he third derivative of -k**7/42 + 5*k**6/12 - 2*k**5 - 20*k**4/3 + 320*k**3/3 + 66*k**2. Determine n so that d(n) = 0.
-2, 4
Suppose -4*q + 2*q = -12. Suppose 2*s + s = -q. Let m(p) = -p**3. Let o(a) = 4*a**4 - 14*a**3 + 9*a**2 - 2*a. Let r(y) = s*m(y) + o(y). Solve r(j) = 0.
0, 1/2, 2
Let s(h) be the first derivative of -2/3*h**2 + 2/9*h**3 + 3 + 2/3*h. Find m, given that s(m) = 0.
1
Let q = 5483/142 + -8/71. Let l = q + -38. Factor 1/2*f**2 - f**3 + 0*f + 0 + l*f**4.
f**2*(f - 1)**2/2
Find q, given that q**2 + 4*q + 0*q**2 - 2*q - 3 = 0.
-3, 1
Let z(i) be the second derivative of i**4/30 + 4*i**3/5 + 11*i**2/5 - 2*i + 43. Find k such that z(k) = 0.
-11, -1
Let q(s) be the first derivative of s**8/2240 - s**3/3 - 2. Let o(x) be the third derivative of q(x). Find y, given that o(y) = 0.
0
Let r(b) be the third derivative of b**9/13608 - b**7/3780 + 3*b**3/2 - 8*b**2. Let n(o) be the first derivative of r(o). Determine i so that n(i) = 0.
-1, 0, 1
Factor -10/3*t**2 + 1/3*t**5 - 1/3 + 10/3*t**3 + 5/3*t - 5/3*t**4.
(t - 1)**5/3
Let j be 4/(-10) + (-85)/(-25). Suppose -5*k + j = -7. Determine g so that 0*g + 0 + 2/3*g**k - 8/3*g**3 + 10/3*g**4 - 4/3*g**5 = 0.
0, 1/2, 1
Suppose -5*k + 71 = 3*p + 28, 34 = 4*p + 2*k. Suppose -p*i**2 + 20*i**5 + 9*i**3 + i**5 - 10*i**4 + 46*i**4 = 0. What is i?
-1, 0, 2/7
Solve 266 - 7*j**2 - 268 + 2*j**3 + 2*j**3 - 2*j**3 + 7*j = 0.
1/2, 1, 2
Determine a so that 0*a**2 - 1/7*a**5 - 3/7*a**3 + 4/7*a**4 + 0*a + 0 = 0.
0, 1, 3
Factor -8/3*b - 4/9*b**2 - 20/9.
-4*(b + 1)*(b + 5)/9
Factor 0 - 1/4*x**4 + 0*x - 1/2*x**3 + 0*x**2.
-x**3*(x + 2)/4
Let j(o) be the first derivative of 3/10*o**4 + 0*o**3 - 1/10*o**6 + 0*o + 0*o**5 - 3/10*o**2 + 6. Factor j(f).
-3*f*(f - 1)**2*(f + 1)**2/5
Let q be 36/21*5/15. Let -2/7 - 2/7*t**5 - 4/7*t**2 - q*t**3 + 6/7*t + 6/7*t**4 = 0. What is t?
-1, 1
Factor 2 + 5/2*a + 1/2*a**2.
(a + 1)*(a + 4)/2
Let v be (-75)/(-7)*(-28)/(-16). Suppose -27 = -4*u + 5. Factor 0 - p - v*p**4 - 85/4*p**3 - u*p**2.
-p*(3*p + 1)*(5*p + 2)**2/4
Let z(r) be the second derivative of 3*r**5/100 - r**4/20 - 3*r**3/5 - 27*r. Factor z(x).
3*x*(x - 3)*(x + 2)/5
Let t be 3 - (1 + 2528/(-20)). Let j = t - 128. Suppose j*a**4 - 2/5*a**2 + 0 + 0*a - 2/5*a**5 + 2/5*a**3 = 0. Calculate a.
-1, 0, 1
Suppose -5*z - 12 = -4*l + 6, 0 = -5*z - 10. Suppose -4*i + 2 = 2*w, 0*i + 10 = 2*i - l*w. Factor 1/2*n**i - n + 1/2.
(n - 1)**2/2
Factor 0 + 20/9*s**4 + 16/9*s**5 + 4/9*s**3 + 0*s**2 + 0*s.
4*s**3*(s + 1)*(4*s + 1)/9
Let w(u) be the first derivative of u**3/3 + 9*u**2/8 + 5*u/4 - 3. Factor w(t).
(t + 1)*(4*t + 5)/4
Factor 3*f**3 + 14*f**2 + 81*f + 13*f**2 + 85 - 4.
3*(f + 3)**3
Let q(f) be the third derivative of f**7/70 + f**6/10 - f**5/20 - f**4/2 - 20*f**2. Factor q(b).
3*b*(b - 1)*(b + 1)*(b + 4)
Let p(b) be the third derivative of b**6/960 + b**5/480 - b**4/192 - b**3/48 - 25*b**2. Factor p(w).
(w - 1)*(w + 1)**2/8
Let z(k) be the first derivative of 3 + 3/2*k**2 - 2/3*k - 7/9*k**3. Factor z(a).
-(a - 1)*(7*a - 2)/3
Let n(f) be the first derivative of -f**4/6 + 2*f**3/9 + f**2/3 - 2*f/3 - 5. Suppose n(x) = 0. What is x?
-1, 1
Let m = -1 - -4. Find v such that -2 + 3 - 2 - v**2 + m*v - v = 0.
1
Let q(k) be the third derivative of 0*k**3 + 1/160*k**6 + 0 + 2*k**2 + 0*k + 1/840*k**7 + 1/96*k**4 + 1/80*k**5. Find t, given that q(t) = 0.
-1, 0
Let v(h) = -h**2 + 4*h. Let p be v(5). Let f = 5 + p. Factor 2/3*r**3 + 0*r**2 + f + 0*r.
2*r**3/3
Let j = 19 - 11. Let x = -4 + j. Solve 23*z**2 - 10*z - 2*z**2 - 2*z**3 - x + 2*z - 7*z**4 = 0.
-2, -2/7, 1
Let p(s) be the second derivative of s**6/195 + 3*s**5/130 + s**4/26 + s**3/39 - 4*s. Factor p(w).
2*w*(w + 1)**3/13
Let y(i) be the third derivative of 0 + 1/8*i**5 - 1/24*i**4 + 0*i**3 + 3*i**2 + 0*i - 1/10*i**6 - 4/105*i**7. What is q in y(q) = 0?
-2, 0, 1/4
Let o(w) be the first derivative of -3*w**2/2 - w - 2. Let x be o(-1). Factor -4*u**5 + 2*u**x + 18*u**3 - 26*u**4 + 8*u**5 + 6*u**5 - 4*u.
2*u*(u - 1)**3*(5*u + 2)
Let p(h) = h**2 - 7*h + 9. Let t be p(6). Factor 10*k**t + 8*k**4 + k + 2*k**2 - 3*k + 2*k.
2*k**2*(k + 1)*(4*k + 1)
Let h(l) be the third derivative of -l**7/315 + 13*l**6/720 - l**5/24 + 7*l**4/144 - l**3/36 + 5*l**2. Factor h(w).
-(w - 1)**3*(4*w - 1)/6
Let n(r) be the third derivative of r**7/70 - 3*r**6/20 + 11*r**5/20 - 3*r**4/4 + 32*r**2. Factor n(d).
3*d*(d - 3)*(d - 2)*(d - 1)
Let b(z) be the first derivative of z**6/18 - z**5/30 - z**4/8 + z**3/18 + z**2/12 + 8. Determine i, given that b(i) = 0.
-1, -1/2, 0, 1
Let z(f) be the third derivative of -f**6/1260 - f**3/2 - f**2. Let g(x) be the first derivative of z(x). Factor g(b).
-2*b**2/7
Factor 2*z - 5*z + 7*z**3 + 2 - 6*z**3.
(z - 1)**2*(z + 2)
Let x(l) be the third derivative of l**6/280 - l**5/140 - l**4/14 + 2*l**3/7 - 7*l**2. Suppose x(c) = 0. What is c?
-2, 1, 2
Let w(x) be the second derivative of x**4/36 - x**3/18 + x. Let w(l) = 0. What is l?
0, 1
Factor 8*i - 15*i**3 + 12*i**2 + 4*i**3 + 15*i**3.
4*i*(i + 1)*(i + 2)
Let x(d) = -10*d - 1. Let k be x(-1). Suppose -2*j + j = 4*r - k, 0 = 3*r + 3*j. Factor 0*m**r - 1/3 - 1/3*m**4 + 2/3*m**2 + 0*m.
-(m - 1)**2*(m + 1)**2/3
Let u be 2 + -2 + 4/1344. Let p(n) be the third derivative of u*n**8 + 0 + 0*n**3 + 2*n**2 + 1/20*n**6 + 1/15*n**5 + 0*n + 1/24*n**4 + 2/105*n**7. Factor p(x).
x*(x + 1)**4
Find b such that 6 + 3*b - 3*b - b**2 - 5 = 0.
-1, 1
Let o(y) be the second derivative of y**7/1260 + y**6/540 - y**3/3 + y. Let u(c) be the second derivative of o(c). What is i in u(i) = 0?
-1, 0
Let h = 87/35 + -11/5. Factor 0 + 0*p + 4/7*p**3 - h*p**4 + 0*p**2.
-2*p**3*(p - 2)/7
Suppose 4*h - 4 = 0, 2*h - 16 = -3*c + h. Suppose -4*t = -t + 4*d - 24, 15 = c*d. Suppose 1 - l**2 - t*l - 5 + 0 = 0. What is l?
-2
Factor 2/5*x + 0 - 2/5*x**2.
-2*x*(x - 1)/5
Let h(f) = f**2 + 11*f + 3. Let o = -5 + -6. Let m be h(o). Solve 0 - u**2 - 3/2*u**m - 1/4*u**5 - u**4 - 1/4*u = 0 for u.
-1, 0
Let a(d) = -d + 7. Let g be a(6). Let b(o) be the first derivative of -7/4*o**4 + o**2 + 5/3*o**3 + g + 0*o. Factor b(y).
-y*(y - 1)*(7*y + 2)
Let g(j) = -j**3 + 12*j**2 + j - 9. Let t be g(12). Let u(r) be the first derivative of 2/3*r**t - r**2 - 1 + 0*r. Factor u(h).
2*h*(h - 1)
Suppose 7*m = 4*m. Find t, given that m*t**3 + t**2 + 0*t - 1/2 - 1/2*t**4 = 0.
-1, 1
Let y = -8 + 8. Let t = -18/13 + 116/65. Suppose 0*w**2 + y + 2/5*w - t*w**3 = 0. What is w?
-1, 0, 1
Let j(q) = 22*q**3 + 2*q. Suppose 0 = -2*y - 4*o + 20, 12 - 34 = -2*y - 2*o. Let z(b) = 9*b**3 + b. Let k(s) = y*z(s) - 5*j(s). Suppose k(g) = 0. Calculate g.
-1, 0, 1
Let g(y) = 3*y**2 - y - 2. Let q(c) = -c**2 + c + 1. Let f(w) = -g(w) - 2*q(w). What is k in f(k) = 0?
-1, 0
Suppose -g = 4*p - 25, -5*g + 50 = 6*p - p. Let b(l) be the second derivative of 0 + 1/18*l**4 + 1/90*l**p + l + 1/9*l**2 + 1/9*l**3. Let b(o) = 0. What is o?
-1
Let f = 231 - 459/2. Suppose -2*z - 2 + f*z**2 = 0. What is z?
-2/3, 2
Let y(i) = i**3 + 7*i**2 - i - 2. Let u be y(-7). Let b be (-21)/(-6) - 1/2. Find t such that 3/2*t**2 + 3/4*t**u - 3/4*t**b + 0*t - 3/2*t**4 + 0 = 0.
-1, 0, 1, 2
Let x be (5/(-10)*-20)/2. Suppose 6*j = x*j. Factor 8/7*c**3 + 2/7*c**2 + j + 0*c.
2*c**2*(4*c + 1)/7
Find q such that 0*q + 0 - 3/2*q**3 - 3*q**2 = 0.
-2, 0
Let d = 273 + -273. Suppose -2/3*f**2 + 2/3*f**3 + 0*f + d = 0. Calculate f.
0, 1
Let y(u) be the second derivative of -u**7/1260 - u**4/12 - 3*u. Let a(k) be the third derivative of y(k). Factor a(q).
-2*q**2
Determine t, given that 0 + 4/5*t**4 + 0*t + 2/5*t**5 + 0*t**2 + 2/5*t**3 = 0.
-1, 0
Let j(g) be the second derivative of g**6/75 - 7*g**5/100 + g**4/10 + g**3/30 - g**2/5 - 26*g. Factor j(c).
(c - 2)*(c - 1)**2*(2*c + 1)/5
Let j(f) be the first derivative of 4 + 0*f**2 - 1/4*f**4 + 2*f + f**3. Let c(s) be the first derivative of j(s). Factor c(n).
-3*n*(n - 2)
Let a be -1*-4*1/3. Let h(v) = v**2 - 7*v + 6. Let m be h(6). Factor m - 2/3*k - a*k**2 - 2/3*k**3.
-2*k*(k + 1)**2/3
Let f(w) be the third derivative of 3*w**5/10 + 19*w**4/24 + 2*w**3/3 - 3*w**2. Let o(v) = 18*v**2 + 18*v + 4. Let t(a) = -4*f(a) + 3*o(a). Factor t(d).
-2*(d + 1)*(9*d + 2)
Determine w, given that 4/7*w + 4/7 + 1/7*w**2 = 0.
-2
Suppose -4*w - 3 = -19. Determine z, given that -21*z**4 - 2*z**2 - w*z**2 + 3*z**2 + 8*z**5 - 17*z**5 -