- f**5/480 + 5*f**4/12 + 5*f**3/6 - 32*f. Let g(v) be the third derivative of t(v). Factor g(y).
(y - 1)*(y + 1)/4
Let x = 2978 - 2978. Let d(c) be the third derivative of x + 0*c - 26*c**2 - 2/75*c**5 - 1/30*c**4 + 1/5*c**3 + 1/150*c**6 + 1/525*c**7. Factor d(t).
2*(t - 1)**2*(t + 1)*(t + 3)/5
Factor -470450/11 - 2/11*m**2 + 1940/11*m.
-2*(m - 485)**2/11
Let o(s) be the first derivative of 24/5*s**3 - 68 + 6/25*s**5 - 9/5*s**4 - 24/5*s**2 + 0*s. Factor o(c).
6*c*(c - 2)**3/5
Let h be (-13)/(-13)*(949 + 0). Let x = -947 + h. Let 2/9*a**x + 2/3*a**4 + 0*a + 0 + 8/9*a**3 = 0. Calculate a.
-1, -1/3, 0
Suppose 2*y + 16*y - 180 = 0. Determine v so that -v**3 - 13*v**2 + 7*v**2 - 8 + y*v**2 - 10*v**2 - 12*v = 0.
-2
Let g(n) = -21*n**3 + 62*n**2 - 50*n - 1374. Let u(v) = -2*v**3 + 4*v**2 - v - 2. Let c(x) = -2*g(x) + 22*u(x). Factor c(h).
-2*(h - 8)*(h + 13)**2
Let c(i) be the third derivative of -i**7/10 + i**6/40 + 7*i**5/20 - i**4/8 - 6*i**2 + 83*i. Factor c(r).
-3*r*(r - 1)*(r + 1)*(7*r - 1)
Let u(t) = 96*t**3 + 575*t**2 + 8*t + 148. Let y be u(-6). What is s in -7/2*s**3 - 107/2*s**2 - y*s - 14 = 0?
-14, -1, -2/7
Let p(r) = 8*r**3 + 28*r**2 - 36*r - 76. Let y(a) = 7*a**3 + 29*a**2 - 38*a - 75. Let x(q) = 3*p(q) - 4*y(q). Factor x(t).
-4*(t - 2)*(t + 1)*(t + 9)
Let w(t) = -31*t**2 - 2446*t - 4936. Let j(u) = -9*u**2 + u - 4. Let z(m) = 4*j(m) - w(m). Solve z(l) = 0 for l.
-2, 492
Let v(j) be the third derivative of 1/90*j**7 - 9*j**2 + 0*j**3 + 0*j**4 - 5/12*j**5 - 1/1008*j**8 + 1/72*j**6 - 4 + 0*j. Factor v(n).
-n**2*(n - 5)**2*(n + 3)/3
Factor 434/3*n - 433/3*n**2 - 1/3*n**3 + 0.
-n*(n - 1)*(n + 434)/3
Let g be (-33)/(-11286)*266*(-338)/(-7). What is n in -g - 2/9*n**2 - 52/9*n = 0?
-13
Factor 130*k + 3*k**4 + k**2 + 3*k**3 - 18 - 22*k**2 - 169*k.
3*(k - 3)*(k + 1)**2*(k + 2)
Let g(p) be the third derivative of 0*p**3 - 35/12*p**4 - 13/12*p**5 - 1/8*p**6 - 35*p**2 + 0 - p. Factor g(r).
-5*r*(r + 2)*(3*r + 7)
Let l(j) be the third derivative of 0 + 47*j**2 + 0*j - 1/180*j**5 - 13/1260*j**7 + 0*j**3 + 0*j**4 + 13/720*j**6 - 1/72*j**8. Find v, given that l(v) = 0.
-1, 0, 1/4, 2/7
Let t = 2453 - 2441. Let m(n) be the second derivative of -1/3*n**4 + 17/40*n**5 - 1/24*n**3 + 1/24*n**7 + 1/4*n**2 - t*n - 13/60*n**6 + 0. Factor m(i).
(i - 1)**4*(7*i + 2)/4
Let s be -8 + ((-52)/(-6))/(296/444). Suppose 2 = -0*r + r. Find i, given that 8/5*i - 2/5*i**3 - 16/5 - 48/5*i**4 + 52/5*i**r - 18/5*i**s = 0.
-2, -1, 2/3
Let o = -946 + 955. Let a be (10/(-7))/((-114)/(-14) - o). What is p in -a*p + 0 - 10/3*p**5 - 40/3*p**4 - 35/2*p**3 - 55/6*p**2 = 0?
-2, -1, -1/2, 0
Let m(b) be the first derivative of -3*b**4 - 43*b**3 + 177*b**2/2 - 36*b - 1293. Let m(x) = 0. What is x?
-12, 1/4, 1
Solve 0 - 4/7*n**4 + 976/7*n**3 - 2900/7*n**2 + 1928/7*n = 0 for n.
0, 1, 2, 241
Let i(k) be the third derivative of 3*k**2 - 1/15*k**5 - 1/6*k**4 + 2/3*k**3 + 1/30*k**6 + k + 0. Factor i(d).
4*(d - 1)**2*(d + 1)
Let s(k) = 4*k**3 - 3*k + 2. Let x be s(1). Solve -2*t**2 - 27*t + 3 - 19*t + 42*t + x = 0.
-3, 1
Let 34 - 858*a + 59 + 165 + 174*a + 424 + 2*a**2 = 0. Calculate a.
1, 341
Let k(i) be the first derivative of -3/2*i**3 - 152 - 18*i + 147/4*i**2 - 3/2*i**4. Let k(o) = 0. What is o?
-4, 1/4, 3
Let w(n) be the second derivative of 0 - 9*n - 4/5*n**3 - 3/100*n**5 + 8*n**2 + 7/20*n**4. Let q(m) be the first derivative of w(m). Let q(o) = 0. What is o?
2/3, 4
Let p(x) be the third derivative of 0 + 0*x**3 - 5/42*x**4 + x - 1/210*x**5 - 6*x**2. Factor p(d).
-2*d*(d + 10)/7
Let u be 5/((-30)/4)*9/(-6). Let x(l) = 4*l**3 - l**2 + 1. Let q be x(u). Factor -3532*w + 3532*w + 3*w**q.
3*w**4
Let -100*u**2 + 96 - 96*u**2 - 85*u**2 + 98*u + 283*u**2 = 0. Calculate u.
-48, -1
Let f(d) be the second derivative of 1/10*d**5 - 15 - 1/3*d**3 - 3*d**2 + 1/2*d**4 + 2*d. Factor f(c).
2*(c - 1)*(c + 1)*(c + 3)
Let y(a) = a**3 + a**2 - 1. Let x(d) be the first derivative of -17 + d**3 - 3*d**2 - 7/4*d**4 + 5*d. Let w(f) = -x(f) - 5*y(f). What is i in w(i) = 0?
0, 1, 3
Let x(t) be the second derivative of 0*t**3 + 0*t**2 - 1/15*t**6 + 1 + 1/10*t**5 + 33*t + 0*t**4. Factor x(z).
-2*z**3*(z - 1)
Let l be (1/2)/(42/8988). Suppose -111 = -r - l. Let 2/3*d**r - 4/3*d**3 + 2/3*d**5 + 2/3*d - 4/3*d**2 + 2/3 = 0. What is d?
-1, 1
Let y(b) be the third derivative of -b**6/240 - 67*b**5/60 - 533*b**4/192 - 133*b**3/48 + 4*b**2 + 982. Solve y(k) = 0.
-133, -1/2
Suppose 10*c - 57 = 43. Suppose -25*f**2 + c*f - 40 - 40*f + 20*f**2 = 0. What is f?
-4, -2
Let s(c) be the third derivative of c**6/1440 + 7*c**5/3 + 9800*c**4/3 + 21952000*c**3/9 + 81*c**2 - 1. Suppose s(t) = 0. Calculate t.
-560
Suppose 50 = 14*s + 11*s. Let f = 91/363 - -10/121. Factor 1/3*i**3 + 0*i**s - f*i + 0.
i*(i - 1)*(i + 1)/3
Let f = 625/748 - 16/187. Solve f + 27/8*h**2 - 21/8*h + 3/8*h**4 - 15/8*h**3 = 0.
1, 2
Let g(h) be the third derivative of h**5/20 + 3*h**4/8 - 54*h**3 + 556*h**2. Factor g(q).
3*(q - 9)*(q + 12)
Suppose -20 = -2*s - 2*f, 4*s - 93 = -2*f - 69. Factor 4/5*o**5 + 0*o**s + 0*o - 8/5*o**4 + 0 + 4/5*o**3.
4*o**3*(o - 1)**2/5
Suppose -4*q + 96 = 2*q. Suppose 8*p - q = -0*p. Determine t, given that t**3 - 5*t**p - 5*t**3 - 3*t**2 + 0*t**2 = 0.
-2, 0
Let w(p) be the second derivative of -p**7/84 - 31*p**6/60 + 33*p**5/20 - p**4/12 - 65*p**3/12 + 33*p**2/4 + 769*p. Factor w(l).
-(l - 1)**3*(l + 1)*(l + 33)/2
Find n such that -1/5*n**2 - 7/5*n + 8/5 = 0.
-8, 1
Suppose 12992/3*p + 25088/3 - 4106*p**2 - 223/3*p**3 - 1/3*p**4 = 0. What is p?
-112, -1, 2
Suppose 0*p + 8 = 2*p - 4*s, 3*p - 52 = -2*s. Suppose 5*h - 9 = 4*h. Factor 26 - h*i**2 + p*i**2 - 6 - 20*i.
5*(i - 2)**2
Factor 224*d**2 - 13 + 8 - 13*d**3 + 5 + 9*d**3 - 3136*d.
-4*d*(d - 28)**2
Let f(a) be the first derivative of -a**5/5 + 401*a**4/4 - 133*a**3 - 401*a**2/2 + 400*a + 1155. Factor f(h).
-(h - 400)*(h - 1)**2*(h + 1)
Let i(k) = -54*k**2 - 3751 - 26*k**2 + 60*k + 1871 + 1876. Let s(n) = -24*n + 4*n**2 + 0 + 2 + 28*n**2. Let q(p) = -5*i(p) - 12*s(p). Factor q(m).
4*(m - 1)*(4*m + 1)
Let h(y) = -2*y**2 - 80*y - 348. Let p be h(-35). Let j(w) be the second derivative of 0*w**p + 9*w + 2/21*w**3 + 1/42*w**4 + 0. Factor j(t).
2*t*(t + 2)/7
Let i(a) = 17*a**3 + 99*a**2 - 31*a + 30. Let v(c) = 42*c**3 + 248*c**2 - 78*c + 72. Let t(k) = -12*i(k) + 5*v(k). Factor t(x).
2*x*(x + 9)*(3*x - 1)
Suppose 31*q = 25*q. Let 0 - 2*j - 2*j**2 + 1 - 1 + 2*j**3 + 2 + q = 0. What is j?
-1, 1
Let c = 322 + -324. Let i(z) = -190*z**2 - 1460*z - 3430. Let u(f) = 7*f**2 + 54*f + 127. Let d(a) = c*i(a) - 55*u(a). Factor d(r).
-5*(r + 5)**2
Let v(c) be the third derivative of -c**6/20 - 68*c**5/15 + 23*c**4/3 + 3086*c**2. Factor v(j).
-2*j*(j + 46)*(3*j - 2)
Suppose -174/7*c**3 + 177/7*c - 48/7*c**4 - 12*c**2 + 132/7 - 3/7*c**5 = 0. Calculate c.
-11, -4, -1, 1
Let m(u) = -32*u**3 - 232*u**2 + 1288*u + 1500. Let c(f) = -19*f**3 - 139*f**2 + 773*f + 900. Let w(g) = 12*c(g) - 7*m(g). Solve w(a) = 0 for a.
-15, -1, 5
Factor 0 - 52/3*w**2 + 0*w - 17/3*w**3 - 1/3*w**4.
-w**2*(w + 4)*(w + 13)/3
Let o be (-1 + (-2 - -4))/(18/12834). Suppose 737 - 3*x**3 + o - 1474 - 36*x - 18*x**2 = 0. What is x?
-2
Let l be 6/(-2 + 26)*8. Let -126*a + 686 + 374*a + 42*a**2 + 46*a + l*a**3 = 0. What is a?
-7
Let z(r) = -1424*r**2 - 16*r + 16. Let v be z(1). Let d = v - -1426. Solve -15/7*u**4 - 3*u + 3*u**3 + 6/7 + 9/7*u**d = 0 for u.
-1, 2/5, 1
Determine t, given that 5/3*t**4 - 49/3*t**2 + 8/3*t + 3*t**3 + 20 - 1/3*t**5 = 0.
-3, -1, 2, 5
Suppose 3*p - 57 = -w, 0 = -7*w + 4*w - 18. Let k(x) be the first derivative of -2*x**5 - 20*x + 5/2*x**2 + 20*x**3 - p + 25/4*x**4. Let k(y) = 0. What is y?
-1, 1/2, 4
Let q(n) be the first derivative of -n**3/4 - 597*n**2/2 - 118803*n + 459. Factor q(a).
-3*(a + 398)**2/4
Let p(g) be the third derivative of 0*g**3 + 1/336*g**8 + 0 - 89*g**2 - 1/60*g**6 + 0*g**7 + 0*g**5 + 1/24*g**4 + 0*g. Factor p(n).
n*(n - 1)**2*(n + 1)**2
Suppose 5*r - 21 = 44. Suppose -2*n - 11*q = -8*q + 11, q = 4*n - r. Factor -16/5*a**2 - n*a**3 - 2/5*a + 4/5.
-2*(a + 1)**2*(5*a - 2)/5
Suppose 0 = -o + 2, -21 = 2*q - 7*q - 3*o. Suppose -80*j + 24*j**3 + 15 - 30*j**3 - 4*j**3 + 35*j**4 + 150*j**2 - 116*j**q + 6*j**3 = 0. What is j?
3/7, 1
Let m = 1468/9 + -1465/9. Let o(v) be the third derivative of -8*v*