. Let z(c) be the first derivative of v(c). Suppose z(f) = 0. Calculate f.
-1, 0, 2/7
Let b(o) be the second derivative of -o**5/4 - 5*o**4/3 - 10*o**3/3 + 65*o. Factor b(x).
-5*x*(x + 2)**2
Let h be 0/((-1 - -1) + (3 - 1)). Factor 1/2*j**4 + 0 + h*j**2 - 1/2*j**3 + 0*j.
j**3*(j - 1)/2
Factor -144*b**2 + 156*b**3 - 5 + 22*b**5 - 66*b**4 - 18*b**2 - 13*b**5 - 7 + 75*b.
3*(b - 4)*(b - 1)**3*(3*b - 1)
Factor -2*p**2 + 2*p**2 + 1 + 2 - 3*p**3 + 3*p - 3*p**2.
-3*(p - 1)*(p + 1)**2
Suppose -8/9*x**2 + 8/9*x + 0 - 10/9*x**3 + 2/3*x**4 = 0. What is x?
-1, 0, 2/3, 2
Let s(y) be the second derivative of -y**5/120 + y**3/12 - y**2/6 - 6*y. Factor s(u).
-(u - 1)**2*(u + 2)/6
Suppose -4*g = 2*i - 3*i - 22, -g + 11 = -3*i. Suppose -z - z - 25 = -g*v, 5*z + 5*v = 25. Find k, given that -k**3 - 1 + 0*k**3 - 3*k**2 - 3*k + z*k**2 = 0.
-1
Suppose 0 = -3*t + 6*t - 9. Let a(r) be the first derivative of 1/10*r**4 + t + 0*r**2 + 0*r - 2/15*r**3. Determine h, given that a(h) = 0.
0, 1
Let s = 21 - 19. Factor -20*v**2 + 13*v**s + 3*v**2 - 4*v.
-4*v*(v + 1)
Let x(i) = -i**3 + 6*i - 10. Let h(d) = -2*d**3 - d**2 + 13*d - 21. Let a(r) = -2*h(r) + 5*x(r). Factor a(n).
-(n - 2)**2*(n + 2)
Factor 4/3*n + 8/3 - 8/3*n**2 - 4/3*n**3.
-4*(n - 1)*(n + 1)*(n + 2)/3
Let v be (-207)/506*(-16)/6. Let b = 35/22 - v. Factor 1/4*g**5 + 0 - 1/4*g**4 - 3/4*g**3 + b*g + 1/4*g**2.
g*(g - 2)*(g - 1)*(g + 1)**2/4
Let q(h) be the first derivative of h**7/63 + h**6/45 - h**5/10 - 5*h**4/18 - 2*h**3/9 - 2*h - 1. Let i(c) be the first derivative of q(c). Factor i(r).
2*r*(r - 2)*(r + 1)**3/3
Let s be -2 - 5/(-1 + 0). Suppose b + 2 = 5. Suppose -3*m**4 + 4*m**4 - 5*m**b - 2 + 2*m**3 + s*m + m**2 = 0. What is m?
-1, 1, 2
Suppose 2*w - 12 = -2*w. Suppose -m + 4*m**w - m**2 + 1 - 3*m**3 + 0*m**3 = 0. Calculate m.
-1, 1
Let k(i) be the third derivative of -i**8/6048 - i**7/1620 - i**6/1620 + i**4/24 - i**2. Let j(c) be the second derivative of k(c). What is d in j(d) = 0?
-1, -2/5, 0
Let a be ((-102)/27 + 4)*(4 + -1). Let d(q) be the second derivative of q - a*q**3 + 1/12*q**4 + 2*q**2 + 0. Factor d(g).
(g - 2)**2
Let a(z) be the second derivative of -z**8/280 - z**7/525 - z**2/2 + z. Let y(p) be the first derivative of a(p). Factor y(v).
-2*v**4*(3*v + 1)/5
Let r(p) = 4*p**4 + 64*p**3 + 384*p**2 + 1027*p + 1027. Let c(y) = 8*y**4 + 128*y**3 + 768*y**2 + 2053*y + 2053. Let z(o) = 3*c(o) - 5*r(o). Factor z(q).
4*(q + 4)**4
Let m(x) = -x**4 + x**3 - 1. Let n(z) = -z**4 + 2*z**3 - z**2 - 2. Let k(f) = -2*m(f) + n(f). Solve k(h) = 0 for h.
-1, 0, 1
Let f = 600 + -5392/9. Let v(k) be the first derivative of 16/9*k**2 - 3 - 14/27*k**3 - f*k. Suppose v(h) = 0. What is h?
2/7, 2
Let v(g) = 13*g**2 + 11*g + 10. Let i(u) = -11*u**2 - 11*u - 10. Let r(t) = 6*i(t) + 5*v(t). Let r(a) = 0. What is a?
-10, -1
Solve -c**4 + 12*c**2 + 58*c - 3*c**4 - 58*c + 8*c**3 = 0 for c.
-1, 0, 3
Let i(v) be the third derivative of v**7/2520 + v**6/360 + v**5/120 + v**4/72 + v**3/3 - 3*v**2. Let j(a) be the first derivative of i(a). Factor j(b).
(b + 1)**3/3
Let c(j) be the first derivative of j**6/2 - 9*j**5/5 - 21*j**4/4 + 7*j**3 + 27*j**2 + 24*j + 26. Find i such that c(i) = 0.
-1, 2, 4
Let p(m) be the third derivative of -m**7/840 - m**6/96 - m**5/30 - m**4/24 - 8*m**2. Solve p(x) = 0.
-2, -1, 0
Let v(p) be the first derivative of 0*p**4 + 1/3*p**3 + 0*p + 3/2*p**2 - 1/30*p**5 - 3. Let b(k) be the second derivative of v(k). Factor b(n).
-2*(n - 1)*(n + 1)
Let o(j) be the second derivative of j**5/80 - j**4/24 - j**3/24 + j**2/4 - 2*j. Suppose o(i) = 0. Calculate i.
-1, 1, 2
Let x(k) = -k**5 - k**4 + 3*k**3 - k**2 - 2*k - 2. Suppose 3 = 2*b - 1. Let m(v) = v**3 - v**2 - v - 1. Let d(w) = b*m(w) - x(w). Factor d(j).
j**2*(j - 1)*(j + 1)**2
Let x(o) be the first derivative of 15*o**4/4 + 2*o**3 - 9*o**2/2 + 1. Let z(b) = 7*b**3 + 3*b**2 - 4*b. Let r(g) = 6*x(g) - 13*z(g). Factor r(j).
-j*(j + 1)*(j + 2)
Let s be 74/18 + 5/(-45). Solve -3*r**3 + 4 + 3*r - r**s + 5*r - 3*r**4 - 5*r**3 = 0.
-1, 1
Suppose 2*o - 5*w + 28 + 1 = 0, 0 = -5*o + 5*w - 35. Let u = 8 + o. Factor -f**2 + 0 + 2*f - u*f - 4.
-(f + 2)**2
Let j be 1 - (-2 + 0 + 0). Let d(p) be the first derivative of 2/9*p**j + 0*p**2 + 4/9*p**6 + 0*p - 1 + 0*p**5 - 1/2*p**4. Factor d(s).
2*s**2*(s + 1)*(2*s - 1)**2/3
Let k = 20 - 14. Suppose 2*s - s**3 + 17*s**4 - 6*s**3 + s**2 + k*s**2 - 47*s**4 = 0. Calculate s.
-2/5, -1/3, 0, 1/2
Let s be (6/21)/(4/(-56)*-8). Solve 0*w + 1/2*w**2 + 0 + s*w**4 - w**3 = 0.
0, 1
Let r be (4/3)/((-22)/(-33)). Let t(w) be the first derivative of 2/9*w**r + 0*w - 5/18*w**4 + 1 - 2/9*w**3. Determine z so that t(z) = 0.
-1, 0, 2/5
Suppose -h + 3 - 4 = 0. Let f be (-2 + 0)*(-2 - h). Find k such that -k - 3*k**2 + k**3 + 1 + 0 + f*k**2 = 0.
-1, 1
Let y(d) be the second derivative of 0 + 0*d**2 + 3*d - 1/6*d**4 - 2/3*d**3. Factor y(z).
-2*z*(z + 2)
Let y(v) = v + 13. Let g be y(-10). Let f be 8/(-12) + 2/g. Factor -6/11*x**4 - 2/11*x**5 + f - 6/11*x**3 - 2/11*x**2 + 0*x.
-2*x**2*(x + 1)**3/11
Suppose 0 = 3*u + 3 + 3, p = -4*u + 6. Suppose 2*a + 3*c - 9 = a, -4*c = 2*a - p. Factor 4/5*y**a + 2/5*y**5 + 2/5 - 6/5*y - 6/5*y**4 + 4/5*y**2.
2*(y - 1)**4*(y + 1)/5
Let d(f) be the second derivative of 1/40*f**5 + 0 - 1/24*f**3 - 1/24*f**4 + 1/8*f**2 + 1/120*f**6 - 1/168*f**7 + 3*f. Factor d(s).
-(s - 1)**3*(s + 1)**2/4
Factor -28*q**3 - 52*q**4 - 448*q**2 + 268*q**3 + 256*q + 3*q**5 - 3*q**5 + 4*q**5.
4*q*(q - 4)**3*(q - 1)
Let a(l) = -l**2 - 3*l. Let z be a(-2). Let g be (z/7)/(27/63). Factor -2/3*n**2 - g*n**4 + 0*n - 4/3*n**3 + 0.
-2*n**2*(n + 1)**2/3
Factor -3/5*o**4 + 0*o - 3/5*o**2 + 0 - 6/5*o**3.
-3*o**2*(o + 1)**2/5
Let z(j) be the first derivative of -j**5/20 - j**4/16 + j**3/4 + 5*j**2/8 + j/2 - 2. Find k, given that z(k) = 0.
-1, 2
Let j = -12 - -14. Factor 12*n - 5*n**2 + 5*n**2 + 8 + 4*n**j.
4*(n + 1)*(n + 2)
Let i(a) be the second derivative of 0*a**2 - 1/15*a**3 - a + 0 + 1/30*a**4. What is k in i(k) = 0?
0, 1
Suppose o - 5 = -1. Let t(a) be the first derivative of 20/3*a**2 + 16/3*a + 4*a**3 + 7/6*a**o + 1 + 2/15*a**5. Factor t(j).
2*(j + 1)*(j + 2)**3/3
Let y = -484 + 487. Solve 0 - 14/11*f**y + 0*f**2 + 6/11*f**4 + 8/11*f = 0.
-2/3, 0, 1, 2
Let o(s) be the first derivative of 2*s**5/45 - 2*s**4/9 + 4*s**3/27 + 4*s**2/9 - 2*s/3 - 19. Find z such that o(z) = 0.
-1, 1, 3
Factor 920 - 10*t**4 + 5*t**3 - 920 - 5*t + 10*t**2.
-5*t*(t - 1)*(t + 1)*(2*t - 1)
Let k(b) be the second derivative of -b**7/42 + 3*b**5/20 + b**4/6 - 5*b. Factor k(s).
-s**2*(s - 2)*(s + 1)**2
Let g(b) be the first derivative of 11*b**5/5 - b**4/2 - 3*b**2 - 11*b + 3. Let d(k) = -7*k**4 + k**3 + 4*k + 7. Let n(u) = 8*d(u) + 5*g(u). Factor n(w).
-(w - 1)*(w + 1)**3
Let p = 7 + -4. Factor -n - 2*n**2 + 6*n**4 - 3*n**p - n**2 - 10*n**4 + 3*n**4.
-n*(n + 1)**3
Let t be (27/6)/3*240/405. Factor 0 - 2/9*y**3 - 8/9*y + t*y**2.
-2*y*(y - 2)**2/9
Determine l so that 2/3*l**3 + 0 + 0*l**2 + 0*l = 0.
0
Let o(x) be the second derivative of 2*x**6/15 - 2*x**5/5 + 4*x**3/3 - 2*x**2 + 9*x. Solve o(h) = 0.
-1, 1
Factor 9/7*q - 3/7*q**2 - 6/7.
-3*(q - 2)*(q - 1)/7
Let k = 207 + -147. Let h be ((-5)/(-4))/(k/24). Find u, given that 5/2*u**3 - 4*u - 1/2*u**5 - 1/2*u**2 - 2 + h*u**4 = 0.
-1, 2
Let m(s) be the first derivative of -s**5/80 + s**4/24 - 3*s - 2. Let w(i) be the first derivative of m(i). Determine f, given that w(f) = 0.
0, 2
Let l(b) be the second derivative of 1/4*b**2 + 1/60*b**6 + 1/12*b**3 + 0 - 1/12*b**4 + 1/84*b**7 - 1/20*b**5 - 3*b. Factor l(t).
(t - 1)**2*(t + 1)**3/2
Let w = 372 + -1487/4. Suppose -3*t = -8*t. Factor 0*p + 0*p**2 - w*p**5 + t - 1/4*p**4 + 0*p**3.
-p**4*(p + 1)/4
Let g(l) be the first derivative of -3*l**5/10 - l**4/4 + l**3/2 + l**2/2 - 5. Factor g(v).
-v*(v - 1)*(v + 1)*(3*v + 2)/2
Let q be 0 - (-4)/(16/(-12)). Let p(h) = -h**3 - 3*h**2 + h + 3. Let i be p(q). Factor i*l - 2/7*l**2 + 0 + 2/7*l**3.
2*l**2*(l - 1)/7
Let c be 2/3 + (-8)/(-6). Let n(a) be the second derivative of -1/3*a**2 - 1/9*a**4 - c*a + 0 - 1/2*a**3. Factor n(z).
-(z + 2)*(4*z + 1)/3
Let j(l) = -5*l**3 + 2*l**2 + 3*l. Let q(g) = -g**3 + g**2 + g. Let p(b) = 2*b + 1. Let u be p(-1). Let r(y) = u*j(y) + 3*q(y). Determine w so that r(w) = 0.
-1/2, 0
Determine k so that 8/3*k + 10/3*k