661. Factor -8/7 - 20/7*h - 4/7*h**u - 16/7*h**2.
-4*(h + 1)**2*(h + 2)/7
Solve 104/5*a - 6/5*a**4 + 102/5*a**2 + 24/5 + 16/5*a**3 = 0.
-2, -1, -1/3, 6
Let y = -74 - -86. Suppose y = 7*r - r. Let -4*g - 6 - 2/3*g**r = 0. Calculate g.
-3
Factor -29*j - 30 + 26 + 8*j**2 + 15*j.
2*(j - 2)*(4*j + 1)
Let c(z) be the second derivative of -1/6*z**6 - z - 1/3*z**4 - 13/30*z**5 + 0*z**2 + 1/2*z**3 + 0. Let p(y) be the second derivative of c(y). Factor p(n).
-4*(3*n + 2)*(5*n + 1)
Let c(s) be the first derivative of -s**5 - 25*s**4/2 - 60*s**3 - 140*s**2 - 160*s - 19. Factor c(a).
-5*(a + 2)**3*(a + 4)
Let y be ((-30)/(-63))/((-100)/(-280)). Let q(x) be the first derivative of 2/9*x**3 - 3 + x**2 + y*x. Solve q(b) = 0 for b.
-2, -1
Find v such that -7/2*v**2 + 0*v**3 + 0 + 1/2*v**4 + 3*v = 0.
-3, 0, 1, 2
Let f(g) be the third derivative of g**7/42 - g**6/8 + g**5/12 - 17*g**3/6 - 2*g**2. Let a(l) be the first derivative of f(l). Suppose a(v) = 0. Calculate v.
0, 1/4, 2
Let a(t) be the third derivative of -t**7/70 - 7*t**6/20 - 5*t**5/4 - 3*t**4/2 - 2*t**2 + 73. Factor a(y).
-3*y*(y + 1)**2*(y + 12)
Let u(q) = q**2 + 40*q - 125. Let d be u(-43). Let k(i) be the first derivative of 2/5*i - 1/5*i**2 + 11 - 2/3*i**3 - 3/10*i**d. Solve k(c) = 0 for c.
-1, 1/3
Let v = -85 - -94. Suppose 3*t = 3*s + v, 3*s + t - 2*t - 1 = 0. Suppose 2/3*d**3 + 0 + 8/3*d + 8/3*d**s = 0. Calculate d.
-2, 0
Suppose 101 = w + 37. Factor 3 + 64*k**2 - 3*k - 2 - w*k**2 + 4*k**3.
(k + 1)*(2*k - 1)**2
Let m(t) = -2*t - 10. Let j be m(-7). Factor 8*s**4 - s - 4*s**j + s**2 - 5*s**4 + s**3 + 0*s**4.
-s*(s - 1)**2*(s + 1)
Let w be (9/150)/(792/110). Let t(c) be the third derivative of 0 - 7*c**2 + 0*c**3 - 1/300*c**5 + 0*c + 1/1050*c**7 - 1/600*c**6 + w*c**4. Solve t(m) = 0.
-1, 0, 1
Factor 50 + 372*x**2 + 328*x**4 - 320*x - 42*x**3 - 318*x**4 - 70*x**3.
2*(x - 5)**2*(x - 1)*(5*x - 1)
Factor 51*t + 0 - 9/2*t**3 - 147/2*t**2.
-3*t*(t + 17)*(3*t - 2)/2
Suppose -7*g + 10*g - 9 = 0. Let u be 4 - -2*(-3)/g. Factor 3*k**2 - 4*k**2 - u*k + k.
-k*(k + 1)
Let m(f) be the second derivative of f**6/5 - 77*f**5/60 + f**4/2 + 4*f**3/9 - f + 6. Find g, given that m(g) = 0.
-2/9, 0, 1/2, 4
Let v = -707/69 - -297/23. Factor -5/6 + v*l + 4/3*l**3 - 1/6*l**4 - 3*l**2.
-(l - 5)*(l - 1)**3/6
Let q(g) be the first derivative of -5*g**6/6 + 145*g**5 - 9900*g**4 + 324000*g**3 - 4665600*g**2 + 8398080*g - 319. What is b in q(b) = 0?
1, 36
Let m(p) be the second derivative of 20*p - p**4 + 0*p**3 + 0 - 1/5*p**5 + 0*p**2. Let m(i) = 0. Calculate i.
-3, 0
Let m(i) = 5*i**3 - 17*i + 10. Let l(g) = g - 1. Let u be l(-1). Let r(n) = -10*n**3 + 35*n - 20. Let s(a) = u*r(a) - 5*m(a). Factor s(z).
-5*(z - 1)**2*(z + 2)
Let a = -943 + 947. Let l(s) be the third derivative of 0 + 1/105*s**6 - 2/735*s**7 + 0*s - 1/21*s**a + 1/105*s**5 + 0*s**3 + 7*s**2. Factor l(k).
-4*k*(k - 2)*(k - 1)*(k + 1)/7
Suppose 0 = -4*m + 5 + 7. Factor 17*t - 4 - t**m + 8*t**4 - 24*t**2 + 5*t - t**3.
2*(t - 1)**2*(t + 2)*(4*t - 1)
Let x(m) = 5*m**2 - 306*m + 644. Let b(q) = -q**2 + 76*q - 160. Let g(p) = 26*b(p) + 6*x(p). Determine y so that g(y) = 0.
-37, 2
Suppose -3*q = -9, -5*u + 2*q - 4*q = -21. Let h = 8439 - 8439. Find i such that h*i**4 + 0*i**2 + 3/2*i + 3/2*i**5 - 3*i**u + 0 = 0.
-1, 0, 1
Let s be -360 + -6*2/4. Let h be (s/18)/(-11) - (-2)/12. Factor 1/3*b + 0*b**4 + 0 + 1/3*b**5 - 2/3*b**3 + 0*b**h.
b*(b - 1)**2*(b + 1)**2/3
Let -49*m**5 + 91*m**5 - 37*m**5 - 15*m**4 = 0. What is m?
0, 3
Let q = -3300/13 + 254. Factor 2/13*i**2 + 0 + q*i.
2*i*(i + 1)/13
Let l be 4*27/252*(-16)/(-12). Factor 12/7 + l*f**2 - 16/7*f.
4*(f - 3)*(f - 1)/7
Let n be (-2 + 3)*3*2. Solve -18*z**3 + n*z**4 + 8*z**3 - 2*z**2 - 10*z**3 + 66*z + 36 - 6*z**3 = 0 for z.
-1, -2/3, 3
Let v = 1065 - 18093/17. Let s = -26/85 + v. Factor s*d - 1/5 - 1/5*d**2.
-(d - 1)**2/5
Suppose 51 = 25*a + 1. Factor -2/11*d**4 - 6/11*d**a - 2/11*d - 6/11*d**3 + 0.
-2*d*(d + 1)**3/11
Suppose 3*l + t + 4*t - 15 = 0, -3 = -t. Suppose 12/5*i**3 - 3*i**2 + l - 3/5*i**4 + 6/5*i = 0. What is i?
0, 1, 2
Let c(i) be the third derivative of -i**7/840 + i**6/240 + i**5/20 + 7*i**4/12 - i**2. Let d(l) be the second derivative of c(l). Let d(b) = 0. What is b?
-1, 2
Let v(t) be the second derivative of 0 + 0*t**2 - 1/18*t**3 + 1/18*t**4 - 14*t - 1/60*t**5. Factor v(l).
-l*(l - 1)**2/3
Let q = 136 + -129. Suppose -q*u + 6*u = -4. Factor -1/2 + 1/2*d**5 + 3/2*d**u - 3/2*d - d**2 + d**3.
(d - 1)*(d + 1)**4/2
Let n(y) be the third derivative of 0*y**3 + 0*y**4 + 0*y + 1/1176*y**8 + 0 + 0*y**6 + 1/735*y**7 - 3*y**2 + 0*y**5. Factor n(z).
2*z**4*(z + 1)/7
Let h be 1/(-10)*4/(-8). Let b(y) be the third derivative of 0*y + h*y**6 - 2/3*y**3 + 1/30*y**5 + 0 - 1/4*y**4 - 4*y**2 + 1/105*y**7. Factor b(d).
2*(d - 1)*(d + 1)**2*(d + 2)
Let c = 655 + -41263/63. Let z(l) be the second derivative of 0*l**2 + 0*l**6 + 0*l**3 + c*l**7 - 2/9*l**4 - 1/5*l**5 + 7*l + 0. Let z(w) = 0. Calculate w.
-1, 0, 2
Let y(h) be the first derivative of 0*h + 0*h**2 - 3/2*h**4 - 4/3*h**3 - 2/5*h**5 + 3. What is a in y(a) = 0?
-2, -1, 0
What is p in 2757*p**2 - 3 - 6 - 2772*p**2 + 21*p + 3*p**3 = 0?
1, 3
Let l = 7 - 4. Suppose 3*o + l*q = 18, 1 = -3*o - q + 13. Suppose 4*x - 3*x + 8 - 2*x**o + x**3 - 7 - x**2 = 0. Calculate x.
-1, 1
Let g(r) = -4*r**4 - 6*r**3 + 31*r**2 - r. Let j(s) = 5*s**4 + 6*s**3 - 35*s**2. Let u(o) = 6*g(o) + 5*j(o). Factor u(i).
i*(i - 3)*(i - 2)*(i - 1)
Suppose -2*g + 4 = -0. Let u(r) = r**2 - 20*r - 67. Let o be u(23). Suppose -m**3 - o*m - 2*m**3 + 0*m**4 + 5*m**g + m**5 - m**4 = 0. Calculate m.
-2, 0, 1
Let v = -49 - -59. Let j be v/2*(-14)/(-35). Find b such that 0 + 2/7*b - 4/7*b**j = 0.
0, 1/2
Let s(t) be the second derivative of -2*t**6/15 - 4*t**5/5 + 2*t**4 + 8*t**3/3 - 10*t**2 + 352*t. Factor s(x).
-4*(x - 1)**2*(x + 1)*(x + 5)
Solve -1/4*g**2 + 0 - 17/4*g = 0 for g.
-17, 0
Let n(u) be the first derivative of -u**3/3 - 67*u**2/2 + 68*u - 61. Factor n(z).
-(z - 1)*(z + 68)
Let q(v) be the second derivative of v**7/630 + 7*v**6/90 + 49*v**5/30 + 13*v**4/6 + 29*v. Let b(p) be the third derivative of q(p). Factor b(c).
4*(c + 7)**2
Let b(k) be the first derivative of -k**5/48 + 43*k**4/96 + 3*k**3/4 + 7*k**2 + 20. Let j(a) be the second derivative of b(a). What is g in j(g) = 0?
-2/5, 9
Factor -1/6*j**3 - 16/3 + 14/3*j - 2/3*j**2.
-(j - 2)**2*(j + 8)/6
Let l = 7163/10 + -185863/260. Let p = l - 9/13. Determine n so that 9/4*n - 3/2 - p*n**2 = 0.
1, 2
Let k(d) be the third derivative of d**5/15 - 29*d**4/30 - 4*d**3/5 - 2*d**2 + 1. Factor k(i).
4*(i - 6)*(5*i + 1)/5
Let i be (-1)/3*30/(-5). Suppose -d = -6*d - 2*m + 11, 5*m + 10 = 0. Let v**i + v**d + 8 + v**2 - 4*v - 16 = 0. Calculate v.
-2, 2
Let h(m) = m**2 + 7*m - 5. Let q be h(-8). Factor 2 - 7*g + 10*g**3 + 12*g**3 - 13*g**q.
(g + 1)*(3*g - 2)*(3*g - 1)
Let y be 68/48 + (-15)/720*8. Factor d + y - 1/4*d**2.
-(d - 5)*(d + 1)/4
Let z(f) be the second derivative of -f**6/105 + f**5/14 + f**4/42 - 17*f**3/21 - 12*f**2/7 - 19*f. Suppose z(p) = 0. Calculate p.
-1, 3, 4
Let m(r) be the first derivative of -r**3/6 + 5*r**2/4 + 3*r + 17. Factor m(x).
-(x - 6)*(x + 1)/2
Let i(l) = -2*l**2 + 9*l + 7. Let b be i(5). Suppose -4*t**4 - 5*t + 5*t - b*t**5 + 0*t = 0. What is t?
-2, 0
Let b(n) be the second derivative of n**5/130 - n**4/39 + 109*n. Factor b(l).
2*l**2*(l - 2)/13
Suppose -3*l + 12 + 9 = 0. Suppose -4*n + y - 2*y = -12, -4 = y. Factor l*a**n + 9*a**5 + 3*a**3 - 6*a**5 - a**4.
3*a**3*(a + 1)**2
Let r be 2/((-18)/(-15))*-6. Let k be ((-1)/2)/(-1*(-4)/r). Factor l**2 - k*l + 1/4.
(l - 1)*(4*l - 1)/4
Let h(p) = -7*p**3 - 38*p**2 + 100*p - 49. Let z(x) = x**3 - 2*x**2 - 1. Let i(m) = h(m) + 3*z(m). Factor i(q).
-4*(q - 1)**2*(q + 13)
Let r = 8 - 5. Let q be ((-20)/(-15))/(1/3). Let -4*c + 4*c**2 + r*c - q*c + c = 0. What is c?
0, 1
Let q be 2/(-10)*(-23 - (-17 - -9)). Suppose 250/9 + 10/3*j**2 + 50/3*j + 2/9*j**q = 0. What is j?
-5
Let 2/23*a**4 - 22/23*a**2 - 8/23*a**3 + 60/23*a + 0 = 0. What is a?
-3, 0, 2, 5
Let r = -412 - -857. Factor -770*v - 4*v**3 - 3645 - r*v - v**3 - 135*v**2.
-5*(v + 9)**3
Let s(x) be the second derivative of 0*x**3 + 11*x + 1/126*x**7 - 1/45*x**6 + 1/60*x**5 + 0 + 0*x**2 + 0*x**4. Factor s(j).
j**3*(j - 1)**2/3
Let x(l) 