i(r). Determine k so that p(k) = 0.
0, 2
Let k(i) = -i**5 + 13*i**4 - 27*i**3 + 28*i**2 - 17*i + 4. Let c(h) = -h**4 + h**3. Let p(q) = 5*c(q) + k(q). Factor p(z).
-(z - 4)*(z - 1)**4
Let w(a) be the second derivative of -a**7/840 + a**6/90 - a**5/40 - a**3/2 - 3*a. Let q(n) be the second derivative of w(n). Let q(m) = 0. What is m?
0, 1, 3
Let q(k) be the first derivative of k**3/15 + 3*k**2/10 + 9. Factor q(x).
x*(x + 3)/5
Suppose 0 + 9 = 3*w. Suppose 0 = -w*t - 3*n + 24, 8*t - 10 = 3*t + n. Suppose 0*m - m**4 + m + 2*m**2 - m**2 - m**t = 0. What is m?
-1, 0, 1
Let f(d) = 5*d**4 + 15*d**3 - 65*d**2 - 130*d - 65. Let b(w) = -2*w**4 - 8*w**3 + 32*w**2 + 65*w + 33. Let n(m) = -5*b(m) - 3*f(m). Find h such that n(h) = 0.
-2, -1, 3
Let r(v) = -2*v**2 - 16*v + 4. Let y(x) = 3*x**2 + 15*x - 3. Let c(n) = -5*r(n) - 6*y(n). Suppose c(w) = 0. Calculate w.
-1, -1/4
Suppose 0 = -0*k - k + 46. Let v be k/14 + (-14)/49. Factor i**v - 2*i**3 + 2*i**2 + 0*i**3.
-i**2*(i - 2)
Let f be 2/(-4)*(-6)/45. Let k(r) be the second derivative of f*r**3 + 0 - 1/100*r**5 + 0*r**2 + 1/60*r**4 - 3*r. Factor k(p).
-p*(p - 2)*(p + 1)/5
Let p = 535/6 - 89. Let w(i) be the first derivative of 2 - p*i**2 - 1/9*i**3 + 2/3*i. Solve w(o) = 0.
-2, 1
Let b(l) be the second derivative of l**5/100 - l**4/5 + 8*l**3/5 - 4*l**2 - 2*l. Let r(x) be the first derivative of b(x). Factor r(w).
3*(w - 4)**2/5
Let h be -10*6*4/12. Let z be (-14)/(-8) - (-10)/h. Find t, given that -1/2 - z*t + 1/4*t**5 + t**3 + t**4 - 1/2*t**2 = 0.
-2, -1, 1
Let p be 12/(-60) + (-32)/(-10). Let r(s) be the second derivative of -1/9*s**p + 0 + 1/36*s**4 + 1/6*s**2 - s. Let r(m) = 0. What is m?
1
Let b(j) = 6*j**2 - 4*j - 2. Let a(o) = -o**3 - 4*o**2 - 3*o - 1. Let k be a(-3). Let t(s) = -s**2 + 1. Let m(h) = k*b(h) - 2*t(h). Solve m(l) = 0 for l.
0, 1
Factor 0 + 4/5*g**3 + 0*g + 4*g**2.
4*g**2*(g + 5)/5
Factor -8/21 + 6/7*i**2 - 32/21*i.
2*(i - 2)*(9*i + 2)/21
Suppose -7*q - 13 = -27. Factor 4/7*o - 2/7*o**q - 2/7.
-2*(o - 1)**2/7
Suppose -3*s = 2*i - 6*i - 7, 3*s - 15 = 0. Solve -3*d**5 - i*d**4 + 3*d**5 + 5*d**4 + 3*d**5 = 0 for d.
-1, 0
Suppose 0 = -5*h - 10, -3*h = 2*m - 0*h - 28. Suppose -30 = -5*v + 2*q, -3*v + 0*v + q + m = 0. Factor 0 - 2/3*w**v + 0*w**3 + 0*w + 0*w**2.
-2*w**4/3
Suppose -2*o - 20 = -6*o. Let r be (0 - -1)/(-1) + 4. Determine i, given that -7*i**o + i**4 + 2*i**3 - i**2 - i**r + 6*i**5 = 0.
-1, 0, 1
Let y(q) be the third derivative of q**7/630 - q**6/180 - q**5/45 + q**4/36 + q**3/6 + 21*q**2. Let y(l) = 0. What is l?
-1, 1, 3
Let v = -17 - -20. Let f(s) be the third derivative of 0 - 1/42*s**4 - 1/210*s**5 - 3*s**2 - 1/21*s**v + 0*s. Factor f(t).
-2*(t + 1)**2/7
Let a(i) = i**5 + i**4. Let x = 17 + -35. Let f(n) = 10*n**5 + 11*n**4 + n**3. Let y(v) = x*a(v) + 2*f(v). Factor y(k).
2*k**3*(k + 1)**2
Solve 4/3 + 2/3*o**2 + 2*o = 0.
-2, -1
Determine r so that 1 - 4*r**2 - 2 + 6*r**2 - 4*r + 3 = 0.
1
Let f(x) be the second derivative of -x**7/840 + x**5/80 - x**4/48 - x**2 + 2*x. Let c(y) be the first derivative of f(y). Suppose c(i) = 0. Calculate i.
-2, 0, 1
Factor -41*v**2 + 243*v + 28*v**4 - 31*v**4 + 33*v**3 - 162 - 94*v**2.
-3*(v - 3)**3*(v - 2)
Let j be (15/(-6) - -3)*(-8)/(-10). Find t such that -j*t - 4/5*t**2 + 2/5*t**3 + 4/5 = 0.
-1, 1, 2
Let u = -11 + 14. Let q(c) be the first derivative of 1/6*c**4 + 4/9*c**u + 1/3*c**2 + 0*c - 2. What is i in q(i) = 0?
-1, 0
Let g(t) be the third derivative of -t**8/2240 + t**7/420 - t**6/240 + 5*t**4/24 + 4*t**2. Let q(p) be the second derivative of g(p). Factor q(v).
-3*v*(v - 1)**2
Let k(m) be the first derivative of m + 0*m**3 + 2 + 0*m**4 + 0*m**2 + 1/50*m**5. Let h(s) be the first derivative of k(s). Factor h(z).
2*z**3/5
Suppose u = 4*u - 2*i - 21, 5*u - 2*i = 31. Let 17*a**u - 2*a**2 - 44*a**5 + 26*a**5 + 3*a**3 = 0. Calculate a.
-2, 0, 1
Let x be 5 + -8 + (-95)/(-30). Factor 0*g**2 + 0*g - x*g**3 + 0.
-g**3/6
Let q = 9 - 9. Let x(n) be the third derivative of 0 + 1/20*n**4 - 1/10*n**3 - 1/100*n**5 + q*n - 3*n**2. Factor x(z).
-3*(z - 1)**2/5
Let n(d) be the first derivative of 3*d**7/70 + d**6/8 - d**5/20 - 5*d**4/8 - d**3 + 5*d**2/2 + 3. Let x(g) be the second derivative of n(g). Factor x(c).
3*(c - 1)*(c + 1)**2*(3*c + 2)
Let l = 21 - 16. Factor -14*n**2 - 4 - 46*n - l - 4 + 1.
-2*(n + 3)*(7*n + 2)
Let u(y) = -8*y + 58. Let w be u(7). Factor 0*i**4 + 0*i**w - 1/7*i**3 + 0 + 1/7*i**5 + 0*i.
i**3*(i - 1)*(i + 1)/7
Let g(o) be the first derivative of -2*o**5/15 + 2*o**3/9 + 7. Suppose g(j) = 0. What is j?
-1, 0, 1
Let t(g) be the first derivative of g**4/8 + g**3/3 - g**2/4 - g + 59. Factor t(j).
(j - 1)*(j + 1)*(j + 2)/2
Let d(b) be the first derivative of 3 - 4/9*b**3 + 1/12*b**4 - 2/3*b + 5/6*b**2. Suppose d(u) = 0. Calculate u.
1, 2
Let l = -23/2 + 85/6. Suppose -5*g + 21 = 11. Solve -4/3*y**g + l*y**3 + 0*y + 0 + 5/3*y**4 = 0 for y.
-2, 0, 2/5
Factor 6 - 8*t**2 + 0*t**2 - 2*t + 0*t**2.
-2*(t + 1)*(4*t - 3)
Let y(j) be the second derivative of j**6/420 + j**2/2 - 3*j. Let g(l) be the first derivative of y(l). Factor g(n).
2*n**3/7
Let 0*o + 0*o**2 - 1/5*o**5 - 2/5*o**4 + 0*o**3 + 0 = 0. What is o?
-2, 0
Let w(f) be the third derivative of f**8/1680 - f**6/600 - 10*f**2. Factor w(p).
p**3*(p - 1)*(p + 1)/5
Let o be (-44)/(-55)*(-10)/(-4). Suppose 4*f = -2*l + 16, 3*f - o*l - 5 = -0*l. What is y in -2/5*y**f - 16/5 - 12/5*y**2 - 24/5*y = 0?
-2
Factor q - 13*q**2 + 0*q + 6 + 4*q**2 + 2*q.
-3*(q - 1)*(3*q + 2)
Let p(c) be the third derivative of -c**6/180 - c**5/126 + c**4/126 - 14*c**2. What is n in p(n) = 0?
-1, 0, 2/7
Let v(y) be the first derivative of 1/3*y**6 + 8/3*y**3 + 0*y + y**2 + 8/5*y**5 + 3*y**4 + 2. Find o such that v(o) = 0.
-1, 0
Let n(g) be the first derivative of g**4/28 - g**3/21 + 5. Find k such that n(k) = 0.
0, 1
Let j be 0/(-3 - -7 - 3). Solve -2*l**4 - l**2 - l**3 + l + j*l**2 + 3*l**4 = 0 for l.
-1, 0, 1
Factor 0*o + 3/5*o**2 + 2/5*o**3 - 1/5.
(o + 1)**2*(2*o - 1)/5
Let l(a) be the third derivative of 1/120*a**5 - 1/48*a**4 + 0 - a**2 + 0*a - 1/6*a**3. Factor l(f).
(f - 2)*(f + 1)/2
Let v(d) be the first derivative of 0*d + 1/12*d**3 - 1/4*d**2 + 1/16*d**4 + 8. Solve v(f) = 0 for f.
-2, 0, 1
Let u(c) be the third derivative of -c**7/210 + c**6/60 - c**5/60 + 3*c**2. Find b such that u(b) = 0.
0, 1
Let d = 731248/563589 - -8/4817. Let t = -14/13 + d. Suppose t*w + 8/9*w**2 + 4/3*w**3 + 2/9*w**5 + 8/9*w**4 + 0 = 0. Calculate w.
-1, 0
Let k(d) be the first derivative of -2*d**3/15 + 8*d**2/5 - 32*d/5 + 4. Factor k(s).
-2*(s - 4)**2/5
Let u(h) be the first derivative of h**6/24 - 3*h**5/20 + 3*h**4/16 - h**3/12 + 32. Factor u(w).
w**2*(w - 1)**3/4
Let s(n) be the first derivative of -n**7/70 + n**6/40 + n**5/20 - n**4/8 - n**2 + 1. Let y(h) be the second derivative of s(h). Factor y(d).
-3*d*(d - 1)**2*(d + 1)
Let w(x) be the third derivative of -x**5/510 + 7*x**4/102 - 49*x**3/51 + 2*x**2. Factor w(r).
-2*(r - 7)**2/17
Let t be -4 - (1 + 68/(-12)). Let q(i) be the first derivative of t*i**3 - 2*i**2 + 1 + 2*i. Suppose q(r) = 0. Calculate r.
1
Let i(q) = -2*q**2 - 6*q. Let g(v) = -1 + 2 - 3*v**2 - 4*v - 7*v + 4*v. Let d(m) = -4*g(m) + 5*i(m). Find o such that d(o) = 0.
-1, 2
Let f(o) be the third derivative of o**5/12 + 5*o**4/24 - 5*o**3 + 7*o**2. Determine w, given that f(w) = 0.
-3, 2
Solve -8/7*b**4 + 8/7*b**2 + 4/7*b**5 + 0*b**3 - 4/7*b + 0 = 0.
-1, 0, 1
Let m be 2/5 + 20/(-50). Let t(z) be the first derivative of 0*z**3 - 1 + 0*z**2 + m*z - 1/10*z**4. Factor t(a).
-2*a**3/5
Let z be 8/3*(-72)/(-48). Solve 0 - 2/7*y + 4/7*y**z + 2/7*y**5 + 0*y**3 - 4/7*y**2 = 0.
-1, 0, 1
Let w(c) be the third derivative of c**7/840 + c**6/160 + c**5/240 - c**4/32 - c**3/12 - c**2. Determine u so that w(u) = 0.
-2, -1, 1
Suppose r + 5*n + 4 = -7, 0 = n + 3. Let h(k) be the third derivative of 0*k**3 + 0*k**r - 1/20*k**6 + 0*k - 1/15*k**5 + 0 + k**2. Factor h(d).
-2*d**2*(3*d + 2)
Factor 3/2*f**2 - 21/4*f**4 + 0*f + 0 + 15/4*f**3.
-3*f**2*(f - 1)*(7*f + 2)/4
What is f in -2/3 - 16/3*f**2 - 14/3*f**3 - 2*f**4 - 3*f - 1/3*f**5 = 0?
-2, -1
Let a(j) = -44*j + 7. Let d be a(-7). Let c = -935/3 + d. Factor -4/3 + 2*i**5 + 20/3*i**3 + 20/3*i**4 + 0*i**2 - c*i.
2*(i + 1)**4*(3*i - 2)/3
Let m be (-10)/(-6)*((-12)/20)/(-3). Factor 0