.
4*(a - 2)**2*(a - 1)**2
Let b(k) be the first derivative of -2 - 9/4*k**4 + 3/5*k**5 + 6*k**2 + 0*k**3 + 0*k. Factor b(s).
3*s*(s - 2)**2*(s + 1)
Factor 2/19*a**2 + 0 + 28/19*a.
2*a*(a + 14)/19
Suppose -58 = -3*v - 52. Solve 1/3*u**3 + 0 - u**v + 0*u = 0.
0, 3
Let y(i) be the third derivative of i**8/672 + i**7/210 - i**6/60 - i**5/60 + i**4/16 - 31*i**2 - i. Factor y(q).
q*(q - 1)**2*(q + 1)*(q + 3)/2
Suppose -138 - 276 = -9*v. Let i be 2/6*(-69)/v*0. Solve q**3 + i - 5/4*q**2 + 1/4*q = 0 for q.
0, 1/4, 1
Let m(s) be the first derivative of -s**6/75 + s**4/15 - s**2/5 - 3*s - 5. Let l(h) be the first derivative of m(h). Factor l(w).
-2*(w - 1)**2*(w + 1)**2/5
Let h be 4*(-2)/4 + -4. Let i(k) = -1. Let w(u) = 55*u**2 - 155*u - 24. Let l(q) = h*i(q) - w(q). Suppose l(t) = 0. Calculate t.
-2/11, 3
Let j = 0 - -4. Factor -4*t**3 - t**2 + 2*t**2 + 9*t**3 + j*t**2.
5*t**2*(t + 1)
Let a(b) be the first derivative of 0*b + 40/3*b**3 + 7*b**5 - 95/4*b**4 + 1 + 10*b**2. Factor a(o).
5*o*(o - 2)*(o - 1)*(7*o + 2)
Let c(n) = 1. Let t(p) be the first derivative of -1/5*p**5 - 1/2*p**2 + 1 + 1/3*p**3 - 2*p + 1/4*p**4. Let y(m) = -2*c(m) - t(m). Factor y(a).
a*(a - 1)**2*(a + 1)
Let c(f) = -f**3 - 4*f**2 + 3*f - 3. Let m = -1 + -4. Let u be c(m). Find k such that 3*k - 6*k**4 - 3*k**3 - 4*k**2 + 3*k**4 + u*k**2 = 0.
-1, 0, 1
Let -174*d - 14*d**4 - 6*d - 9*d**3 - 4*d**4 + 3227*d**5 - 3224*d**5 + 156*d**2 = 0. What is d?
-3, 0, 2, 5
Let g(f) = -7*f**2 + 74*f + 65. Let b(o) = -19*o**2 + 221*o + 196. Let k(l) = -4*b(l) + 11*g(l). Factor k(a).
-(a + 1)*(a + 69)
Let z(w) = -3*w**2 + 22*w + 6. Suppose -4 + 10 = -3*c. Let a(v) = -v. Let d(l) = c*z(l) - 10*a(l). Factor d(r).
2*(r - 6)*(3*r + 1)
Suppose -13 = -0*i - i. Let g(s) = -s**2 + 14*s - 11. Let w be g(i). Factor 15*f**2 + 3*f**2 - 16*f + 4 - 2*f**w.
4*(2*f - 1)**2
Let r(g) be the first derivative of g**5/5 - 17*g**4/2 + 32*g**3 - 47*g**2 + 31*g - 594. Let r(u) = 0. What is u?
1, 31
Solve 110*i**4 - 40*i**4 - 10*i - 32*i**4 - 15*i**2 - 33*i**4 = 0 for i.
-1, 0, 2
Let -36/7 - 18*b + 8/7*b**4 + 66/7*b**3 + 88/7*b**2 = 0. Calculate b.
-6, -3, -1/4, 1
Let l(y) = -3*y - 6. Let k be l(-4). Let v(j) be the first derivative of -8/75*j**5 + 8/5*j**2 - k - 8/15*j - 74/45*j**3 + 7/10*j**4. Find n such that v(n) = 0.
1/4, 1, 2
Let l(c) be the second derivative of -c**6/6 - c**5 - 25*c**4/12 - 5*c**3/3 - 19*c - 1. Solve l(h) = 0.
-2, -1, 0
Let c(w) = -w**3 + 4*w**2 + 6*w + 2. Let r be c(5). Suppose -5 - r = -3*t. Factor -4 + 2*x**3 + 0*x**3 + t*x**2 - 2 - 2*x + 2.
2*(x - 1)*(x + 1)*(x + 2)
Suppose n + n - 4*g - 72 = 0, -n + 3*g + 38 = 0. Determine w, given that 24*w**2 - n*w - 70*w**2 - 128 + 19*w**2 + 25*w**2 = 0.
-8
Let n(j) be the third derivative of 0*j + 0 + 0*j**3 - 1/90*j**5 - 1/540*j**6 - 15*j**2 - 1/54*j**4. Suppose n(s) = 0. What is s?
-2, -1, 0
Let w(a) be the third derivative of -a**6/60 + 19*a**5/30 + a**4/12 - 19*a**3/3 + a**2 - 24. Find f, given that w(f) = 0.
-1, 1, 19
Let f(z) be the third derivative of 169/18*z**3 + 38*z**2 + 1/360*z**6 + 0*z + 143/72*z**4 - 5/36*z**5 + 0. Factor f(p).
(p - 13)**2*(p + 1)/3
Let j(a) be the first derivative of -2*a**6/15 + 4*a**4/3 + 3*a - 26. Let y(c) be the first derivative of j(c). Factor y(u).
-4*u**2*(u - 2)*(u + 2)
Suppose -8 = -2*i - 32. Let z be 133/38*i/(-49). Factor -10/7*c - 4/7 - z*c**2.
-2*(c + 1)*(3*c + 2)/7
Let n = 136 + -66. Let v be n/20*(-4)/(-7). Find m, given that 27 + 6*m - 29 - 3*m - m**v = 0.
1, 2
Let x be (5/25)/((-4)/(-60)). Suppose -4*c + 2 = -x*c. Factor -3/4*i**c + 1 + i + 1/4*i**4 - 1/2*i**3.
(i - 2)**2*(i + 1)**2/4
Suppose 11*y = 15*y. Factor y - 3*c - 2*c + 3*c**3 - 2 + c**2 + c**4 + 2*c.
(c - 1)*(c + 1)**2*(c + 2)
Let h(m) be the first derivative of 9/2*m**2 + 1/12*m**4 + 2*m + 4 - m**3. Let z(o) be the first derivative of h(o). Factor z(l).
(l - 3)**2
Determine k, given that -28*k**2 + 32 - 2*k**5 + 925*k**4 + 40*k + 16 - 42*k**3 - 941*k**4 = 0.
-3, -2, 1
Let h be (155/(-10) - -5) + 11. Let k(y) be the third derivative of -4*y**2 + 0*y**4 + 0 + 0*y + h*y**3 - 1/20*y**5. Factor k(u).
-3*(u - 1)*(u + 1)
Let l(f) be the first derivative of -3 + 4/3*f**2 - 8/3*f - 2/9*f**3. Solve l(g) = 0 for g.
2
Let p(u) = 35*u - 1012. Let m be p(29). Factor -1/3*f**2 + 1/3*f**m + 0*f + 0.
f**2*(f - 1)/3
Let k(x) be the third derivative of -x**7/1155 - x**6/220 - x**5/165 - 21*x**2. Factor k(n).
-2*n**2*(n + 1)*(n + 2)/11
Let h(k) be the third derivative of k**5/330 - 17*k**4/44 - 206*k**2. Find p such that h(p) = 0.
0, 51
Factor -47 - 25*f**3 - 3 - 15777*f**2 + 15762*f**2 + 85*f + 5*f**4.
5*(f - 5)*(f - 1)**2*(f + 2)
Let i(q) be the third derivative of q**6/60 + 3*q**5/2 + 161*q**4/4 - 529*q**3/3 - 71*q**2. Factor i(n).
2*(n - 1)*(n + 23)**2
Let h(q) = 130*q**3 + 540*q**2 + 825*q + 405. Let y(d) = -d**4 + d**3 + d + 1. Let t(z) = -h(z) + 5*y(z). Let t(a) = 0. What is a?
-20, -2, -1
Let -1/2*h**3 - 1/2*h + 0 - h**2 = 0. What is h?
-1, 0
Let i(a) = a**2 + 4*a + 5. Let g be i(-5). Suppose 12 = g*w - 6*w. Suppose 7/2*h**w + h**2 + 0*h + 0 = 0. What is h?
-2/7, 0
Let u(t) be the first derivative of -8/9*t**3 + 1/6*t**4 + 22 - 4/3*t + 5/3*t**2. Solve u(s) = 0.
1, 2
Let 9*l**3 + 25*l**4 + 25*l**4 - 3*l**2 - 4*l - 5*l - 47*l**4 = 0. Calculate l.
-3, -1, 0, 1
Let m(c) be the second derivative of 49*c**6/45 - 14*c**5/15 - 32*c**4/3 + 112*c**3/9 - 16*c**2/3 - 16*c. Determine u, given that m(u) = 0.
-2, 2/7, 2
Find z, given that 2/5*z - 2/3*z**2 + 0 - 16/15*z**3 = 0.
-1, 0, 3/8
Let y(g) be the first derivative of g**6/120 + g**5/30 - g**4/6 - 4*g**3/3 + 4*g**2 + 28. Let b(v) be the second derivative of y(v). Let b(i) = 0. What is i?
-2, 2
Let c(h) = 51*h - 4. Let g be c(-1). Let y = g - -57. Factor 2/9*j**y - 2/9 + 2/9*j - 2/9*j**3.
-2*(j - 1)**2*(j + 1)/9
Let d(q) = -q**3 - q**2 + 2*q. Let x(o) = 8*o**3 + o**2 - 45*o + 36. Let l(p) = 14*d(p) + 2*x(p). Factor l(k).
2*(k - 9)*(k - 1)*(k + 4)
Let w = 49465 - 49461. Factor -4/7*v - 10/7*v**w - 2/7*v**5 - 2*v**2 + 0 - 18/7*v**3.
-2*v*(v + 1)**3*(v + 2)/7
Let z(c) be the second derivative of c**4/36 - 5*c**3/9 + 8*c**2/3 - 83*c + 2. Find v, given that z(v) = 0.
2, 8
Solve -540*s**4 + 559*s**4 + 3*s**5 - 6*s**5 + 14*s**3 = 0 for s.
-2/3, 0, 7
Let w(d) be the first derivative of -3/2*d + 1/6*d**3 + 1/2*d**2 - 6. Suppose w(z) = 0. What is z?
-3, 1
Let k(j) be the second derivative of 0*j**2 + 1/315*j**7 + 42*j - 1/225*j**6 + 0 - 1/50*j**5 - 2/45*j**3 + 1/18*j**4. Let k(z) = 0. What is z?
-2, 0, 1
Let o(c) = 9*c**4 + 21*c**3 - 33*c**2 + 3*c. Let i(j) = -5*j**2 - 2*j**4 + j**4 + 6*j**2. Let n(v) = -18*i(v) - o(v). Factor n(t).
3*t*(t - 1)**2*(3*t - 1)
Determine p so that -144/5*p**3 - 108/5*p**2 + 0 - 3/5*p**5 - 39/5*p**4 + 0*p = 0.
-6, -1, 0
Let a(b) be the third derivative of -b**6/35 - 5*b**5/21 + b**4/42 + 40*b**3/21 - 109*b**2. Find g such that a(g) = 0.
-4, -1, 5/6
Let r(f) = -6*f**3 + 498*f**2 - 362*f - 122. Let o(x) = 23*x**3 - 1994*x**2 + 1447*x + 488. Let m(c) = 2*o(c) + 9*r(c). Find n such that m(n) = 0.
-1/4, 1, 61
Factor -t**2 - 9*t**2 + 3*t**2 - 58*t**3 + 10*t**4 - 5*t**2 + 0*t**2.
2*t**2*(t - 6)*(5*t + 1)
Determine p, given that -82/7*p**3 - 30/7*p + 4/7 + 6*p**4 - 8/7*p**5 + 74/7*p**2 = 0.
1/4, 1, 2
Suppose 2*s + s = 2673. Let k be (-4)/(-22) + 333/s - -3. Factor k*j + 14/9*j**2 + 8/9.
2*(j + 2)*(7*j + 2)/9
Let g(k) be the second derivative of k**4/24 - 11*k**3/3 + 43*k**2/4 + 320*k. Find m, given that g(m) = 0.
1, 43
Let p(w) be the first derivative of -5*w**7/42 - w**6/3 + 5*w**4/6 + 5*w**3/6 + 8*w + 14. Let i(x) be the first derivative of p(x). What is f in i(f) = 0?
-1, 0, 1
Let i be (-12)/48 + (-322)/(-8). Let v = i - 118/3. Factor 0 - 2/3*m**3 + 4/3*m - v*m**2.
-2*m*(m - 1)*(m + 2)/3
Let a(d) be the third derivative of 0*d + 1/4*d**5 - 3/8*d**4 + 0*d**3 - 1/70*d**7 - 1/40*d**6 + 0 - 9*d**2. Factor a(h).
-3*h*(h - 1)**2*(h + 3)
Factor 22/7*b + 0 + 2/7*b**2.
2*b*(b + 11)/7
Let r = 2812 - 2809. Let q(c) be the first derivative of -1/10*c**2 - 2/5*c + 1/15*c**r + 12. Solve q(w) = 0.
-1, 2
Let f(i) = -3*i**2 - 14*i + 17. Let l(m) = -m**2 - 9*m + 2. Let q(p) = p + 1. Let a(o) = -l(o) - 4*q(o). Let r(x) = 17*a(x) + 6*f(x). Find z such that r(z) = 0.
0, 1
Let t(j) = -5*j + 61. Let o be t(9). Suppose 9*m - 4 =