
Let m(t) be the third derivative of 0*t**3 - 1/4*t**4 + 0*t + 0 + 1/5*t**6 - 1/20*t**5 + 32*t**2 - 1/14*t**7. Factor m(y).
-3*y*(y - 1)**2*(5*y + 2)
Let p be 56/8 + (2 - 1)*1. Find t, given that 5 - 3*t**3 - 5 + p*t**2 - 5*t**2 = 0.
0, 1
Find r, given that 0 - 9/5*r**3 + 12*r - 177/5*r**2 = 0.
-20, 0, 1/3
Let q(t) be the second derivative of 0 - 1/20*t**5 + t + 7/12*t**4 + 1/14*t**7 - 7/30*t**6 + 0*t**2 - 1/3*t**3. What is n in q(n) = 0?
-1, 0, 1/3, 1, 2
Let g = -27 + 45. Let a be (-5)/(-4) - g/(-24). Let -4*p**a + p**2 + p + p**2 + p**4 - 7*p**3 - 5*p**4 = 0. What is p?
-1, 0, 1/4
Let m(g) be the first derivative of -2/21*g**3 + 0*g + 13 + 2/7*g**2. Let m(j) = 0. Calculate j.
0, 2
Suppose 5 - 19 = 2*a - 2*h, 2*a + 4*h - 16 = 0. Let i(g) = -6*g**3 + 6*g**2 + 19*g. Let c(q) = -2*q**3 + 2*q**2 + 6*q. Let u(d) = a*i(d) + 7*c(d). Factor u(k).
-2*k*(k - 2)*(k + 1)
Let w = -157/7 - -193/7. Factor 4/7 - w*x**4 - 16/7*x**2 + 10/7*x**5 - 6/7*x + 44/7*x**3.
2*(x - 1)**4*(5*x + 2)/7
Determine c so that 6/7*c**5 + 2*c**4 + 0 + 2/7*c**2 + 10/7*c**3 + 0*c = 0.
-1, -1/3, 0
Factor 96/5 + 24*f**3 + 256/5*f + 256/5*f**2 + 2/5*f**5 + 26/5*f**4.
2*(f + 1)*(f + 2)**3*(f + 6)/5
Solve 1720*i - 880*i + 3*i**2 - 896*i - i**2 = 0.
0, 28
Let h(f) = 5 + 3*f**4 - 6 - 4*f + 2*f**3 + 0*f. Let s(l) = 4*l**4 + 2*l**3 - 5*l - 1. Let t(i) = -3*h(i) + 2*s(i). Factor t(b).
-(b - 1)*(b + 1)**3
Solve -62/13*l**3 + 0 - 12/13*l**2 - 10/13*l**4 + 0*l = 0.
-6, -1/5, 0
Let l be 3/18*6*1/6. Determine r, given that 0*r + 2/3 - l*r**3 - 1/2*r**2 = 0.
-2, 1
Let k = 23 - 35. Let r be k/(-5) + (-18)/(-30). Factor -13*a**2 - 2*a**2 + 3*a**4 - 4*a**3 + 13*a**r - 3*a**5 + 6*a.
-3*a*(a - 1)**3*(a + 2)
Let h(c) be the second derivative of -c**5/20 + c**4/4 + c**3/6 - 3*c**2/2 + 13*c. Find v such that h(v) = 0.
-1, 1, 3
Let m(c) be the third derivative of -c**6/126 + 2*c**5/35 - 2*c**4/21 - c**3 + 2*c**2. Let q(y) be the first derivative of m(y). Factor q(t).
-4*(t - 2)*(5*t - 2)/7
Let f(m) be the second derivative of -m**6/420 - m**5/105 + 6*m**2 - 29*m. Let h(w) be the first derivative of f(w). Factor h(t).
-2*t**2*(t + 2)/7
Let c(z) = z**3 - 6*z**2 + 7*z - 8. Let n be c(5). Find j, given that 15*j**3 + 28*j**n + 44*j**2 + 8*j**5 - 2*j**5 + 6 - 21*j**4 - 57*j**2 - 21*j = 0.
-1, 1/2, 1, 2
Find t, given that 3 + 3/8*t**4 - 17/4*t**2 - 13/8*t**3 + 5/2*t = 0.
-2, -2/3, 1, 6
Factor 1/3*g**2 - 1/3*g**4 + 1/9*g**5 + 1/9*g**3 + 0 - 2/9*g.
g*(g - 2)*(g - 1)**2*(g + 1)/9
Let y(a) be the third derivative of a**7/525 - a**6/75 + a**5/25 - a**4/15 + a**3/15 + 14*a**2. Factor y(z).
2*(z - 1)**4/5
Factor -5*i**4 - i**5 - 5 + 7 + 1 + 8*i + 1 - 7*i**3 + i**2.
-(i - 1)*(i + 1)**2*(i + 2)**2
What is c in 32/13*c - 8/13 - 10/13*c**5 + 34/13*c**4 - 22/13*c**3 - 2*c**2 = 0?
-1, 2/5, 1, 2
Let k(x) be the second derivative of x**6/75 - 4*x**5/75 + 7*x**4/90 - 2*x**3/45 - 35*x - 4. Factor k(p).
2*p*(p - 1)**2*(3*p - 2)/15
Factor 0 - 2/7*g**4 - 10/7*g**2 + 8/7*g**3 + 4/7*g.
-2*g*(g - 2)*(g - 1)**2/7
Let s(g) = -5*g**2 - 7*g. Let p be (-2)/3 - (-120)/18. Let f(c) = 0 + p*c + 0 + 6*c**2. Let x(j) = 5*f(j) + 4*s(j). Factor x(u).
2*u*(5*u + 1)
Suppose 0*m - 3*m + 17 = o, -51 = -3*o - 5*m. Factor 13*x**4 - o*x**4 - 8*x + 14*x**3 + 4 - 6*x**3.
-4*(x - 1)**3*(x + 1)
Let d(g) = 9*g**4 + 28*g**3 + 43*g**2 + 8*g - 16. Let h(s) = -19*s**4 - 56*s**3 - 86*s**2 - 16*s + 33. Let y(x) = 9*d(x) + 4*h(x). Determine r so that y(r) = 0.
-3, -2, -1, 2/5
Let u(i) = i**3 - i**2 + 1. Let b be u(2). Let z(s) be the second derivative of s + 0*s**3 - 1/30*s**6 + 0*s**2 + 0*s**4 + 0 + 0*s**b + 1/42*s**7. Factor z(q).
q**4*(q - 1)
Factor -2 - 4*c - 21*c**2 + 7 + 20*c**2.
-(c - 1)*(c + 5)
Let w(o) = 14*o**3 - 801*o**2 - 52272*o - 1149984. Let a(p) = -6*p**3 + 400*p**2 + 26136*p + 574992. Let z(q) = -9*a(q) - 4*w(q). Solve z(g) = 0.
-66
Let q = 3582 - 3580. Factor 0 - 8/5*u**3 - 4/5*u + q*u**2 + 2/5*u**4.
2*u*(u - 2)*(u - 1)**2/5
Let c(j) = -3*j**4 - 10*j**3 + 17*j**2 + 2*j. Let l(w) = -80*w**4 - 270*w**3 + 460*w**2 + 55*w. Let n(p) = -55*c(p) + 2*l(p). What is y in n(y) = 0?
-3, 0, 1
Let o(x) = -x**2 + 7*x + 4. Let d be o(6). Let i = d - 8. Factor 3*m**3 + 0*m**3 + 12*m**i + 24 + 36*m + 0*m**3 + 6*m**2.
3*(m + 2)**3
Factor 8/3 + 8/3*f**2 + 34/3*f.
2*(f + 4)*(4*f + 1)/3
Let a = -862 - -5179/6. Let w(b) be the first derivative of a*b**3 - 9/4*b**2 + b + 3. Factor w(n).
(n - 1)*(7*n - 2)/2
Let y be (-30)/(-9) + (-88)/66. Let w(c) be the second derivative of 3*c**y + 2*c**3 + 0 - 6*c + 5/8*c**4 + 3/40*c**5. Factor w(g).
3*(g + 1)*(g + 2)**2/2
Let m be 1/3*-1*(-11 + -1). Suppose 171*k - 10*k**2 + 5*k**3 - 171*k + 5*k**m = 0. What is k?
-2, 0, 1
What is q in 122/9*q**2 + 8 - 28/9*q**3 + 2/9*q**4 - 56/3*q = 0?
1, 6
Let t(h) be the second derivative of 3*h**8/3920 - h**7/1960 - h**6/420 + 2*h**3/3 - 4*h. Let c(n) be the second derivative of t(n). Factor c(u).
3*u**2*(u - 1)*(3*u + 2)/7
Suppose -z - s - s = 4, -4*z - 5*s - 4 = 0. Suppose z*i**3 - 12*i + 2*i - 8 - 2*i = 0. Calculate i.
-1, 2
Let u(c) = c**3 + 5*c**2 + 3*c + 5. Let f be u(-5). Let b = 15 + f. Find m such that -5*m**3 + 7 - 4*m**4 - m**b - 7 - 2*m**2 = 0.
-2, -1, 0
Let i = -1064 + 1068. Find w such that 66/5*w**2 + i*w**3 + 16*w + 2/5*w**4 + 32/5 = 0.
-4, -1
Suppose -24*n + 12 = -36. Factor 2/5*i**3 - 2/5*i**4 + 0 + 0*i**n + 0*i.
-2*i**3*(i - 1)/5
Factor -2/9*g**3 + 16/9*g + 0 - 4/9*g**2.
-2*g*(g - 2)*(g + 4)/9
Let h = -48 + 70. Let k(q) = -2*q + 44. Let w be k(h). Factor 0*g + 3/8*g**4 - 1/8*g**5 + w*g**2 + 0 - 1/4*g**3.
-g**3*(g - 2)*(g - 1)/8
Let p(x) be the second derivative of x**7/1680 - x**6/90 + 7*x**5/80 - 3*x**4/8 + 11*x**3/6 - 14*x. Let t(h) be the second derivative of p(h). Factor t(f).
(f - 3)**2*(f - 2)/2
Let s(n) be the first derivative of 4*n**5/5 + 28*n**4 - 120*n**3 + 184*n**2 - 124*n - 54. Factor s(h).
4*(h - 1)**3*(h + 31)
Let p(x) = -18*x**4 + 50*x**3 - 36*x**2 + 4*x + 4. Let g(a) = -5*a**2 + a - 5 + a**2 + 4 + a**4 - a**3 + 3*a**2. Let u(k) = 4*g(k) + p(k). Factor u(z).
-2*z*(z - 2)*(z - 1)*(7*z - 2)
Let b be (33/(-55))/((-7)/((-56)/(-6))). Factor -2/5*x + 0 - 2/5*x**3 + b*x**2.
-2*x*(x - 1)**2/5
Let c = -2601/98 + 1374/49. What is r in -9/2 + 6*r - c*r**2 = 0?
1, 3
Factor -2/3*i**2 + 1/3*i**3 - 8/3*i + 0.
i*(i - 4)*(i + 2)/3
Let w(h) = -h**2 + 18*h - 15. Let p be w(17). Factor 3*u**2 + 7*u**p + 0*u**2 - 6*u - 9 - 7*u**2.
3*(u - 3)*(u + 1)
Let f(p) be the third derivative of 17/150*p**5 - 7/60*p**6 + 0*p - 13*p**2 + 0 - 4/15*p**3 + 23/525*p**7 + 1/15*p**4 - 1/168*p**8. Suppose f(o) = 0. What is o?
-2/5, 1, 2
Let h(w) = w**3 + 1. Suppose 7 = 7*j + 14. Let n(q) = -q**3 - q**2 - 5*q - 5. Let s(b) = j*n(b) - 6*h(b). Factor s(c).
-(c - 1)*(c + 1)*(5*c - 1)
Let 28 + 32*y + 65*y**2 - 30*y**2 - 31*y**2 = 0. What is y?
-7, -1
Solve 5*o - 125*o + 148*o**2 - 24*o**3 + 12*o**5 + 6*o**3 - 22*o**4 + 16 - 23*o**4 + 7*o**4 = 0 for o.
-2, 1/6, 1, 2
Let d = -12595 - -188927/15. Factor -4/15*p**3 - d*p**2 + 0 + 0*p - 2/15*p**4.
-2*p**2*(p + 1)**2/15
Suppose -a**2 + 9/4*a**4 - a**3 + 9/4*a**5 + 0 + 0*a = 0. What is a?
-1, -2/3, 0, 2/3
Let z(k) be the third derivative of -k**8/588 - 2*k**7/735 + k**6/35 + 2*k**5/15 + 11*k**4/42 + 2*k**3/7 - 6*k**2. Factor z(m).
-4*(m - 3)*(m + 1)**4/7
Let y(n) = n**2 - 21*n + 41. Let k be y(19). Let a be k - (-1 + 0) - 1. Find d, given that 2*d**2 + 2/3*d + 2*d**a + 2/3*d**4 + 0 = 0.
-1, 0
Suppose 0 = 4*s + 27 + 33. Let a be (10/s)/((-2)/15). Determine p, given that 3*p**4 - p**a + 0*p**5 - 2*p**2 - p**4 + 0*p**4 + p = 0.
-1, 0, 1
Solve -15/7 - 1/7*p**2 + 8/7*p = 0.
3, 5
Find t such that -14 - 2/9*t**2 + 128/9*t = 0.
1, 63
Let s(r) be the third derivative of 0 - 1/280*r**7 + 10*r**2 + 0*r**3 - 1/5*r**5 + 0*r + 0*r**4 + 1/20*r**6. Factor s(f).
-3*f**2*(f - 4)**2/4
Let h(x) = -8*x**2 + 3*x. Let i(f) = 23*f**2 - 8*f. Let w = 25 + -21. Let t(d) = w*i(d) + 11*h(d). Let t(l) = 0. What is l?
-1/4, 0
Let k(m) = 2*m**3 + 4*m**2 - 6*m + 8. Let u(h) = -h**2 + h - 1. Let y(x) = 6 + 2 + x**2 + x + 0*x**2. Let n be y(0). Let v(g) = n*u(g) + k(g). Factor v(z).
2*z*(z - 1)**2
Let k = 3/4460 + 17819/31220. What is d in 0 + k*d - 4/7*d**2 = 0?
0, 1
Suppose 55*v - 53*v - 2 = 3*c, c = 4*v - 4. Let d(k) be the first derivative of -5/2*k**2 - 14*k**5 + 95/4*k**4 - 5 - 20/3*k**3