29 - 25. Determine r, given that -19 + 5*r - 3*r**2 - c*r + 25 = 0.
-1, 2
Suppose -4*b + 3*b + 4 = 0. Let r be b/14 + 52/14. Let 12*a**5 + 9*a**4 + 9*a**5 - 57*a**r + 17*a**3 + 16*a**3 - 6*a**2 = 0. Calculate a.
0, 2/7, 1
Let g(j) be the first derivative of j**3/21 + 2*j**2/7 - 12*j/7 - 139. Factor g(b).
(b - 2)*(b + 6)/7
Factor 64/19*p**2 - 134/19*p + 2/19*p**3 + 68/19.
2*(p - 1)**2*(p + 34)/19
Solve -20 - 29/5*l**2 + 1/5*l**3 + 104/5*l = 0.
2, 25
Let d(z) be the first derivative of -4*z**3/3 - 2*z**2 - 2*z - 14. Let v(w) = 5*w**2 + 4*w + 3. Let u(r) = 3*d(r) + 2*v(r). Let u(q) = 0. What is q?
-2, 0
Factor -4/5*f - 4/5 - 1/5*f**2.
-(f + 2)**2/5
Let m be 1 + (1888/(-210) - -3) + 5. Let j(w) be the second derivative of 0*w**3 - 1/25*w**6 + 0*w**2 + 0*w**5 - 2*w + m*w**7 + 2/15*w**4 + 0. Factor j(a).
2*a**2*(a - 2)**2*(a + 1)/5
Suppose 0 = 7*i - 34*i + 108. Let u(b) be the second derivative of -1/2*b**3 - 1/20*b**6 + 0*b**5 + 3/8*b**i + 0 + 0*b**2 + b. Factor u(h).
-3*h*(h - 1)**2*(h + 2)/2
Let f = 1609/9726 - -2/1621. Suppose -f*j**2 + 0 + 1/6*j = 0. Calculate j.
0, 1
Suppose -3*r = -4*w - 0*r, -5*r = 5*w. Let z = -1294/5 + 1298/5. Find x, given that 2/5*x**5 + w + z*x**3 + 0*x + 0*x**2 + 6/5*x**4 = 0.
-2, -1, 0
Let t = 342/415 - 2/83. Let q = 1412 + -1407. Determine y, given that 2/5*y + t*y**2 - 4/5*y**4 + 0 + 0*y**3 - 2/5*y**q = 0.
-1, 0, 1
Find q, given that -6*q + 3887*q**3 + 4*q**4 - 4*q**2 + 3902*q**3 - 10*q**5 - 7773*q**3 = 0.
-1, -3/5, 0, 1
Factor 38/5*n - 12 + 2/5*n**3 + 4*n**2.
2*(n - 1)*(n + 5)*(n + 6)/5
Let y be -1 + -9 - 120/(-12). Determine i so that 1/2*i**2 - 1/4*i**3 + y - 1/4*i = 0.
0, 1
Let h(n) be the first derivative of -1/10*n**6 - 3/10*n**5 + 0*n**3 - 1/4*n**4 + 0*n**2 + 5*n - 4. Let s(j) be the first derivative of h(j). Factor s(f).
-3*f**2*(f + 1)**2
Find f such that -9/7*f + 15/7*f**2 - 27/7 - 3/7*f**3 = 0.
-1, 3
Determine f so that -47*f**2 + 49*f + 7*f**2 + 18*f**3 - 41*f = 0.
0, 2/9, 2
Let u = 4058 + -8109/2. Factor -z**2 + u*z**3 + 0 + 0*z.
z**2*(7*z - 2)/2
Let n(r) be the first derivative of -81*r**5/40 - 9*r**4/2 - 15*r**3/4 - 3*r**2/2 - 33*r - 1. Let m(t) be the first derivative of n(t). Factor m(c).
-3*(3*c + 1)**2*(3*c + 2)/2
Suppose -5*z = -3*z - 22. Suppose 4*f - 4*b - 17 = -b, -5*f + 23 = -2*b. Factor -z*h - 3*h + f*h**2 + 19*h.
5*h*(h + 1)
Let a(b) be the first derivative of b**6/720 - b**5/120 + b**4/48 - 6*b**3 + 21. Let k(l) be the third derivative of a(l). Factor k(c).
(c - 1)**2/2
Suppose -5*u = -4*x - 10, 27*x - 28*x = -2*u + 4. Let 6/7*y**3 + 9/7*y**4 + 0*y**2 + x + 0*y + 3/7*y**5 = 0. Calculate y.
-2, -1, 0
Let r be ((-45)/20 - -2)/(3 + -5). Let j(k) be the second derivative of -7*k - r*k**2 + 1/8*k**3 - 1/16*k**4 + 0 + 1/80*k**5. Let j(t) = 0. What is t?
1
Let n be (-3)/(-6) - (-3)/(-6). Suppose 4*b + n*b = 12. Suppose 8*w**3 + 9*w**2 + 2*w + 0*w**4 + 4*w**b + 5*w**4 + 0*w**4 = 0. What is w?
-1, -2/5, 0
Let y(r) be the first derivative of r**8/840 - r**6/90 + r**4/12 - 11*r**3/3 + 13. Let m(k) be the third derivative of y(k). Factor m(l).
2*(l - 1)**2*(l + 1)**2
Find l such that 0 - 40/11*l + 64/11*l**2 - 10/11*l**4 + 94/11*l**3 = 0.
-1, 0, 2/5, 10
Let b(h) be the second derivative of h**8/16800 - h**7/3150 - h**6/1800 + h**5/150 - h**4/2 - 9*h. Let o(k) be the third derivative of b(k). Factor o(i).
2*(i - 2)*(i - 1)*(i + 1)/5
Let g(i) = 35*i**4 + 25*i**3 + 4*i - 8. Let u(x) = -70*x**4 - 50*x**3 - 9*x + 18. Let f(z) = 9*g(z) + 4*u(z). Factor f(t).
5*t**3*(7*t + 5)
Factor -1/4*s**4 + 0 + 7*s + 1/4*s**2 - 7*s**3.
-s*(s - 1)*(s + 1)*(s + 28)/4
Let h = 3951 - 3951. Solve h - 1/7*t**2 - 3/7*t = 0 for t.
-3, 0
What is d in -3*d**2 - 19*d - 18*d - 83 - 8*d + 41 = 0?
-14, -1
Let z(t) be the first derivative of t**4/12 - t**3/3 - 2*t**2/3 + 4*t - 609. Factor z(s).
(s - 3)*(s - 2)*(s + 2)/3
Let c(l) be the third derivative of -l**6/90 - 4*l**5/45 + 11*l**4/18 - 4*l**3/3 + 9*l**2 + 1. Determine t so that c(t) = 0.
-6, 1
Factor -264*x**3 - 5*x**4 - 80*x + 20*x**2 + 522*x**3 - 238*x**3.
-5*x*(x - 4)*(x - 2)*(x + 2)
Suppose 23*s = 18*s + 15. Factor -s - b**2 + 2 + 4*b**2 - 2.
3*(b - 1)*(b + 1)
Suppose 0 = -34*y + 189 - 121. Solve -1/3*x + 0 + 1/6*x**y = 0 for x.
0, 2
Let s(v) be the second derivative of -v**7/14 - v**6/10 + 9*v**5/10 + 7*v**4/2 + 11*v**3/2 + 9*v**2/2 + 107*v. Factor s(o).
-3*(o - 3)*(o + 1)**4
Let c(m) = -m**2 + 13*m - 17. Let w(y) = y**2 - 7*y + 9. Let z(t) = -t**3 - 3*t**2 + 5*t + 1. Let a be z(-4). Let l(u) = a*c(u) - 5*w(u). Factor l(i).
-2*(i - 1)*(i + 3)
Let d(o) = -o**3 - o**2. Let b(v) = 2*v**3 + 7*v**2 + 7*v - 10. Let r(g) = -b(g) - 3*d(g). Factor r(j).
(j - 5)*(j - 1)*(j + 2)
Suppose -r + 2 = -4. Suppose -r = -4*a + a. Find u such that -6/13*u - 4/13 - 2/13*u**a = 0.
-2, -1
Suppose 5*x**2 + 0*x**3 - 4*x**4 + 9*x**4 + 10*x**3 = 0. Calculate x.
-1, 0
Let d = -6694/77 - -613/7. Find o, given that 1/11*o**3 + d*o + 0 + 8/11*o**2 = 0.
-7, -1, 0
Let k(j) be the second derivative of -j**9/5040 - j**8/1120 + j**7/840 + j**6/120 + 19*j**4/12 - 19*j. Let f(y) be the third derivative of k(y). Solve f(v) = 0.
-2, -1, 0, 1
Suppose -22 + 7 = -5*m. Factor -245*h - 5*h**3 - h**m + 3*h**3 - 70*h**2 - 2*h**3.
-5*h*(h + 7)**2
Let a(t) be the first derivative of t**6/720 + t**5/48 - 7*t**3/3 - 4. Let u(i) be the third derivative of a(i). What is y in u(y) = 0?
-5, 0
Let u(z) be the first derivative of z**4/20 - z**3/5 - 9*z**2/10 + 4*z + 33. Let i(b) be the first derivative of u(b). Factor i(o).
3*(o - 3)*(o + 1)/5
Suppose -3/2*p**3 + 57/2*p - 21 - 6*p**2 = 0. What is p?
-7, 1, 2
Let b be (231/(-49))/(-11) + (-22)/(-14). Let n be (-1 - (-32)/(-2))/(-2). Suppose -3 - n*s - 5/2*s**b = 0. What is s?
-3, -2/5
Let j(q) = q**3 + 15. Let y be j(0). Let a be 19/3 - 5/y. Solve 9*n**3 + a*n**3 + 2*n**2 + 6*n**3 + 4*n**2 = 0.
-2/7, 0
Suppose -213 = -3*b - 5*w + 12, 154 = 2*b + 2*w. Let j be (-8)/(-10)*b/48. Factor -j*s**2 - 20/3*s - 16/3.
-4*(s + 1)*(s + 4)/3
Let o be (((-24)/3)/32)/(-1)*8. Let i(c) be the first derivative of 4/3*c + 10 + 2/3*c**4 + 3*c**o + 8/3*c**3. Factor i(u).
2*(u + 2)*(2*u + 1)**2/3
Suppose -p = p - 6. Suppose 5*c = -p + 33. What is k in -2 + 2*k**2 + 3*k**5 + 1 + 4*k + 2*k - 3*k - c*k**3 - k**4 = 0?
-1, 1/3, 1
Let t(u) be the third derivative of 2*u**7/105 + 2*u**6/15 + u**5/3 + u**4/3 + 9*u**2 + 6*u. Factor t(v).
4*v*(v + 1)**2*(v + 2)
Let 167*i**2 + 3*i**3 + 3*i - 1 - 173*i**2 + 5 - 4 = 0. What is i?
0, 1
Let j(v) be the first derivative of v**4/2 - 34*v**3/3 + 10*v**2 + 192*v - 66. Factor j(q).
2*(q - 16)*(q - 3)*(q + 2)
Let c(k) = 36*k**2 + 42*k + 15. Let g(y) = 5*y**2 + 6*y + 2. Suppose 0 = 7*b + 102 + 3. Let f(x) = b*g(x) + 2*c(x). Factor f(i).
-3*i*(i + 2)
Let l be 39/21 - ((-22)/(-33))/((-14)/3). Factor 5/4*p**4 + 5/2*p + 0*p**3 + 0 - 15/4*p**l.
5*p*(p - 1)**2*(p + 2)/4
Let x(b) be the first derivative of b**6/6 - 3*b**5/5 - b**4/2 + 2*b**3 + b**2/2 - 3*b + 110. Factor x(q).
(q - 3)*(q - 1)**2*(q + 1)**2
Let d(x) be the first derivative of -12 - 324*x + 36*x**2 - 4/3*x**3. Suppose d(v) = 0. What is v?
9
Suppose -3*q + 15 = 0, -3*k + 12*q = 11*q - 4. Let p(t) be the third derivative of 0 + k*t**2 - 1/240*t**5 + 0*t**3 + 0*t**4 + 0*t + 1/480*t**6. Factor p(d).
d**2*(d - 1)/4
Let t(o) be the first derivative of 3/4*o**2 - 3/8*o**4 + 0*o + 0*o**3 - 13. Let t(k) = 0. Calculate k.
-1, 0, 1
Let r(m) be the second derivative of m**5/35 + 5*m**4/21 - 26*m**3/21 + 2*m**2 - 35*m. Factor r(j).
4*(j - 1)**2*(j + 7)/7
Let h be 42/((-56)/(-756) - (-141)/7938). Suppose -504*s**3 - 2548/3*s**4 + 0 - 32/3*s - 368/3*s**2 - h*s**5 = 0. Calculate s.
-1, -2/7, 0
Let n be ((-9)/6)/(6/(-8)). Suppose -l = 5*h - 18, -3*h = -n*l - h. Factor 3 + 3*i**2 - l + 0.
3*i**2
Let l(u) be the second derivative of -u**5/10 - 13*u**4/3 - 64*u**3 - 288*u**2 + 8*u - 3. Find t, given that l(t) = 0.
-12, -2
Let m(s) be the first derivative of 3*s**4/8 + 143*s**3/3 + 1680*s**2 - 2304*s - 267. Determine q, given that m(q) = 0.
-48, 2/3
Factor -21*q**2 - 10 - 27*q**2 + 0*q**3 - 95 - 9 + 3*q**3 - 165*q.
3*(q - 19)*(q + 1)*(q + 2)
Let t(o) be the first derivative of -5*o**6/6 + 5*o**5 - 5*o**4 - 80*o**3/3 + 80*o**2 - 80*o + 162. Factor t(i).
-5*(i - 2)**3*(i - 1)*(i + 2)
Suppose 30/7*d**3 - 6/7*d**4 + 18/7*d + 0 - 6*d**2 = 0