- 2)*(q - 1)*(q + 1)**2
Let x be 1/3 - 5/75*-43. Determine i, given that -94/5*i**3 + 26/5*i + 32/5*i**5 + x*i**4 + 16/5*i**2 + 4/5 = 0.
-2, -1/4, 1
Let f be 1/(-7)*(25 - 29). Determine k so that 2/7 + 2/7*k**2 - f*k = 0.
1
Let v(n) be the third derivative of n**5/330 - n**4/132 - 2*n**3/33 + 5*n**2. Find s, given that v(s) = 0.
-1, 2
Let z be (-14)/(-4)*(-40)/(-70). Let i(o) be the third derivative of 2*o**z + 0 + 1/90*o**6 - 1/630*o**7 + 1/36*o**4 - 1/36*o**5 + 0*o + 0*o**3. Solve i(g) = 0.
0, 1, 2
Let l = -3/53 - -62/159. Factor 0*j + l*j**5 + 0 + 0*j**2 - 2/3*j**4 + 1/3*j**3.
j**3*(j - 1)**2/3
Let i(x) be the second derivative of x**9/7560 - x**8/1120 + x**7/420 - x**6/360 - x**4/4 - 3*x. Let l(t) be the third derivative of i(t). Factor l(o).
2*o*(o - 1)**3
Let s = 282 + -282. Factor -2/5*o**2 + 1/5*o**5 - 3/5*o**3 + 0*o + s + 0*o**4.
o**2*(o - 2)*(o + 1)**2/5
Let s(c) be the first derivative of 2/3*c**3 + 3 + 0*c + 0*c**2 + 3/10*c**5 - 1/24*c**6 - 3/4*c**4. Factor s(t).
-t**2*(t - 2)**3/4
Let c(x) be the first derivative of -x**6/4 + 6*x**5/5 - 15*x**4/8 + x**3 + 58. Factor c(k).
-3*k**2*(k - 2)*(k - 1)**2/2
Suppose -120*f - 4 = -122*f. Find s, given that 0 + 1/2*s**f + 0*s = 0.
0
Let j(c) be the third derivative of -c**9/30240 + c**8/10080 - c**5/60 + 4*c**2. Let m(w) be the third derivative of j(w). Solve m(y) = 0 for y.
0, 1
Factor -4/9*c**2 - 2/9*c + 0.
-2*c*(2*c + 1)/9
Let f = 5/8 + -3/8. Let z(l) be the first derivative of -1/12*l**3 - 2 - f*l - 1/4*l**2. Factor z(k).
-(k + 1)**2/4
Factor 3/4 + 3/4*n**2 - 3/2*n.
3*(n - 1)**2/4
Suppose -4*b + 2 = -3*b. Let i(y) = -4*y - 5*y - 1 - 9*y**b - 2*y. Let g(s) = 5*s**2 + 6*s + 1. Let t(n) = 5*g(n) + 3*i(n). Suppose t(x) = 0. What is x?
-2, 1/2
Let h be 2*1 - 24/14. Let x be -118 + 109 - 67/(-7). Let -6/7*a - h*a**2 - x = 0. What is a?
-2, -1
Factor 2/13*v**3 + 4/13*v**2 + 2/13*v + 0.
2*v*(v + 1)**2/13
Let f be 1*(-2 + 2) - -5. Suppose f = 5*t - 10. Factor 0*w**3 - 8*w**4 - 8*w**3 - 2*w**t + 2*w**2 - 4*w**2.
-2*w**2*(w + 1)*(4*w + 1)
Let 10*q**4 + 4*q**3 - 3*q**5 - 12*q**4 + q**5 = 0. Calculate q.
-2, 0, 1
Let y be (-176)/132*(-1)/(2/6). Let h be (0 - -5) + 0/1. Factor -y*r**3 - 1/4 - 1/2*r**h - 9/4*r**4 - 3/2*r - 7/2*r**2.
-(r + 1)**4*(2*r + 1)/4
Let b(k) be the first derivative of k**7/105 - k**6/30 + k**5/30 - 7*k**2/2 - 10. Let v(n) be the second derivative of b(n). Solve v(a) = 0 for a.
0, 1
Let y(x) be the second derivative of -x**5/20 - 7*x**4/12 - 5*x**3/6 + 7*x**2/2 + x. Let o be y(-6). Factor p - p**2 - 1 + o.
-p*(p - 1)
Let f(o) be the first derivative of -o**5/10 - o**4/3 + 2*o + 1. Let l(s) be the first derivative of f(s). Solve l(g) = 0.
-2, 0
Let y(j) = 2*j**4 - 18*j**3 - 32*j**2 + 12*j. Let i(h) = h**4 - 7*h**3 - 13*h**2 + 5*h. Let a(s) = 12*i(s) - 5*y(s). Factor a(z).
2*z**2*(z + 1)*(z + 2)
Let i(d) be the third derivative of d**6/300 + 11*d**5/150 + 7*d**4/12 + 5*d**3/3 - 11*d**2. Factor i(m).
2*(m + 1)*(m + 5)**2/5
Let g(p) be the third derivative of 1/180*p**5 - 6*p**2 - 1/18*p**3 + 0*p + 0 - 1/90*p**6 + 1/18*p**4. Factor g(a).
-(a - 1)*(a + 1)*(4*a - 1)/3
Let m(h) = -9*h**4 + 2*h**3. Suppose u + 0*u = 11. Let r(i) = 5*i**4 - i**3. Let l(g) = u*r(g) + 6*m(g). Factor l(o).
o**3*(o + 1)
Let y(d) be the third derivative of -3*d**2 - 1/1440*d**6 - 2/3*d**3 + 0*d**5 + 0*d**4 + 0 + 0*d. Let c(n) be the first derivative of y(n). Factor c(t).
-t**2/4
Let s(m) = 13*m**4 + 17*m**3 - 9*m**2 - 12*m + 1. Let o(j) = -38*j**4 - 50*j**3 + 26*j**2 + 36*j - 2. Let h(y) = -5*o(y) - 14*s(y). Factor h(v).
4*(v - 1)*(v + 1)**2*(2*v + 1)
Let h(c) be the second derivative of 0*c**2 - 1/66*c**4 + 1/231*c**7 - 1/110*c**5 + 0 + 0*c**3 + 1/165*c**6 + 3*c. Determine l so that h(l) = 0.
-1, 0, 1
Let x(g) be the first derivative of -2*g**5/5 + 3*g**4/2 - 4*g**2 + 12. Factor x(o).
-2*o*(o - 2)**2*(o + 1)
Let h(n) be the third derivative of -n**6/24 + 5*n**4/8 - 5*n**3/3 + 9*n**2. Factor h(c).
-5*(c - 1)**2*(c + 2)
Factor 16*l**2 - 5 + 24*l**2 - 35*l**2.
5*(l - 1)*(l + 1)
Let d(y) = y**3 + 2*y**2 - 1. Let l be d(-1). Let b(a) be the third derivative of 0*a + 1/240*a**5 + 1/24*a**3 - 2*a**2 + l - 1/48*a**4. Factor b(c).
(c - 1)**2/4
Let f be 263*19*(-4 + 5). Factor -799*x**4 - 48 + 1469*x**2 + 8232*x**3 - f*x**2 - 419*x + 1091*x - 6404*x**4.
-3*(7*x - 2)**4
Let g(a) be the first derivative of -a**4/10 - 4*a**3/15 - a**2/5 - 3. What is m in g(m) = 0?
-1, 0
Let h = 791 - 2333/3. Let l = h - 13. Factor 0*d + l*d**2 - 1/3.
(d - 1)*(d + 1)/3
Let h(a) = a**3 - a**2 - a + 2. Let k be h(0). Suppose 0 = -5*d + 4*r + 31, 0 = k*r - 3*r - 4. Solve -m**5 - m + 6*m**d - 5*m**3 + m**3 = 0 for m.
-1, 0, 1
Suppose 2*t = t + 1. Factor 2*i - 3*i - i**2 - i - t.
-(i + 1)**2
Let o = -3/16 + 47/80. Factor 0*a + 2/5*a**2 - o.
2*(a - 1)*(a + 1)/5
Let m(a) = -2*a**2 - 3*a + 2. Let b be m(2). Let k be b/(-16) - (-3)/(-12). Suppose 7/4*x - k + 5/4*x**4 - 7/4*x**3 - 3/4*x**2 = 0. Calculate x.
-1, 2/5, 1
Let d be -2 + -5*(-2)/(-2). Let m = d - -9. Factor -2/5*i**3 + 0 - 2/5*i**4 + 0*i + 0*i**m.
-2*i**3*(i + 1)/5
Let n(y) be the first derivative of -14*y**3/3 - 2*y**2 - 4. Let n(i) = 0. What is i?
-2/7, 0
Let c be (-26*1/(-2))/(-1). Let y(s) = s**2 + 13*s + 3. Let a be y(c). Let -2/3*i + 2/3*i**a + 0*i**2 + 0 = 0. What is i?
-1, 0, 1
Let d(i) be the third derivative of i**4/24 + 7*i**3/6 + 4*i**2. Let n be d(-7). Factor 0 + 1/4*b**5 + n*b**4 - 1/2*b**3 + 0*b**2 + 1/4*b.
b*(b - 1)**2*(b + 1)**2/4
Let m(r) = -1. Let v = -15 + 16. Let w(q) = -q**2 + 2*q - 6. Let i(f) = v*w(f) - 5*m(f). Suppose i(k) = 0. Calculate k.
1
Let m = -59 - -237/4. Determine d, given that -1/4*d**2 + m + 1/4*d - 1/4*d**3 = 0.
-1, 1
Let w(f) = -16*f + 102. Let g be w(6). Let j(b) be the first derivative of 0*b**3 + 1/21*b**g - 1/7*b**4 + 1/7*b**2 + 0*b + 0*b**5 - 4. Factor j(k).
2*k*(k - 1)**2*(k + 1)**2/7
Let p = -50 - -52. Factor -2/3*y + 2/3*y**p - 4/3.
2*(y - 2)*(y + 1)/3
Let s(m) be the first derivative of 4*m**3/3 - 4*m**2 + 4*m - 14. Factor s(n).
4*(n - 1)**2
Let q(a) be the second derivative of -3*a - 5/9*a**3 - 7/18*a**4 - 1/3*a**2 - 1/10*a**5 + 0. Let q(f) = 0. What is f?
-1, -1/3
Let k(y) = y**2 + 17*y - 134. Let j be k(-23). Determine l so that 0 + l**3 + 0*l + 1/3*l**j + 2/3*l**2 = 0.
-2, -1, 0
Let -r**3 + 2 - 17/3*r + 14/3*r**2 = 0. Calculate r.
2/3, 1, 3
Solve -1/10*g - 1/5 + 2/5*g**2 - 1/5*g**4 - 1/10*g**5 + 1/5*g**3 = 0.
-2, -1, 1
Let q(s) = -3*s**2 + 4*s + 8. Let v(i) = 24*i**2 - 33*i - 66. Let k(c) = 33*q(c) + 4*v(c). Find r, given that k(r) = 0.
0
Let t(y) be the third derivative of y**6/480 - y**4/96 + 3*y**2. Determine p, given that t(p) = 0.
-1, 0, 1
Let v(j) be the second derivative of -j**9/3780 + j**7/315 - j**5/30 + j**4/12 + 2*j. Let o(f) be the third derivative of v(f). Factor o(r).
-4*(r - 1)**2*(r + 1)**2
Let h = 2 + -8. Let i = h + 8. Factor 1/3 - 1/3*f + 1/3*f**3 - 1/3*f**i.
(f - 1)**2*(f + 1)/3
Let v(k) be the first derivative of k**7/350 + k**6/200 - k**5/100 - k**4/40 - k**2 - 5. Let z(t) be the second derivative of v(t). Find g such that z(g) = 0.
-1, 0, 1
Factor 2*n**3 - 6*n**2 + 10*n**3 + 7*n**2 - 4*n**2.
3*n**2*(4*n - 1)
Let z(b) be the second derivative of -1/20*b**5 + 1/6*b**3 + 3*b - 1/12*b**4 + 0*b**2 + 0 + 1/30*b**6. Factor z(o).
o*(o - 1)**2*(o + 1)
Let x(s) = 8*s - 4. Let p be x(4). Let z = -19 + p. Factor 7*r**4 - 3*r**3 - 2*r - z*r**3 + 4*r + 3*r**2.
r*(r - 1)**2*(7*r + 2)
Let r(f) be the second derivative of f**7/840 + f**6/360 - f**5/120 - f**4/24 + f**3/3 - 3*f. Let l(c) be the second derivative of r(c). Factor l(k).
(k - 1)*(k + 1)**2
Find r such that 6/5*r**5 - 2/5*r**3 + 2*r**2 + 0 - 2*r**4 - 4/5*r = 0.
-1, 0, 2/3, 1
Determine t so that 6/7*t**3 - 2/7*t**4 - 6/7*t + 4/7 - 2/7*t**2 = 0.
-1, 1, 2
Suppose p + p = 6. Let 4*h - h**2 + 6*h**2 + h**2 + 2*h**p = 0. Calculate h.
-2, -1, 0
Suppose 0 = 3*h + 10*h. Factor 2/9*d**4 + 4/9*d**2 + h*d + 0 + 2/3*d**3.
2*d**2*(d + 1)*(d + 2)/9
What is v in 2*v**3 - 10*v**5 - 8 - 3*v + 2*v + v - 26*v**4 + 8*v + 34*v**2 = 0?
-2, -1, 2/5, 1
Let o = -37029/7 - -5299. Let n(m) be the first derivative of 2 - o*m - 160/21*m**3 + 9/7*m**6 + 108/35*m**5 - 36/7*m**4 + 16*m**2. Factor n(l).
2*(l + 2)**2*(3*l - 2)**3/7
Let r(c) = 6*c - 10. Let a be r(-7). Let v be (-6)/(-39) - 96/a. Fa