, 1
Let b(i) = -2*i**3 + i**2 + 4*i + 3. Let h(p) = 14*p**3 - 8*p**2 - 28*p - 22. Let w(a) = 44*b(a) + 6*h(a). Find y such that w(y) = 0.
-2, 0, 1
Find t such that 1/2*t**3 + t**2 + 0 + 0*t = 0.
-2, 0
Let x(u) be the second derivative of 0*u**5 + 0*u**3 + 0*u**2 + 0*u**6 + 0 - 1/6300*u**7 + u - 1/12*u**4. Let q(d) be the third derivative of x(d). Factor q(n).
-2*n**2/5
Let u(c) be the third derivative of 3*c**2 + 0 - 1/105*c**7 + 0*c**4 + 0*c + 1/15*c**5 - 1/3*c**3 + 0*c**6. Solve u(g) = 0.
-1, 1
Let o(j) be the first derivative of -j**8/504 - j**7/105 - j**6/60 - j**5/90 - j**3 - 6. Let y(l) be the third derivative of o(l). Factor y(t).
-2*t*(t + 1)**2*(5*t + 2)/3
Let f = 139 + -416/3. Let q = -80/3 - -28. Determine x so that -1/3*x + 0 + 4/3*x**2 - f*x**5 + q*x**4 - 2*x**3 = 0.
0, 1
Suppose 4*q + l = -q + 22, 5*l = 3*q - 2. Let -16*w**2 - 2*w**q - w**4 + 22*w**2 - 3*w**3 = 0. What is w?
-2, 0, 1
Let l(u) be the third derivative of u**5/180 + u**4/72 - u**3/9 + u**2. Let l(z) = 0. What is z?
-2, 1
Suppose 2*y + 3 = -4*a - 13, -y + 12 = -2*a. Let q be (-3)/6 + a/(-2). Determine u so that -3*u + 4*u**3 + u - q*u**3 + 4*u**2 + 4*u = 0.
-1, 0
Let o(c) be the first derivative of c**7/735 - c**6/420 - c**5/210 + c**4/84 + 3*c**2/2 + 1. Let s(y) be the second derivative of o(y). Factor s(i).
2*i*(i - 1)**2*(i + 1)/7
Let k = 12 - -3. Suppose 0 = 4*z - k - 1. Factor 0 - 4/7*q + 2/7*q**z +