 -68. Factor 1 + 2*q**2 + q**4 - 91*q**3 + g*q**3 - 1.
q**2*(q - 2)*(q - 1)
Let x(r) be the first derivative of 2*r**3/27 - 2*r**2/3 + 2*r + 50. Factor x(u).
2*(u - 3)**2/9
Let n(z) = -27*z - 318. Let p be n(-12). Let v(s) be the first derivative of 0*s - 1/6*s**4 + 2/9*s**p - 2/15*s**5 + 0*s**3 - 7 + 0*s**2. Factor v(o).
2*o**3*(o - 1)*(2*o + 1)/3
Let s(j) be the second derivative of j**4/42 + 30*j**3/7 + 2025*j**2/7 - 83*j. Factor s(m).
2*(m + 45)**2/7
Let a(f) = -45*f**3 + 1185*f**2 - 1536*f + 375. Let q(s) = 30*s**3 - 790*s**2 + 1025*s - 250. Let c(g) = -5*a(g) - 7*q(g). Determine x, given that c(x) = 0.
1/3, 1, 25
Let g(p) = 9*p**2 - 45*p + 21. Let l(t) = 2*t**2 - 11*t + 5. Let c(x) = -5*g(x) + 21*l(x). Determine q, given that c(q) = 0.
-2, 0
Let -6*q**3 + 2*q**3 + 5*q + 6*q + 2*q + 300 + 7*q - 28*q**2 = 0. What is q?
-5, 3
Let c(b) be the third derivative of 0*b**3 + 1/6*b**4 + 0 + 1/84*b**8 + 1/5*b**6 + 41*b**2 + 4/15*b**5 + 8/105*b**7 + 0*b. Factor c(j).
4*j*(j + 1)**4
Let m be 2*(-1)/(2/(-3)). Suppose -m*y + x - 2 = 1, 0 = x - 3. Factor y*h - 6/7*h**3 - 2/7*h**5 + 0 - 2/7*h**2 - 6/7*h**4.
-2*h**2*(h + 1)**3/7
Let z = -9 + 14. Let a be (-1)/(-3) - 35/(-3). Factor -3*l**z + 24*l**4 + 3*l - a*l**2 - 6*l - 18*l**3 - 36*l**4.
-3*l*(l + 1)**4
Suppose -9 + 27 + 6 = 8*m. Factor 1/4 - 1/4*k**2 + 1/8*k - 1/8*k**m.
-(k - 1)*(k + 1)*(k + 2)/8
Let h(k) be the second derivative of 0 + 1/160*k**6 - 7/2*k**2 - 1/16*k**4 + 0*k**3 - 1/80*k**5 + 6*k. Let p(l) be the first derivative of h(l). Factor p(f).
3*f*(f - 2)*(f + 1)/4
Let i(l) be the second derivative of 29/60*l**4 - 9/100*l**5 + 0 - 1/5*l**3 + 0*l**2 + 9*l. Suppose i(r) = 0. Calculate r.
0, 2/9, 3
Let x(u) be the first derivative of u**6/2 - 12*u**5/5 - 39*u**4/2 - 44*u**3 - 93*u**2/2 - 24*u - 80. Factor x(t).
3*(t - 8)*(t + 1)**4
Let w(k) be the first derivative of -k**6/12 + 4*k**5/5 - 3*k**4/2 - k**3/3 + 13*k**2/4 - 3*k - 17. Factor w(s).
-(s - 6)*(s - 1)**3*(s + 1)/2
Let h(b) = b**2 - 1. Let u(o) = -o**3 - 4*o**2 - 24*o - 21. Let x = 3 - 1. Let f(r) = x*u(r) - 10*h(r). Suppose f(i) = 0. Calculate i.
-4, -1
Let v(x) be the second derivative of x**6/40 + 3*x**5/16 - 9*x**4/16 - 81*x**3/8 - 81*x**2/2 - 106*x. Solve v(a) = 0.
-3, 4
Let a(o) = o**3 + 32*o**2 - 77*o - 303. Let u be a(-34). Factor 0*f + 0*f**2 + 3/5*f**u + 0 + 0*f**4 - 3/5*f**5.
-3*f**3*(f - 1)*(f + 1)/5
What is q in 220*q**3 + 0*q - 8*q + 37*q**2 + 63*q**2 + 3*q = 0?
-1/2, 0, 1/22
Let z(x) be the first derivative of x**5/5 - 5*x**4/4 - 7*x**3 - 23*x**2/2 - 8*x + 111. Factor z(d).
(d - 8)*(d + 1)**3
Let f(n) be the first derivative of n**6/12 - 13*n**5/10 + 29*n**4/4 - 53*n**3/3 + 85*n**2/4 - 25*n/2 - 263. Suppose f(s) = 0. What is s?
1, 5
Factor -1064 - 170*x - 696 + 3*x**2 - 3*x**2 - 5*x**2 + 315.
-5*(x + 17)**2
Let 3*r**3 - 26 - 152*r + 107*r + 6*r**2 + 26 = 0. What is r?
-5, 0, 3
Let q = -349 - -351. Let d(x) be the second derivative of 0*x**q - 2*x - 1/210*x**7 - 1/30*x**4 + 1/75*x**6 + 0 + 0*x**5 + 1/30*x**3. Factor d(j).
-j*(j - 1)**3*(j + 1)/5
Let a(k) = k**4 + 3*k**3 + 10*k**2 + 2*k - 1. Let v(p) = -p**4 - 2*p**3 - 8*p**2 - 2*p + 1. Let m(u) = 4*a(u) + 5*v(u). Factor m(n).
-(n - 1)**3*(n + 1)
Let x(h) = -2*h**3 + 30*h**2 - 124*h - 147. Let l(z) = 4*z**3 - 32*z**2 + 124*z + 148. Let q(g) = 3*l(g) + 4*x(g). Factor q(j).
4*(j - 4)*(j + 1)*(j + 9)
Suppose 20 = -4*i, 0*h - 17 = -3*h + i. Let n be (h/6)/((-10)/(-6)). Determine x, given that 0 - 1/5*x + 1/5*x**5 + 0*x**3 - n*x**4 + 2/5*x**2 = 0.
-1, 0, 1
Let s = 686 + -681. Let t(b) be the second derivative of 0 + 2/21*b**7 - 2/5*b**6 + 0*b**2 - 2*b + 0*b**3 + 3/5*b**s - 1/3*b**4. Suppose t(l) = 0. Calculate l.
0, 1
Let x(g) be the first derivative of 6*g**3/5 + 7*g**2/5 - 4*g/5 - 34. Let x(v) = 0. What is v?
-1, 2/9
Solve -8092*d**2 + 22*d + 8087*d**2 + 163*d - 180 = 0.
1, 36
Let t(g) be the second derivative of -4*g**4/21 + 62*g**3/7 + 144*g**2/7 - 265*g. Factor t(q).
-4*(q - 24)*(4*q + 3)/7
Let 258/5*g**3 + 18/5*g**4 + 768/5 + 684/5*g**2 - 1728/5*g = 0. What is g?
-8, 2/3, 1
Suppose 1803*m - 1842*m + 78 = 0. Factor 0*k + 2/3*k**5 + 8/3*k**4 + 0 + m*k**3 + 0*k**2.
2*k**3*(k + 1)*(k + 3)/3
Let c(u) be the third derivative of u**8/40320 + u**7/1260 + u**6/90 - 7*u**5/60 + u**2. Let g(m) be the third derivative of c(m). Find v such that g(v) = 0.
-4
Suppose -9*g = -5*g - 16. Let m(h) be the third derivative of 1/120*h**5 + 0 + 1/24*h**g - h**2 + 1/12*h**3 + 0*h. Factor m(r).
(r + 1)**2/2
Suppose 1417*s = 1427*s. Let f(o) be the second derivative of -8*o + 0*o**2 - 7/54*o**4 + 2/27*o**3 + s. Solve f(d) = 0 for d.
0, 2/7
Let -2243/2*p**2 + 2145*p + 33*p**3 - 1/4*p**4 - 4225/4 = 0. What is p?
1, 65
Let v(l) = -l**4 + 3*l**3 - 21*l + 18. Let u(q) = -2*q**3 + q**2. Let i(x) = u(x) - v(x). Factor i(y).
(y - 3)**2*(y - 1)*(y + 2)
Let d = -206 + 214. Let s be (-2)/5 + (d - 588/80). Solve -s*b**2 + 0 - b = 0.
-4, 0
Let t(f) be the first derivative of -11*f + 5/3*f**3 - 4*f**2 - 1/6*f**4 + 12. Let a(d) be the first derivative of t(d). What is l in a(l) = 0?
1, 4
Let z(c) = -17*c**2 + 32*c + 4. Let d(b) = -16*b**2 + 30*b + 4. Let t(f) = -5*d(f) + 4*z(f). Let t(i) = 0. What is i?
-1/6, 2
Factor 4/7*p**4 - 4/7*p**5 + 0 + 0*p**2 + 0*p + 80/7*p**3.
-4*p**3*(p - 5)*(p + 4)/7
Let k be -9 - 1/(-2)*3818/207. What is a in -2/9*a**2 - k + 4/9*a = 0?
1
Let w = 19886 - 19882. Solve -2/3*a**2 - w - 58/9*a = 0.
-9, -2/3
Suppose 0 = -h + 4 - 1. Suppose -14 = -h*t + 13. Factor t*z**4 + 6*z**2 - 3*z**3 + 1 + 5*z - 2*z**3 + 3*z**3 - 3*z**5 - 16*z**4.
-(z - 1)*(z + 1)**3*(3*z + 1)
Suppose 2*i - 3*a - 159 = -i, 0 = 2*i - a - 104. Suppose -6*z - 51 = -i. Factor -1/3*k + z - 1/3*k**2.
-k*(k + 1)/3
Factor -544/11*v + 578/11*v**2 + 128/11.
2*(17*v - 8)**2/11
Let v be -10*(-18)/28 - 6. Let l(k) be the second derivative of -k**2 + 0 + 1/3*k**3 + v*k**7 + 3*k - k**5 + 5/3*k**4 - 3/5*k**6. Find b such that l(b) = 0.
-1, -1/3, 1/3, 1
Let i be (-96)/(-44) + 20/(-110). Let d(m) be the first derivative of -8 - 1/7*m**i + 4/7*m - 2/21*m**3. Determine t, given that d(t) = 0.
-2, 1
Let n = -12830 - -38491/3. Factor 1/2*o - 1/6*o**2 - n.
-(o - 2)*(o - 1)/6
Suppose t - 16 = 4*s, -4*s + 32 = 5*t - 0*s. Let g(x) = -2*x + 19. Let b be g(t). Factor 3*h**2 + 3*h**b - 3*h**3 + 3*h**2 - 9*h - h**3.
-h*(h - 3)**2
Let i(f) be the first derivative of 1/18*f**4 - 20 - 20/27*f**3 - 16/9*f + 17/9*f**2. Factor i(x).
2*(x - 8)*(x - 1)**2/9
Solve -7 + 10*i**2 - 13*i + 14 - 10 = 0 for i.
-1/5, 3/2
Let v(n) be the second derivative of 1/120*n**5 - 1/360*n**6 + 0*n**4 - 2*n + 0 + 2/3*n**3 + 0*n**2. Let k(s) be the second derivative of v(s). Factor k(r).
-r*(r - 1)
Let v(m) be the first derivative of -1/5*m**4 - 4 + 3/5*m - 2/15*m**3 - 1/25*m**5 + 2/5*m**2. Factor v(t).
-(t - 1)*(t + 1)**2*(t + 3)/5
Let n = -15 + 26. Suppose 2*t + 3 = n. Determine z so that -326/15*z**3 + 76/15*z**2 + 14*z**t + 56/15*z - 16/15 = 0.
-2/5, 2/7, 2/3, 1
Let q(y) = -4*y - 31. Let t = -5 + -4. Let r be q(t). Find x such that -8*x**2 + 3*x**4 + 5*x**r - 2*x**5 + 8*x**2 - 6*x**3 = 0.
-2, 0, 1
Determine a, given that -3*a**5 + 18*a**3 - 10*a**2 + 0*a**5 - 21*a**3 - 9*a**4 + 19*a**2 + 6*a = 0.
-2, -1, 0, 1
Let d(s) = s**2 + s. Let t(n) = -3*n**2 - 24*n - 44. Let g(c) = -4*d(c) - t(c). Let h be g(22). Factor -2/11*j + h - 2/11*j**2.
-2*j*(j + 1)/11
Let n = -16 - -131. Factor n*i**2 + 81*i + 24*i**3 - 34*i**2 + 3*i**3 + 3*i**4.
3*i*(i + 3)**3
Let z(v) be the third derivative of 0 - 51*v**2 + 0*v - 11/240*v**5 + 0*v**3 - 1/96*v**6 - 1/48*v**4. Let z(t) = 0. Calculate t.
-2, -1/5, 0
Let s = 1590 + -4634/3. Factor s*h + 40/3 - 14/3*h**2.
-2*(h - 10)*(7*h + 2)/3
Let y be (-3 - 6/(-4))*12/(-9). Determine f so that 48*f**2 + 8*f - 26*f**y - 18*f**2 - 4*f**3 = 0.
-1, 0, 2
Let j be 162/(-80) + 55/825 + 2. Let a(s) be the third derivative of 0*s - 5/12*s**5 + j*s**6 + 2*s**2 - 5/2*s**3 + 0 + 35/24*s**4. Factor a(f).
5*(f - 3)*(f - 1)**2
Let z(y) be the second derivative of -y**6/2340 + y**5/260 - y**4/78 + 10*y**3/3 + 4*y. Let x(a) be the second derivative of z(a). Factor x(k).
-2*(k - 2)*(k - 1)/13
Suppose 0 = -9*f - 1139 - 1480. Let j = f + 591/2. What is b in -3/2*b**5 - 12*b**2 + 0*b**4 + j*b + 9*b**3 + 0 = 0?
-3, 0, 1
Let d(q) be the second derivative of -2*q**5/5 + 11*q**4