r(p) = 0.
-4, -2, -2/3
Let k(j) be the third derivative of 25/24*j**4 - 5*j**3 + 1/12*j**5 + 0*j - 31*j**2 + 0. Suppose k(u) = 0. What is u?
-6, 1
Factor 10/3*q**2 + 0 - 2/3*q**3 - 2/3*q**4 - 2*q.
-2*q*(q - 1)**2*(q + 3)/3
Let -288*c - 350 + 336*c + 138*c + 5*c**3 + 519*c - 360*c**2 = 0. Calculate c.
1, 70
Let u(k) = -k**3 + k**2 + 43*k + 8. Let v be u(-6). Let j be (5/12)/((-2)/(-8)). Factor j*t - t**v - 2/3.
-(t - 1)*(3*t - 2)/3
Let y = 36 - 33. Determine d, given that d**2 - y*d**4 - 115*d**3 + 2*d**2 + 112*d**3 + 3*d = 0.
-1, 0, 1
Suppose -44 - 14 = -2*p. Suppose -p*i + 4 = -27*i. Factor -2/7*z**i + 0 - 4/7*z.
-2*z*(z + 2)/7
Let y = -176 - -177. Let x be 0 - (-7 - 4/(-1)) - y. Factor -1/4*p**x + 0 + 0*p.
-p**2/4
Suppose 103*l + 11 = 104*l. Determine v so that -32 - 15*v**2 + 24*v - 5 + 1 + l*v**2 = 0.
3
Let v(z) be the third derivative of -z**8/84 + 10*z**7/21 - 28*z**6/5 + 48*z**5/5 + 90*z**2. Determine h so that v(h) = 0.
0, 1, 12
Let z(x) be the second derivative of 2*x**7/147 - 4*x**6/21 + 6*x**5/35 + 32*x**4/21 - 94*x**3/21 + 36*x**2/7 - 347*x + 2. Factor z(f).
4*(f - 9)*(f - 1)**3*(f + 2)/7
Suppose 0*h + 2*h = 0. Suppose c + h*c - 13 = 5*a, 3*c - 5*a - 19 = 0. Factor c*w**2 + 2*w**2 - 4*w**2 - 1.
(w - 1)*(w + 1)
Let g(r) be the first derivative of r**4/16 - r**3/6 + 188. Factor g(s).
s**2*(s - 2)/4
Let r**3 - 14*r + 6 - 16*r**3 + 36*r**2 + r - 14*r = 0. Calculate r.
2/5, 1
Let h = -12149/106524 + 1/2421. Let c = h - -191/132. What is m in 10/3*m**2 - c*m - 2*m**3 + 0 = 0?
0, 2/3, 1
Let j be (2/4)/((-10)/(-480)). Let g be 1/((-4)/j*-2). Find t, given that -17*t**2 + 2*t**2 + 14*t**3 - 35*t**g + 6*t = 0.
-1, 0, 2/7
Let y = -27 - -34. Let z(x) = -x + 11. Let l be z(y). Factor -3*n**4 + 11*n**2 + 7*n**l + 13*n**3 - n**3 - 3*n**2.
4*n**2*(n + 1)*(n + 2)
Let y = 3 - 6. Let t = 6 + y. Let 4*h**t + 0*h**3 - 3*h**4 + 6*h**4 - h**3 = 0. Calculate h.
-1, 0
Suppose 10/3*d**4 + 0*d + 0 - 16/3*d**2 + 4/3*d**3 + 2/3*d**5 = 0. What is d?
-4, -2, 0, 1
Let n(v) = 19*v**2 + 145*v + 84. Let g be n(-7). Factor -2/5*b**3 + 0 + g*b + 0*b**2.
-2*b**3/5
Suppose -84*i + 237*i + 119*i = -290*i. Factor i - 2/5*t**2 - 3/5*t + 1/5*t**3.
t*(t - 3)*(t + 1)/5
Suppose 2*y + 3 = 3*w - y, -2*w + 3*y + 3 = 0. What is k in -7 - 3 + 6 + w + k**2 = 0?
-2, 2
Let a(d) be the second derivative of -5*d**8/1344 - 13*d**7/504 - d**6/36 + d**5/6 - d**4/3 - 38*d. Let h(j) be the third derivative of a(j). Factor h(z).
-5*(z + 1)*(z + 2)*(5*z - 2)
Let f be (2/6)/(5/60). Suppose 43*x**4 - 21*x**5 - 119*x**3 - 4*x**2 - 5*x**2 - 2*x - 14*x**f + 122*x**3 = 0. What is x?
-1/3, -2/7, 0, 1
Suppose -2*k + 2*h = 2, 0 = -h - 49 + 52. Let l(u) be the second derivative of -1/4*u**k + 0 - u - 7/24*u**3 - 1/40*u**5 - 7/48*u**4. Factor l(j).
-(j + 1)*(j + 2)*(2*j + 1)/4
Let j(b) be the second derivative of b**8/336 + b**7/168 - b**6/72 - b**5/24 - 5*b**3/6 + 12*b. Let d(x) be the second derivative of j(x). Factor d(c).
5*c*(c - 1)*(c + 1)**2
Factor 4323/8*j**2 + 111/4*j**3 + 3/8*j**4 + 999*j + 486.
3*(j + 1)**2*(j + 36)**2/8
Let k = 198 - 791/4. Let g(q) be the first derivative of 3/8*q**4 + k*q**3 - 3/2*q**2 - 9/4*q - 1. Solve g(c) = 0 for c.
-1, 3/2
Factor 19/4*p**2 + 5/4*p**4 - 21/4*p**3 + 0 - 3/4*p.
p*(p - 3)*(p - 1)*(5*p - 1)/4
Let o(b) be the second derivative of -b**6/6 - b**5/2 + 5*b**4/12 + 5*b**3/3 + 104*b. Factor o(i).
-5*i*(i - 1)*(i + 1)*(i + 2)
Factor -6*l**2 + 1/4*l**3 + 4*l + 0 + 1/4*l**5 + 3/2*l**4.
l*(l - 1)**2*(l + 4)**2/4
Factor 0*f - f**4 + 0 - 16/7*f**3 - 12/7*f**2 - 1/7*f**5.
-f**2*(f + 2)**2*(f + 3)/7
Let o(n) be the second derivative of -1/135*n**6 + 15*n + 2/45*n**5 + 0 - 1/9*n**2 + 4/27*n**3 - 1/9*n**4. Determine v, given that o(v) = 0.
1
Let a(s) = 18*s**2 + 143*s + 159. Let t(d) = -8*d**2 - 71*d - 81. Let g(y) = 3*a(y) + 5*t(y). Let g(m) = 0. Calculate m.
-4, -9/7
Let w(x) be the third derivative of x**10/10080 - x**9/6048 - x**8/1344 + x**7/504 + x**5/15 - 17*x**2. Let b(u) be the third derivative of w(u). Factor b(o).
5*o*(o - 1)*(o + 1)*(3*o - 2)
Let x = -1134 - -2269/2. Find a such that x*a**2 - 1/2*a**4 - 7/4*a**5 + 0*a + 0 + 7/4*a**3 = 0.
-1, -2/7, 0, 1
Find d, given that 555/2*d + 51/2*d**4 + 1413/4*d**2 + 9/8*d**5 + 75 + 1401/8*d**3 = 0.
-10, -1, -2/3
Let t(q) = 5*q - 12 - 6*q + 2*q. Let b be t(14). Factor 3*u + u**b + 3*u**2 - 15*u.
4*u*(u - 3)
Factor 248/7*c**2 - 18*c**3 - 4/7 - 118/7*c.
-2*(c - 1)**2*(63*c + 2)/7
Let c(x) be the third derivative of 0 + 0*x**3 - 1/60*x**6 - 1/336*x**8 + 0*x + 1/70*x**7 + 0*x**4 - 15*x**2 + 0*x**5. Suppose c(w) = 0. Calculate w.
0, 1, 2
Let m(a) be the third derivative of a**8/112 - a**7/70 - 3*a**6/20 - a**5/10 + 5*a**4/8 + 3*a**3/2 - 23*a**2 - a. Determine w, given that m(w) = 0.
-1, 1, 3
Let z(u) be the first derivative of u**3 + 3*u**2/2 - 18*u + 107. Determine q so that z(q) = 0.
-3, 2
Let n be ((-1)/(-6))/((-48)/(-864)). Factor -3/2*s**2 - 1/4*s**4 - 5/4*s**n + 2 + s.
-(s - 1)*(s + 2)**3/4
Let r(x) be the third derivative of -x**5/12 - 5*x**4/8 + 10*x**3/3 - 2*x**2 - 40*x. Factor r(g).
-5*(g - 1)*(g + 4)
Let w = -24347/780 + 406/13. Let g(s) be the second derivative of 0*s**2 + 2*s + 1/24*s**4 - w*s**6 - 1/24*s**3 + 0 + 1/80*s**5. Suppose g(l) = 0. What is l?
-1, 0, 1/2, 1
Let h(i) be the second derivative of -1/24*i**3 - i + 1/80*i**5 + 0 + 0*i**4 + 0*i**2. Factor h(f).
f*(f - 1)*(f + 1)/4
Let v(w) be the second derivative of 1/60*w**4 + 0 + 1/10*w**3 - 23*w + 0*w**2. Factor v(l).
l*(l + 3)/5
Let w be 8/32 + (-7)/(-4). Suppose 3*z - 2*z = w. Factor 0 - 3*y + 6 - 7*y**2 + 3*y**2 + y**z.
-3*(y - 1)*(y + 2)
Suppose -4*y + y = -2*u + 7, -2*y + 22 = 4*u. Factor -1 - 16*f**2 - 6*f**4 + f**u + 63*f - 54*f - 1 + 14*f**3.
(f - 2)*(f - 1)**4
Let t(h) be the third derivative of h**6/360 - h**5/5 + 6*h**4 - 14*h**3/3 - 3*h**2. Let r(v) be the first derivative of t(v). What is i in r(i) = 0?
12
Factor -8/9 - 2/9*q**2 - 8/9*q.
-2*(q + 2)**2/9
Suppose -5*h = -2*i - 2*i + 33, -3*i = 2*h + 4. Let o(a) = -2*a**2 - 10*a - 11. Let j(n) = 2*n**2 + 10*n + 10. Let g(s) = i*o(s) + 3*j(s). Factor g(u).
2*(u + 1)*(u + 4)
Factor 10*u**2 - 5/4*u**3 + 15 - 95/4*u.
-5*(u - 4)*(u - 3)*(u - 1)/4
Let n(h) be the first derivative of -h**3/18 + 11*h**2/12 - 5*h/3 + 9. Suppose n(q) = 0. Calculate q.
1, 10
Let c(l) be the first derivative of -l**6/1620 + 2*l**5/135 - 4*l**4/27 + 2*l**3 + 19. Let y(k) be the third derivative of c(k). Factor y(z).
-2*(z - 4)**2/9
Suppose 0 = -70*s + 72*s - 22. Let 3125*a**2 + 9 + 309*a + 0 + s + 191*a = 0. What is a?
-2/25
Let y be (0 - 4) + (-12 - (-1026)/63). Let h = 6/35 + 2/5. Factor y*a**2 + h*a - 6/7.
2*(a - 1)*(a + 3)/7
Let m(r) be the second derivative of r**6/165 + 38*r**5/55 + 722*r**4/33 - 267*r. Factor m(g).
2*g**2*(g + 38)**2/11
Let f(u) = 0*u**2 + 2*u**2 + 2*u**3 - 528 + u**4 + 529. Let d(l) = -l**4 - l**3 - 1. Let a(t) = -4*d(t) - 2*f(t). Factor a(c).
2*(c - 1)**2*(c + 1)**2
Let v(i) be the first derivative of i**5/10 - 25*i**4/8 - 53*i**3/6 - 27*i**2/4 - 51. Determine l, given that v(l) = 0.
-1, 0, 27
Suppose 0*c = 4*c - 72. Let g = c + -12. Determine n, given that g*n - 4*n - 2*n + 8 - 2*n**2 = 0.
-2, 2
Let k be 3 - (8 + 93/(-18)). Factor 0 + 1/6*d**3 - k*d**2 - 1/3*d.
d*(d - 2)*(d + 1)/6
Let n be -18 + (11 - (-13 + 3)). Factor 1/2*d**n + 0 + 0*d - 1/2*d**2.
d**2*(d - 1)/2
Suppose 5*y + 39 - 69 = 0, 3*y - 22 = -2*r. Determine g, given that 1/9*g**3 + 2/9 + 5/9*g + 4/9*g**r = 0.
-2, -1
Let v(y) = -2003*y**2 + 4 + 2002*y**2 - 5 + y. Let o(z) = 9*z**2 - 104*z + 504. Let d(c) = o(c) + 4*v(c). Factor d(r).
5*(r - 10)**2
Let h = 12 - 12. Let i(u) be the third derivative of -1/48*u**4 + u**2 + 0*u + 0*u**3 + h + 1/240*u**5. Determine a, given that i(a) = 0.
0, 2
Factor -q**3 - 2*q**3 - 3*q**4 + 11*q**3 - 3*q**2 - 2*q**3.
-3*q**2*(q - 1)**2
Suppose -32*z + 22 = 25*z - 46*z. What is a in 1/6*a**4 + 1/6*a**3 + 0*a**z + 0*a + 0 = 0?
-1, 0
Let a = 205 - 1024/5. Let j(o) be the first derivative of 0*o**3 - 1/5*o**2 - 1/25*o**5 + 2 + a*o + 1/10*o**4. Factor j(y).
-(y - 1)**3*(y + 1)/5
Let t(u) = u**2 - 2*u - 5. Let m(x) = -x**2 + 4. Let n(c) = -2*m(c) - 3*t(c). Factor n(q).
-(q - 7)*(q + 1)
Let y(c) be the first derivative of -25/2*c**4 + 50/3*c**3 + 5*c**5 - 25/2*c**2 + 5*c - 5/6*c**6 + 13. Factor y(a).
-5*(a - 1)**