530. Let c(q) = -10*q + 1. Let h(f) = -4*c(f) + y(f). Factor h(k).
2*(k - 67)**3*(k - 1)
Let u(c) be the third derivative of c**5/120 - 5*c**4/12 + 2*c**2 + 2*c. Solve u(h) = 0.
0, 20
Let p(b) = -37*b - 74. Let g be p(-2). Factor -4/3*w**2 + g + 2/3*w + 2/3*w**3.
2*w*(w - 1)**2/3
Let z(a) be the third derivative of a**7/1995 - 13*a**6/1140 + a**5/10 - 5*a**4/12 + 50*a**3/57 + 27*a**2. Let z(y) = 0. What is y?
1, 2, 5
Let p(x) be the first derivative of x**6/90 + x**5/10 + 10*x**3/3 - 2. Let n(b) be the third derivative of p(b). Factor n(m).
4*m*(m + 3)
Let i be (-3)/(-14)*(-13)/((-1872)/84). Let s(l) be the third derivative of 0*l - 1/40*l**5 - i*l**3 + l**2 - 3/32*l**4 + 0. Let s(t) = 0. What is t?
-1, -1/2
Factor -5*f**3 - 55/4*f - 95/4*f**2 + 5.
-5*(f + 1)*(f + 4)*(4*f - 1)/4
Let x(g) = -19*g - 394. Let v be x(-21). Let q(l) be the third derivative of 0*l**3 + 0 + 0*l - 1/60*l**v - 1/480*l**6 - 1/24*l**4 + 6*l**2. Factor q(f).
-f*(f + 2)**2/4
Factor -10*y**3 - 20*y**2 - 14*y**2 - 586*y + 574*y.
-2*y*(y + 3)*(5*y + 2)
Factor l**4 + 31*l - 5*l**4 + 15*l**3 + 13*l**3 + 17*l - 64*l**2.
-4*l*(l - 3)*(l - 2)**2
Determine c, given that -15*c**3 + 18*c**2 + 17*c**2 - 16 + 35*c + 100*c + 106 - 5*c**4 = 0.
-3, -2, -1, 3
Let q(w) be the third derivative of -w**10/37800 - w**9/5040 - w**8/2520 + 2*w**5/15 - 12*w**2. Let t(l) be the third derivative of q(l). Factor t(a).
-4*a**2*(a + 1)*(a + 2)
Find a such that 76/3*a**2 + 28/9*a**4 + 14*a + 0 + 128/9*a**3 + 2/9*a**5 = 0.
-7, -3, -1, 0
Let a be -2 + 10 - 30/5. Let s be (-22)/165 + a/15. Find r such that 2/7*r**2 + 0 + s*r = 0.
0
Factor 4*m**3 - 7*m**3 - 103*m + 223*m + 216*m - 2838 + 726 + 15*m**2.
-3*(m - 8)**2*(m + 11)
Let l(v) be the first derivative of v**5/540 - v**4/216 - v**3/27 - 4*v**2 - 1. Let r(h) be the second derivative of l(h). Factor r(s).
(s - 2)*(s + 1)/9
Find z such that -64/9*z**4 - 208/9*z**3 - 83/3*z**2 - 130/9*z - 25/9 = 0.
-1, -5/8
Let k = 724393/13 - 56566. Let a = -843 - k. Factor -a*x**2 - 2/13 - 8/13*x.
-2*(x + 1)*(3*x + 1)/13
Suppose 0 = -28*i + 23*i + 345. Let o = 75 - i. Find p, given that 58/5*p**3 + 82/5*p**4 - 8/5 - 18/5*p**2 - 32/5*p + o*p**5 = 0.
-1, -2/5, 2/3
Let r(f) = 40*f + 8. Let g be r(-1). Let x be ((-8)/(-78))/(2 - g/(-18)). Factor 0 - 4/13*j**3 + 10/13*j**4 - x*j**5 + 0*j**2 + 0*j.
-2*j**3*(j - 1)*(3*j - 2)/13
Let m(w) be the second derivative of w**8/210 - w**7/420 + w**3/3 - 7*w. Let d(a) be the second derivative of m(a). Suppose d(i) = 0. What is i?
0, 1/4
Let v be (-5)/((-450)/1095) + 16/2. Let v - 1/6*l**3 - 143/6*l + 23/6*l**2 = 0. What is l?
1, 11
Let d(w) be the third derivative of -w**10/50400 + w**9/20160 + w**5/15 - w**2. Let k(i) be the third derivative of d(i). Let k(p) = 0. What is p?
0, 1
Let h(a) be the second derivative of a**6/6 + a**5/4 - 25*a**4/2 + 190*a**3/3 - 140*a**2 - 2*a + 136. Factor h(s).
5*(s - 2)**3*(s + 7)
Let d(p) be the second derivative of -1/4*p**4 + 2/3*p**2 + 0 - 2/3*p**3 + 7/60*p**5 + 7*p. Factor d(f).
(f - 2)*(f + 1)*(7*f - 2)/3
Let j = -8 + 10. Suppose -3*v + j*f = -12, -v + 3*f = -5*v - 1. Determine y so that -2 + 1 - y**2 - y**v + 3 = 0.
-1, 1
Let u = -93 + 97. Factor -31*o**3 - 16*o - 18*o**3 + 61*o**3 - u*o**4.
-4*o*(o - 2)**2*(o + 1)
Let k be 30/9 + (-1)/3. Factor 0*w**2 + 5*w**2 + 0*w**3 - k*w**2 - 2*w**3.
-2*w**2*(w - 1)
Let b(c) be the third derivative of -c**6/40 + 13*c**5/30 + 55*c**4/8 + 26*c**3/3 + 574*c**2. Factor b(g).
-(g - 13)*(g + 4)*(3*g + 1)
Factor 3*i**3 + 17556*i**2 - 4*i**5 - 17556*i**2 + i**5.
-3*i**3*(i - 1)*(i + 1)
Factor -1/6*o - 17/2 + 1/6*o**3 + 17/2*o**2.
(o - 1)*(o + 1)*(o + 51)/6
Let q(v) = -v**2 + 5*v + 6. Let c be q(3). Suppose 2*o + 6 - c = 0. Factor 12/5*f**o + 54/5*f**2 + 33/5*f + 6/5 - 24/5*f**4.
-3*(f - 2)*(2*f + 1)**3/5
Let u(h) be the third derivative of h**8/840 + 2*h**7/525 - h**6/50 - 2*h**5/75 + 13*h**4/60 - 2*h**3/5 - 190*h**2. Find p, given that u(p) = 0.
-3, -2, 1
Let c = 391 - 7037/18. Let a(j) be the second derivative of 1/3*j**2 + 0 + 6*j - c*j**3 - 1/36*j**4. Factor a(h).
-(h - 1)*(h + 2)/3
Let q(p) be the second derivative of p**7/42 - 9*p**6/2 + 1188*p**5/5 - 3266*p**4/3 - 88*p**3 + 8712*p**2 + 501*p. Factor q(g).
(g - 66)**2*(g - 2)**2*(g + 1)
Let r(n) be the second derivative of -n**5/70 - 8*n**4/21 - 5*n**3/7 + 21*n - 5. Factor r(f).
-2*f*(f + 1)*(f + 15)/7
Let f(x) be the second derivative of x**6/30 + x**5/5 - 9*x**4/4 + 19*x**3/3 - 8*x**2 + 32*x - 2. What is n in f(n) = 0?
-8, 1, 2
Suppose -4*p - 18 = -6. Let y be ((-8)/(-6))/((-2)/p). Find u such that -1 + 6*u**2 + 15*u - y - 3 - 15*u**3 = 0.
-1, 2/5, 1
Let a be 2/(-6)*528/(-968). Let 6/11*y**2 - a*y**4 + 0 + 0*y**3 - 4/11*y = 0. Calculate y.
-2, 0, 1
Suppose -3*p + 5*w + 624 = 0, 4*p - 2*w + 1009 = 9*p. Let s = 219 - p. Factor s*c + 4*c**2 + 16/3 - 20/3*c**3.
-4*(c - 2)*(c + 1)*(5*c + 2)/3
Let b(s) be the third derivative of -s**7/2520 - s**6/1080 + s**5/360 + s**4/72 + 5*s**3/6 + 10*s**2. Let c(o) be the first derivative of b(o). Factor c(j).
-(j - 1)*(j + 1)**2/3
Let a(q) = q**5 - q**4 - q**3 - q - 1. Let j(p) = 7*p**5 - 12*p**4 - 9*p**3 + 6*p**2 - 8*p - 8. Let f(u) = 24*a(u) - 3*j(u). Let f(o) = 0. What is o?
-3, -2, 0, 1
Let g(c) be the second derivative of -c**4/24 - c**3/12 + 15*c - 1. Determine q so that g(q) = 0.
-1, 0
Factor -2/5*f**2 + 0*f + 8/5.
-2*(f - 2)*(f + 2)/5
Let x(f) be the second derivative of -f**4/120 - 4*f**3/15 - 3*f**2/4 - 52*f + 2. Determine d so that x(d) = 0.
-15, -1
Let g(l) be the first derivative of 0*l**2 - 5 + 1/4*l**3 - 3/4*l. Factor g(s).
3*(s - 1)*(s + 1)/4
What is c in 56 - 2/7*c**5 - 284/7*c**3 + 848/7*c**2 + 40/7*c**4 - 142*c = 0?
1, 4, 7
Let x be (3 + -8 + -8)/(-1). Suppose 58 - x = 9*j. Factor -2/7*l**4 + 0*l + 2/7*l**j - 2/7*l**3 + 2/7*l**2 + 0.
2*l**2*(l - 1)**2*(l + 1)/7
Let m be (-3)/7 - 26868/(-168). Let d = m - 156. Let -d*c**2 + 0 - c = 0. Calculate c.
-2/7, 0
Let l(j) = -6*j**3 + 27*j**2 - 10*j - 1. Let r(d) = 3*d**2 - 8*d + 3*d**3 - 17*d**2 - 9*d + 22*d. Let a(h) = 3*l(h) + 5*r(h). What is u in a(u) = 0?
-1/3, 1, 3
Factor -4/3*l**3 - 8*l**2 - 16/3 - 12*l.
-4*(l + 1)**2*(l + 4)/3
Let s be (2600/(-28))/(-10) - 7. Solve -2/7*l**2 - 4/7*l + s = 0 for l.
-4, 2
Let a(z) be the third derivative of -23*z**2 + 0*z - 1/36*z**4 + 1/720*z**6 + 0*z**3 + 1/1260*z**7 - 1/90*z**5 + 0. Factor a(g).
g*(g - 2)*(g + 1)*(g + 2)/6
Let j(h) be the third derivative of 0*h**3 - 10*h**2 - 1/4*h**5 + 0*h + 0 + 5/24*h**4 - 1/6*h**6. Let j(i) = 0. Calculate i.
-1, 0, 1/4
Let o(x) be the second derivative of x**4/6 - 5*x**3 - 54*x**2 + 398*x. Factor o(j).
2*(j - 18)*(j + 3)
Let w(k) = -8*k**2 - 12*k - 16. Let v(m) = -3*m**2 - 4*m - 5. Suppose -2*b - 32 + 0 = 0. Let c(r) = b*v(r) + 5*w(r). Factor c(h).
4*h*(2*h + 1)
Let b(g) = 9*g**2 + 69*g - 100. Let k(s) = -2*s**2 - 14*s + 20. Let w(z) = -2*b(z) - 11*k(z). Factor w(p).
4*(p - 1)*(p + 5)
Factor -3*x**2 - 1/4*x**4 + 3/2*x**3 + 5/2*x - 3/4.
-(x - 3)*(x - 1)**3/4
Suppose 0*x - 3*x + 0*x + 11*x = 0. Factor -1/4*h**4 + 0 + x*h - 1/4*h**2 - 1/2*h**3.
-h**2*(h + 1)**2/4
Find p such that 0 - 16/5*p**4 + 0*p + 4/5*p**5 + 16/5*p**2 - 4/5*p**3 = 0.
-1, 0, 1, 4
Let i(l) = l**3 + 2*l**2 - 2*l + 1. Let v(y) = 7*y**3 + 3*y**2 - 13*y + 15. Let b(t) = -6*i(t) + v(t). Let b(j) = 0. What is j?
-1, 1, 9
Let h = -325/42 + 173/21. Factor 9/2*r + h*r**4 + 7/2*r**3 + 15/2*r**2 + 0.
r*(r + 1)*(r + 3)**2/2
Let -27*c**3 - 4*c**4 + 117692*c - 17*c**3 - 8*c**3 - 156*c**2 - 117800*c = 0. What is c?
-9, -3, -1, 0
Let c be 0 + 1 + (6 - 3). Suppose 0 = -2*l + 4 + c. Suppose 163*x**4 + 35*x**5 + 2*x**3 + l*x + 32*x**2 + 4*x**3 + 81*x**3 - 69*x**4 = 0. What is x?
-1, -2/5, -2/7, 0
Let 1/9 - 7/9*x**2 + 2/9*x + 4/9*x**3 = 0. What is x?
-1/4, 1
Let n be (-43)/(-301) - (-3)/231*101. Suppose 10/11*p**3 + 6/11*p - n*p**2 + 0 = 0. What is p?
0, 3/5, 1
Let q(m) = m**4 - 62*m**3 + 1320*m**2 - 10400*m + 15995. Let u(w) = 1. Let n(z) = q(z) + 5*u(z). Let n(l) = 0. Calculate l.
2, 20
Let x(l) = -l**2 + 61*l - 1027. Let m(h) = h + 1. Let d(s) = -6*m(s) - 2*x(s). Determine c, given that d(c) = 0.
32
Suppose -26*q + 28*q = 4. Solve -9*d**q - 6*d + 3*d**2 - 9 + 5*d**2 = 0.
-3
Suppose -3*x + w - 3*w = -2, 2*x + w = 2. Let u(l) be the second derivative of -l - 27/4*l**x + 0 - 1/8*l**4 - 3