2/4
Factor 2/3*j**4 - 1/6*j**2 + 0 + 1/2*j**3 + 0*j.
j**2*(j + 1)*(4*j - 1)/6
Let r = -6 + 5. Let c = -12 + 7. Let z(i) = -i**4 - i**2 - i + 1. Let l(y) = 7*y**4 - 4*y**3 + 7*y**2 + 5*y - 5. Let o(v) = c*z(v) + r*l(v). Factor o(f).
-2*f**2*(f - 1)**2
Let l(q) be the third derivative of -3*q**2 + 1/60*q**4 + 0 + 0*q**3 + 0*q - 1/150*q**5. Determine y, given that l(y) = 0.
0, 1
Let c(k) be the second derivative of -k**5/5 - 2*k**4/3 + 12*k. Factor c(l).
-4*l**2*(l + 2)
Let t(d) = d**3 + 3*d**2 - d + 3. Let n(q) = -q**3 - 3*q**2 - 2. Let s(k) = -3*n(k) - 2*t(k). Factor s(c).
c*(c + 1)*(c + 2)
Factor 6/7*n + 4/7 + 2/7*n**2.
2*(n + 1)*(n + 2)/7
Suppose -3*h = 4*s - 20, 3*s + 18*h = 19*h + 2. Let 1/3*u**s + 2/3*u + 1/3 = 0. What is u?
-1
Let y(j) be the second derivative of j**6/50 - 21*j**5/100 + 3*j**4/4 - 13*j**3/10 + 6*j**2/5 - 13*j. Factor y(o).
3*(o - 4)*(o - 1)**3/5
Let r(m) = m**4 + m**3 - m + 1. Let z(b) = 2*b**5 - 5*b**4 + b**3 + b - 1. Let t(w) = -2*r(w) - 2*z(w). Find a such that t(a) = 0.
0, 1
Let j(d) be the first derivative of 3/8*d**4 - 3/20*d**5 + 0*d**2 + 0*d**3 - 2 + 0*d. Factor j(x).
-3*x**3*(x - 2)/4
Let h(u) be the first derivative of u**3 - 3*u**2/2 - 6*u - 4. Factor h(a).
3*(a - 2)*(a + 1)
Let q(z) be the first derivative of -18/5*z**5 - 2*z**3 - 9/8*z**6 - 3/8*z**2 + 0*z - 3 - 33/8*z**4. Determine i so that q(i) = 0.
-1, -1/3, 0
Let i(y) be the second derivative of y - 1/6*y**4 + 0 - 1/9*y**3 + 0*y**2 - 1/45*y**6 - 1/10*y**5. Suppose i(r) = 0. Calculate r.
-1, 0
Let r(h) be the second derivative of h**4/4 - 3*h**3/2 + 3*h**2 + 2*h. Find b, given that r(b) = 0.
1, 2
Let k = 13 + -9. Suppose 5*d = k*b - 8, -4*d - 4 = 3*b - 10. Factor 5*h**2 + d*h**2 + h**2 + 2*h - 4*h**2.
2*h*(h + 1)
Let v(f) = f**3 - 6*f**2 + 3*f + 10. Let s be v(5). Let h(p) be the first derivative of 1/3*p**3 + 2 + 0*p**2 + s*p. Find t such that h(t) = 0.
0
Let b(d) be the second derivative of -d**5/120 + d**4/36 - d**3/36 + 7*d. Factor b(w).
-w*(w - 1)**2/6
Let k(j) be the first derivative of -2*j**5/25 + 3*j**4/10 - 4*j**2/5 + 27. Factor k(g).
-2*g*(g - 2)**2*(g + 1)/5
Let q(d) be the second derivative of -1/42*d**7 - 1/6*d**3 + 0*d**6 + d + 0 + 0*d**2 + 0*d**4 + 1/10*d**5. Factor q(v).
-v*(v - 1)**2*(v + 1)**2
Let w(p) be the second derivative of -p**6/120 + p**4/8 + p**3/3 + 3*p**2/2 + p. Let y(h) be the first derivative of w(h). Let y(q) = 0. Calculate q.
-1, 2
Let x be (12/(-20))/((-1)/5). Factor -7*q - x*q**3 + 2 + 9*q**2 - 2*q**2 + q**2 + 0.
-(q - 1)**2*(3*q - 2)
Let f = 70/3 - 23. Let r(m) = -2*m. Let v be r(-2). Factor 0*b + 0 + 1/3*b**2 + f*b**v - 2/3*b**3.
b**2*(b - 1)**2/3
Let a(m) = 5*m**2 + 17*m - 65. Let t(o) = 2*o**2 + 9*o - 33. Let u(b) = -3*a(b) + 7*t(b). Find q such that u(q) = 0.
6
Let z(w) be the third derivative of w**5/180 + 2*w**4/9 + 32*w**3/9 - 39*w**2. Factor z(y).
(y + 8)**2/3
Let k = 311 - 308. Factor -1/6*w**4 + 1/2*w**2 + 0*w**k + 0 - 1/3*w.
-w*(w - 1)**2*(w + 2)/6
Factor -16/11*l - 2/11*l**2 - 32/11.
-2*(l + 4)**2/11
Let y = 282 + -845/3. Let y + 0*n - 1/3*n**2 = 0. What is n?
-1, 1
Let s = -94 - -472/5. Solve 2/5*a**2 - s*a**4 + 0*a**3 + 0 + 0*a = 0.
-1, 0, 1
Let i(q) be the third derivative of -q**7/2940 + q**6/252 - q**5/140 - 3*q**4/28 - q**3/6 - 4*q**2. Let n(s) be the first derivative of i(s). Solve n(j) = 0.
-1, 3
Let b(t) be the third derivative of -t**8/252 + 2*t**7/315 + t**6/45 - 2*t**5/45 - t**4/18 + 2*t**3/9 - 7*t**2. Factor b(v).
-4*(v - 1)**3*(v + 1)**2/3
Let v(h) be the third derivative of 0 + 0*h - 1/70*h**7 + 1/20*h**5 + 0*h**6 + 2*h**2 - 1/16*h**4 + 0*h**3 + 1/224*h**8. Find z such that v(z) = 0.
-1, 0, 1
Let b(n) be the second derivative of n**7/2520 - n**6/720 + n**4/3 + 8*n. Let l(u) be the third derivative of b(u). Factor l(j).
j*(j - 1)
Solve 10/13*h + 8/13*h**2 + 4/13 + 2/13*h**3 = 0.
-2, -1
Let i(g) be the third derivative of g**5/15 - g**4/6 - 4*g**3 + 2*g**2 - 12*g. Factor i(t).
4*(t - 3)*(t + 2)
Suppose -3*k + 4*k = 4. Suppose -k*p - 2 = -5*p. Let -p - 2*d + 3 - 3*d + 4*d**2 = 0. What is d?
1/4, 1
Let s(o) be the first derivative of -o**6/24 + o**5/10 - o**4/16 + 12. Let s(j) = 0. Calculate j.
0, 1
Factor 2/5*i**2 + 0 - 2/5*i**3 + 0*i.
-2*i**2*(i - 1)/5
Let r(a) = 8*a**3 + 13*a**2 + 7*a. Let d(o) = 2*o**2 - 3*o**2 - 5 + 4. Let i(l) = -2*d(l) + 2*r(l). Suppose i(u) = 0. Calculate u.
-1, -1/2, -1/4
Let h(f) = -5 + 0*f**3 + f + f**3 + 3*f**2 - 10*f**2. Let v be h(7). What is o in 1/3*o + 1/3*o**4 - 1/3*o**3 + 0 - 1/3*o**v = 0?
-1, 0, 1
Solve 28*p - 3*p**4 - 31*p - 39*p + 21*p**3 - 6*p - 24*p**2 = 0.
-1, 0, 4
Let t(j) = j**2 + 4*j + 10. Let c be t(14). Let v = c + -1306/5. Factor 0 + 0*z**2 - v*z**3 + 2/5*z**4 + 0*z.
2*z**3*(z - 2)/5
Let d = 81 + -77. Find v, given that 9/5*v - 7/5*v**d + v**2 + 2/5 - 9/5*v**3 = 0.
-1, -2/7, 1
Let d(t) = 10*t**3 - 17*t**2 + 7*t. Let r(h) = 30*h**3 - 50*h**2 + 20*h. Let u(b) = 8*d(b) - 3*r(b). Find f, given that u(f) = 0.
0, 2/5, 1
Let k be 31/(-12) + 3/1. Let o(q) be the second derivative of -5/4*q**5 + 8/3*q**3 + 2*q + 0 - k*q**4 - 2*q**2. Determine m, given that o(m) = 0.
-1, 2/5
Let p be 5/(50/(-4))*20. Let g = p + 8. Factor 1/2*r**4 + 1/2*r**3 - 1/2*r - 1/2*r**2 + g.
r*(r - 1)*(r + 1)**2/2
Let m(o) be the third derivative of 0 + 4*o**2 + 0*o - 1/100*o**5 - 2/5*o**3 + 1/5*o**4 - 3/200*o**6. Factor m(i).
-3*(i - 1)*(i + 2)*(3*i - 2)/5
Let k(v) be the second derivative of -v**7/11340 + v**6/810 - v**5/135 + v**4/12 + 6*v. Let q(h) be the third derivative of k(h). Factor q(x).
-2*(x - 2)**2/9
Let c(t) be the second derivative of t**4/6 + t**3/3 - 9*t. Suppose c(r) = 0. What is r?
-1, 0
Let o be 10/(-4)*48/(-40). Let n be o - (-3 - -6) - -3. Factor -z**2 - 4*z - 1 + z + n + 4*z.
-(z - 2)*(z + 1)
Let v(h) = -h**5 - h**3 + h**2 + h + 1. Let m(r) = 8*r**5 + 7*r**4 + 2*r**3 - 32*r**2 - r + 7. Let x(b) = 4*m(b) + 36*v(b). Determine c so that x(c) = 0.
-1, 1, 4
Let j be (-2)/9 - 116/(-36). Find i such that i**2 + 0*i**2 + 2*i**4 - j*i**2 - 5*i**3 + 2*i + 3*i**3 = 0.
-1, 0, 1
Determine h, given that -22/5*h**2 - 2*h - 14/5*h**3 - 2/5*h**4 + 0 = 0.
-5, -1, 0
Factor 4/9 - 4/9*b**2 + 2/9*b**3 - 2/9*b.
2*(b - 2)*(b - 1)*(b + 1)/9
Let v(x) be the second derivative of -x**8/504 + x**6/90 - x**4/36 + x**2/2 + 3*x. Let u(m) be the first derivative of v(m). Factor u(i).
-2*i*(i - 1)**2*(i + 1)**2/3
Let f(h) be the third derivative of 2*h**7/315 - h**6/45 - h**5/9 + h**4/3 - 4*h**2. Suppose f(k) = 0. What is k?
-2, 0, 1, 3
Determine x, given that 3*x**2 - 3*x**5 + 9*x**4 - 9*x**3 + 0*x**5 - 51*x + 51*x = 0.
0, 1
Let w(z) be the third derivative of -z**5/60 - z**4/3 - z**2. Let s(x) = -x**2 - x. Let a(b) = -6*s(b) + w(b). Factor a(k).
k*(5*k - 2)
Let b = 6/323 + -5647/8398. Let h = -2/13 - b. Find n such that -3/4*n + 3/4*n**3 - 1/4*n**2 - 1/4*n**4 + h = 0.
-1, 1, 2
Suppose 0 = 4*w - 9*w + 25. What is c in 23*c**w + 14*c**4 + 2 - 16*c**2 - 15*c**5 - 4*c**3 - 3*c - c = 0?
-1, 1/4, 1
Factor -12*o + o**2 + 0*o**2 + 0*o**2 + 3*o**2 + 8.
4*(o - 2)*(o - 1)
Let l(z) be the third derivative of -z**7/840 + z**6/160 + z**5/40 - 7*z**4/24 + z**3 + 10*z**2. Suppose l(b) = 0. What is b?
-3, 2
Let q be 8/(8/4) + -3. Let t(k) be the first derivative of q - 1/6*k**3 + 0*k + 1/4*k**2. Let t(j) = 0. Calculate j.
0, 1
Find m such that 5*m + 3*m**3 + 4*m**2 - 10*m + m**3 - 3*m = 0.
-2, 0, 1
Let w(g) = 2*g**2. Let l be w(-1). Find d such that 2 + 7*d**2 - 21*d**3 + 32*d**3 - 6*d**4 - l*d**2 + d**2 - 9*d = 0.
-1, 1/3, 1/2, 2
Let i(v) = -35*v + 238*v**2 + 0 - 49*v - 2 + 10. Let n(p) = -p**2 + p. Let j(u) = -i(u) + 4*n(u). Factor j(f).
-2*(11*f - 2)**2
Let h(c) = c**3 + 5*c**2 + 2*c + 1. Let d be h(-2). Let r(p) = p**2 - 8*p - 7. Let v be r(d). Factor 4*f**v + 2/3 - 8/3*f**3 - 8/3*f + 2/3*f**4.
2*(f - 1)**4/3
Suppose -4*p = -p - 6. Let r(t) = t**3 - t**2 + t - 1. Let j(x) = -18*x**3 + 13*x**2 - 4*x + 9. Let g(d) = p*j(d) + 22*r(d). Determine z, given that g(z) = 0.
-1, 2/7, 1
Suppose -4*p = -5*p. Suppose -i + 2 = -p*i. Factor -5/4*h**3 - h + 1/4*h**4 + 0 + 2*h**i.
h*(h - 2)**2*(h - 1)/4
Suppose 0 = -3*x + 8*x. Let k be ((-8)/22)/(658/(-517)). Solve 0*m - 2/7*m**3 + k*m**5 + 2/7*m**2 + x - 2/7*m**4 = 0 for m.
-1, 0, 1
Let o be 36/63 + 471*(-6)/(-567). Factor -16/9*k**4 - 56/9*k - o*k**3 - 76/9*k**2 - 16/9