*3/3 - 18*u**2 - 71*u/2 - 415. Factor t(l).
(l - 1)*(l + 1)**2*(l + 71)/2
Factor 1/4*m - 1/4*m**3 + 0 + 1/4*m**4 - 1/4*m**2.
m*(m - 1)**2*(m + 1)/4
Let u(s) be the first derivative of -s**7/168 + s**5/24 - 5*s**3 + 13. Let m(p) be the third derivative of u(p). Suppose m(t) = 0. Calculate t.
-1, 0, 1
Factor 4/7*h**4 + 0 + 0*h - 72/7*h**2 + 68/7*h**3.
4*h**2*(h - 1)*(h + 18)/7
Suppose 15 = 6*r - 9. Let s(a) be the third derivative of 4*a**2 + 1/3*a**3 - 1/30*a**5 - 1/120*a**6 + 0*a + 1/24*a**r + 0. Find w, given that s(w) = 0.
-2, -1, 1
Factor 0 - 2/3*s - 16/9*s**2 - 10/9*s**3.
-2*s*(s + 1)*(5*s + 3)/9
Let s(d) = -27*d**2 - 81*d + 12. Let p(z) = -2*z**2 - z + 1. Let k(w) = -12*p(w) + s(w). Let k(u) = 0. Calculate u.
-23, 0
Let f be 30/(-9)*(-72)/180. Let m = 1 - -2. Factor f*w**m + 2*w**2 + 1/3*w**4 + 1/3 + 4/3*w.
(w + 1)**4/3
Let o(n) be the first derivative of -2/9*n**3 + 6*n - 31 + 8/3*n**2. Solve o(u) = 0.
-1, 9
Let u(h) be the first derivative of -3*h**4/28 - 103*h**3/7 - 600*h**2/7 - 1188*h/7 - 330. Factor u(k).
-3*(k + 2)**2*(k + 99)/7
Let m(x) be the first derivative of -x**4/2 - 2*x**3 + 8*x - 104. Find t such that m(t) = 0.
-2, 1
Let o be -4*(-5)/(-20) - -7. Let k(m) be the second derivative of 0*m**5 + 1/45*m**o + 1/18*m**3 + 0 - 5*m - 1/18*m**4 - 1/126*m**7 + 0*m**2. Factor k(n).
-n*(n - 1)**3*(n + 1)/3
Factor -2 + 239*j**2 - 241*j**2 - 74 - 42*j.
-2*(j + 2)*(j + 19)
Let y(k) be the first derivative of 4*k**5/35 - 4*k**4/7 - 4*k**3 + 467. Factor y(n).
4*n**2*(n - 7)*(n + 3)/7
Factor -3066*f - 3*f**2 - 117 + 42 + 3144*f.
-3*(f - 25)*(f - 1)
Determine o so that -27*o**2 + 10 + 14*o + 19*o - 10 + 36*o**4 - 30*o**3 - 9*o**2 - 3*o**5 = 0.
-1, 0, 1, 11
Suppose -12*r - 7*r = -5*r. Let g(w) be the second derivative of r - w**2 - 1/54*w**4 + 2/9*w**3 + 4*w. Solve g(c) = 0.
3
Let v be (9 - (34 + -7)/3)/(-2). Find y such that v - y**2 + 0*y + 19/2*y**3 = 0.
0, 2/19
Let s = 102 + -102. Let f(r) be the third derivative of 0*r + 1/60*r**5 + 1/12*r**4 + s + 4*r**2 + 0*r**3. Determine j, given that f(j) = 0.
-2, 0
Suppose 0 = -373*s + 370*s. Let d(v) be the first derivative of s*v**3 + 0*v + 4/5*v**5 + 0*v**2 + 2 + 0*v**4 + 2/3*v**6. Let d(b) = 0. What is b?
-1, 0
Let c(q) = -7*q**4 - 3*q**3 - 8*q**2 - 12*q + 6. Let g(s) = -6*s**4 - 2*s**3 - 7*s**2 - 10*s + 5. Let r(t) = -5*c(t) + 6*g(t). Factor r(d).
-d**2*(d - 2)*(d - 1)
Let k be ((-7029)/3834)/((-22)/2). Factor 0*u + 0 - k*u**2.
-u**2/6
Suppose 10 + 9 - 16*t**3 - 128*t + 15*t**3 + 9*t**3 + 94*t**2 + 7 = 0. Calculate t.
-13, 1/4, 1
Let h be (-4)/(-4)*0/(-1). Suppose -34*v + 32*v + 4 = h. Suppose 4/5*u - 6/5*u**v + 0 + 2/5*u**3 = 0. Calculate u.
0, 1, 2
Let f(o) be the second derivative of o**9/52920 - o**7/980 - o**6/630 + o**5/35 - 3*o**4/4 + 2*o + 11. Let q(a) be the third derivative of f(a). Factor q(d).
2*(d - 3)*(d - 1)*(d + 2)**2/7
Suppose 6*h**2 - 3*h**2 - 5*h**3 - 149*h**4 - 4*h**3 + 146*h**4 + 3*h**5 + 6*h = 0. What is h?
-1, 0, 1, 2
Suppose -13*z - 18*z = 31*z - z. Factor -1/4*r + 1/4*r**3 + z - 1/8*r**4 + 1/8*r**2.
-r*(r - 2)*(r - 1)*(r + 1)/8
Let q = 2/761 + 3801/1522. Let u(a) be the first derivative of 2/5*a**5 + q*a**3 + 1/2*a + 7/4*a**2 + 13/8*a**4 + 1. Factor u(m).
(m + 1)**3*(4*m + 1)/2
Let n be (6/28)/((3456/(-84))/(-16)). Let w(v) be the first derivative of -1/8*v**2 + 9 + 0*v + n*v**3. Suppose w(i) = 0. What is i?
0, 1
Suppose -76246*i + 5*i**3 + 76246*i + 16*i**2 - i**3 = 0. Calculate i.
-4, 0
Let f = 6765 - 6763. Factor -1/6*l**3 - 5/6*l**f - 2/3 - 4/3*l.
-(l + 1)*(l + 2)**2/6
Determine s so that -48*s**2 + 6*s**3 - 21 + 57 + 27*s**2 + 3*s**4 - 24*s = 0.
-3, -2, 1, 2
Find n such that -7 + 69*n**2 + 169*n**4 + 443*n**3 + 44*n + 11 - 729*n**3 = 0.
-2/13, 1
Let c(k) be the second derivative of 3*k**5/40 - 25*k**4/4 + 97*k**3/4 - 36*k**2 + 8*k - 27. Factor c(s).
3*(s - 48)*(s - 1)**2/2
Let g be 3/12 + (-9555)/572 + 17. Find k, given that 36/11 + g*k**2 + 30/11*k = 0.
-3, -2
What is x in 0 - 44/17*x**2 + 0*x + 2/17*x**4 - 18/17*x**3 = 0?
-2, 0, 11
Suppose -3*g = -2 + 173. Let w = 343/6 + g. Suppose -1/3 + 1/6*r**2 - 1/2*r + 1/2*r**3 + w*r**4 = 0. What is r?
-2, -1, 1
Let h(d) = 8*d**2 - 81*d + 94. Let z(q) = q**2 - 10*q + 12. Let n(c) = -6*h(c) + 51*z(c). Determine k so that n(k) = 0.
4
Let k = -7446 - -7449. Factor -8/5*l + 8/5*l**k - 4/5*l**4 + 0 + 4/5*l**2.
-4*l*(l - 2)*(l - 1)*(l + 1)/5
Let i(b) be the third derivative of -1/204*b**4 - 1/255*b**5 + 0*b - 1/1020*b**6 - 3*b**2 + 0*b**3 + 0. Factor i(m).
-2*m*(m + 1)**2/17
Suppose 8/7*u**3 + 16/7 + 20/7*u**4 - 60/7*u**2 + 16/7*u = 0. Calculate u.
-2, -2/5, 1
Let z(t) = -t**3 - 8*t**2 - 10*t - 75. Let d be z(-8). Factor -1/4*v**3 + 0 - 1/4*v**d - 1/2*v**4 + 0*v + 0*v**2.
-v**3*(v + 1)**2/4
Let j(t) be the second derivative of -7*t**7/66 - 259*t**6/330 - 87*t**5/44 - 75*t**4/44 - t + 15. Factor j(w).
-w**2*(w + 1)*(7*w + 15)**2/11
Let s(y) be the second derivative of -y**5/20 + 3*y**3/2 + y**2 + 12*y. Let i be s(3). Factor 1/4*d**4 - 1/4*d**i + 0 - 1/4*d**3 + 1/4*d.
d*(d - 1)**2*(d + 1)/4
Let w = -2748 - -2751. Let v(t) be the first derivative of 6*t - 9 - 3*t**w + 15/2*t**2. Factor v(i).
-3*(i - 2)*(3*i + 1)
Suppose d**3 - 17*d**2 + 4*d**3 + 5*d + 35 + 8*d**2 - 11*d**2 - 5 = 0. Calculate d.
-1, 2, 3
Let a(z) be the second derivative of -z**5/5 - 7*z**4/3 - 10*z**3 - 18*z**2 + 9*z + 3. Find k such that a(k) = 0.
-3, -1
Let h(k) be the third derivative of 1/150*k**6 + 0*k**5 + 0 + 0*k + 1/420*k**8 - 4/525*k**7 + 0*k**4 - 20*k**2 + 0*k**3. Determine l so that h(l) = 0.
0, 1
Let i(m) be the third derivative of 0*m**3 - 7*m**2 - 1/120*m**5 - 1/96*m**4 + 0*m + 0 - 1/480*m**6. Solve i(a) = 0 for a.
-1, 0
Let g(q) = -q**2 + 4*q. Suppose -4*t = -3*u - 21, 0*t + 3*t + 3 = -4*u. Let x be g(t). Suppose -7*z + z**x + 3*z - 3*z**3 - 6*z**2 = 0. Calculate z.
-2, -1, 0
Let r(l) be the first derivative of l**5 - 5/3*l**3 - 5/2*l**4 + 0*l + 5*l**2 + 5. Factor r(g).
5*g*(g - 2)*(g - 1)*(g + 1)
Let -33*a**3 - 29 + 17 - 195*a**4 - 21*a**5 + 195*a**2 + 12 + 54*a = 0. What is a?
-9, -1, -2/7, 0, 1
Let j(l) = l**2 + l. Let d(t) = 22*t**2 + 966*t + 632. Let x(h) = -d(h) + 10*j(h). Factor x(n).
-4*(n + 79)*(3*n + 2)
Let b = 73/133 + -5/19. Let v be (-94)/14 + (-23 - -30). Find x, given that -v*x**3 + 8/7*x**2 - 8/7*x**4 + b*x + 0 = 0.
-1, -1/4, 0, 1
Let q = -6258 - -6260. Factor 2/7*j + 15/7*j**3 + 9/7*j**q + 0 + 11/7*j**4 + 3/7*j**5.
j*(j + 1)**3*(3*j + 2)/7
Let 8/3*a**3 + 0*a + 0 - 2/3*a**5 + 8*a**2 - 2*a**4 = 0. What is a?
-3, -2, 0, 2
Solve -9/2*b**2 + 0 + 40/3*b**4 + 4*b**3 + 2/3*b = 0 for b.
-4/5, 0, 1/4
Solve -8/7 + 16/7*r + 10/7*r**2 = 0.
-2, 2/5
Let d(r) be the third derivative of 0*r + 0 + 1/80*r**5 - 3*r**2 - 1/8*r**4 + 0*r**3. Find q, given that d(q) = 0.
0, 4
Let k(d) be the second derivative of 9/2*d**3 + 27*d**2 + 3/8*d**4 + 2*d + 0 + 1/80*d**5. Factor k(n).
(n + 6)**3/4
Let f(u) be the third derivative of u**7/1680 - 7*u**6/480 + 3*u**5/40 - u**4/8 + 10*u**2. Let z(l) be the second derivative of f(l). Solve z(o) = 0.
1, 6
Suppose -13*u + 59*u = -102*u + 1776. Factor -243/2*f**5 + 0*f + 0 - 2*f**2 + u*f**3 + 27/2*f**4.
-f**2*(3*f + 1)*(9*f - 2)**2/2
Let r = -7256/87 + 60/29. Let f = 82 + r. Factor 0*n + 0 - 2/3*n**2 - f*n**3.
-2*n**2*(n + 1)/3
Find s, given that 15*s + 9/2*s**3 - 51/2*s**2 + 0 = 0.
0, 2/3, 5
Suppose -2*k - 21 = -25. Suppose 12*v + 4 = 14*v. Let 4/5 + k*d + 2/5*d**3 + 8/5*d**v = 0. Calculate d.
-2, -1
Let i(d) be the first derivative of d**8/1512 - d**6/270 + d**4/108 - 15*d**2 + 1. Let v(o) be the second derivative of i(o). Solve v(z) = 0 for z.
-1, 0, 1
Let m(f) be the second derivative of f**7/1800 - f**6/1200 - f**5/150 - 8*f**4/3 - 11*f. Let w(o) be the third derivative of m(o). Factor w(v).
(v - 1)*(7*v + 4)/5
Suppose 4 = 4*t + d, 6*d = -2*t + 7*d + 2. Let w(o) = 4*o**3 - o**2 + o - 1. Let v be w(t). Factor -4/3*k**v + 0 - 2/3*k**4 + 4/3*k + 2/3*k**2.
-2*k*(k - 1)*(k + 1)*(k + 2)/3
Let v(y) = -9*y**3 + 168*y**2 - 1262*y - 3238. Let o(n) = 245*n**3 - 4535*n**2 + 34075*n + 87425. Let u(r) = -2*o(r) - 55*v(r). Solve u(f) = 0.
-2, 18
Let s be (4 - 8) + 1/((-2)/(-8)). Let g(k) be the second derivative of -1/24*k**4 + k + 1/12*k**3 + s + 0*k**2. Factor g(t).
-t*(t - 1)/2
Let v = 14 + -10. Suppose 2*a = -4*g + 30, -8*a =