3 + 7/2*i**2 - 1/4*i**4. Let n(w) be the second derivative of t(w). Factor n(q).
2*q*(q - 3)
Let l(t) = 1 - 18*t + 16*t + 1. Let c be l(-10). Let -3*o**2 + 12*o**4 - 1 - 2*o**5 + 29*o - c*o**3 - 5*o - 15 + 7*o**2 = 0. Calculate o.
-1, 1, 2
Factor 35*m - 30*m**3 - 42*m**3 + 7*m**3 - 9*m**4 - 22*m**3 + 13*m - 114*m**2.
-3*m*(m + 2)*(m + 8)*(3*m - 1)
Let k = 82 + -71. Let j be (-10)/(-25) - k/(-10). Factor -j*s**2 + 1/2 - s.
-(s + 1)*(3*s - 1)/2
Factor -2*y**3 + 5*y**5 + 5*y**3 - 2*y**3 - 8*y**4 + 2*y**2.
y**2*(y - 1)**2*(5*y + 2)
Let a = 10271/10 + -1027. Solve 3/10*k + 1/10*k**3 + 3/10*k**2 + a = 0.
-1
Let z(m) be the first derivative of -m**5/30 - m**4/9 + m**3/3 - 16*m + 16. Let w(t) be the first derivative of z(t). Factor w(v).
-2*v*(v - 1)*(v + 3)/3
Let g(n) = -5*n**2 + 3*n - 4. Let m(r) = 9*r**2 - 5*r + 7. Let v(w) = -7*g(w) - 4*m(w). Let u(o) = -7*o**2 - 9*o. Let b(s) = 3*u(s) - 24*v(s). Factor b(p).
3*p*(p - 1)
Let u(k) be the third derivative of -k**6/160 - 9*k**5/80 - k**4/4 + 63*k**2. Factor u(c).
-3*c*(c + 1)*(c + 8)/4
Solve -123*a**2 - 68 + 56 - 3*a**3 - 15*a - 222*a - 105 = 0.
-39, -1
Factor 4/7*t - 10/7*t**2 + 0 + 6/7*t**3 + 2/7*t**4 - 2/7*t**5.
-2*t*(t - 1)**3*(t + 2)/7
Let h(k) be the third derivative of 0*k - 2*k**2 + 0 + 1/840*k**7 + 0*k**4 + 1/1344*k**8 + 0*k**5 + 0*k**3 + 0*k**6. Factor h(w).
w**4*(w + 1)/4
Suppose 325*i - 474 = 167*i. Factor 0*q**2 - 6/23*q - 4/23 + 2/23*q**i.
2*(q - 2)*(q + 1)**2/23
Let f(l) be the second derivative of -l**4/12 + l**3/3 - l**2/2 - 50*l. Let f(a) = 0. Calculate a.
1
Let n(t) = t**2 + 2*t + 16. Let p(q) be the third derivative of -q**4/24 - q**3/6 + 20*q**2. Let f(d) = -3*n(d) - 24*p(d). Solve f(l) = 0 for l.
2, 4
Let r(s) be the second derivative of -s**4/42 + 23*s**3/21 + 108*s**2/7 - 31*s + 4. Determine a so that r(a) = 0.
-4, 27
Let q(g) be the third derivative of g**8/1008 - g**7/630 - g**6/360 + g**5/180 + 4*g**2 + 5. Factor q(b).
b**2*(b - 1)**2*(b + 1)/3
Let w(m) be the first derivative of 7*m**4/30 + 34*m**3/45 - 4*m**2/5 - 211. Factor w(d).
2*d*(d + 3)*(7*d - 4)/15
Determine s so that -2/5*s**3 + 38/5*s**2 + 0 - 36/5*s = 0.
0, 1, 18
Suppose 242 = 4*x - 2*y, -3*x + y + 2*y = -186. Suppose 3*z - 97 = x. Factor 16 + w**3 - 9*w**3 - 2*w**3 - 4*w**3 - 40*w - z*w**2.
-2*(w + 2)**2*(7*w - 2)
Let l(d) be the third derivative of 0*d**6 + 0*d**4 + 0*d**3 + 0*d + 2/45*d**5 - 1/315*d**7 + 11*d**2 + 0. Factor l(g).
-2*g**2*(g - 2)*(g + 2)/3
Suppose 57 = 6*r + 21. Factor h + 3*h - r*h + 4*h**4 + 2*h**5 - 4*h**2.
2*h*(h - 1)*(h + 1)**3
Let z = 47467/2 + -23733. Solve -3/2*f + 3/2*f**3 - 1 + 1/2*f**2 + z*f**4 = 0 for f.
-2, -1, 1
Let y = -27283 + 109147/4. Solve -9/4*t - 3/2 + y*t**2 = 0.
-2/5, 1
Suppose -17*x = -84 + 33. Suppose x*i - 9 = -3. Factor 0 + 2/3*q**3 + i*q**2 + 4/3*q.
2*q*(q + 1)*(q + 2)/3
Factor 6 + 111/2*p + 27/2*p**2.
3*(p + 4)*(9*p + 1)/2
Let x(u) = -2*u - 20. Let m be x(-11). Let 0*n + 0 + 4 + 2*n - 2*n**m = 0. What is n?
-1, 2
Let a(m) be the third derivative of -m**5/240 + 7*m**4/96 - 5*m**3/12 - 126*m**2. Determine q so that a(q) = 0.
2, 5
Let r(a) be the third derivative of 0*a + 0 - 2/3*a**3 + 1/6*a**5 + 1/3*a**4 - 7/90*a**6 - 6*a**2. Let w(d) be the first derivative of r(d). Factor w(f).
-4*(f - 1)*(7*f + 2)
Let y be 141 + (2 - -2 - 0). Factor -3*d**5 - y*d**4 + 145*d**4 + 3*d**3.
-3*d**3*(d - 1)*(d + 1)
Suppose 2*r**4 - 2*r**4 - 25*r**3 - 18*r**2 + 6*r**3 - r**4 = 0. What is r?
-18, -1, 0
Let g be (48/(-40))/(3/(-10)). Let y = -1372/5 + 276. Suppose -y*t**2 + 28/5*t**3 + 16/5*t**g + 0*t + 0 = 0. What is t?
-2, 0, 1/4
Factor -1083 + 186*o + o**3 + 417*o + 35*o**2 - 356*o.
(o - 3)*(o + 19)**2
Let r(f) be the third derivative of 1/45*f**5 + 1/6*f**4 - 21*f**2 + 0*f**3 + 0*f + 0. Factor r(m).
4*m*(m + 3)/3
Let f(d) be the first derivative of -4*d**5/7 - 62*d**4/7 - 316*d**3/21 - 44*d**2/7 - 66. What is b in f(b) = 0?
-11, -1, -2/5, 0
Solve 0 + 2/13*z**2 - 18/13*z = 0.
0, 9
What is k in -10*k**2 - 53*k + 13 + 58*k + 5*k**3 - 13 = 0?
0, 1
Let a be 10*((-12)/8 + 2). Factor a*v**3 + 333 + 44*v - 20*v**2 - 349 - 13*v**3.
-4*(v - 1)*(v + 4)*(2*v - 1)
Let c(t) be the third derivative of -t**6/120 + t**5/6 - 17*t**4/24 + 4*t**3/3 - 32*t**2 + t. Factor c(f).
-(f - 8)*(f - 1)**2
Let u be (1/4 + (-65)/4)/(-2). Suppose 3*t - 8 = -u. Factor 2/11*h**3 + 0 + 0*h + 2/11*h**4 + t*h**2.
2*h**3*(h + 1)/11
Let q(w) be the third derivative of -w**7/1260 - w**6/144 - w**5/120 + 5*w**4/144 + w**3/9 - 230*w**2. Factor q(h).
-(h - 1)*(h + 1)**2*(h + 4)/6
Let c = 2/13 - -25/91. Let x(k) = -k**3 + 5*k + 5. Let v be x(-2). Determine n so that -6/7 + 6/7*n**2 - c*n**v + 3/7*n = 0.
-1, 1, 2
Let n = -25982 - -25986. Let -14/11*b - 18/11*b**3 + 0 - 2/11*b**n - 30/11*b**2 = 0. Calculate b.
-7, -1, 0
Suppose 9/4*y**2 - 27/2 + 27/4*y - 7/4*y**3 + 1/4*y**4 = 0. What is y?
-2, 3
Let r = 8209/6 + -1368. Factor r*g - 1/6*g**2 + 0.
-g*(g - 1)/6
Let x(k) be the second derivative of 0 + 46*k - 17/21*k**3 + 17/21*k**4 + 17/70*k**5 - 12/35*k**6 + 2/7*k**2. Let x(w) = 0. What is w?
-1, 2/9, 1/4, 1
Find a such that 83*a**2 - 28*a**2 - 115*a**4 + 120*a**4 + 25*a + 35*a**3 = 0.
-5, -1, 0
Suppose 9*n = 11*n. Determine a, given that -3*a - 9*a + 4 + n*a - 4*a**3 + 16*a**2 - 4*a**2 = 0.
1
Let w = -104 - -51. Let k = 55 + w. Find b such that 0*b**3 + 2/5*b - 4/5*b**4 + 0 + 4/5*b**k - 2/5*b**5 = 0.
-1, 0, 1
Let w be ((-2)/5)/((-1)/5). Let m(q) be the second derivative of -1/15*q**6 - 1/3*q**4 - 3/10*q**5 + 0 + w*q + 0*q**2 + 0*q**3. Factor m(l).
-2*l**2*(l + 1)*(l + 2)
Let o = -302 + 371. Suppose 11 = -29*g + o. Factor 9/8 + 3/8*m**g + 3/2*m.
3*(m + 1)*(m + 3)/8
Let s(a) be the second derivative of 1/5*a**5 - 1/21*a**7 - 8/9*a**3 + 0*a**2 + 0 - 6*a - 7/45*a**6 + 2/3*a**4. Determine m, given that s(m) = 0.
-2, 0, 2/3, 1
Let s be (1311/(-18))/(-23)*(0 + 3). Find m, given that -s*m**3 + 1 - 3*m**4 - 7*m**2 + 1/2*m = 0.
-2, -1, -1/2, 1/3
Let a = 23 + -18. Suppose -3*m + 6 = 4*x, -a*m + 4 = x - 6. Find c such that 0*c - 2/5*c**2 - 1/5*c**3 + x + 1/5*c**4 = 0.
-1, 0, 2
Let m(b) be the second derivative of b**8/70560 + b**7/8820 + b**6/3780 - 2*b**4/3 + 6*b. Let j(y) be the third derivative of m(y). Solve j(h) = 0 for h.
-2, -1, 0
Let w be 5/(-15)*(-18)/12. Let r(s) be the first derivative of 7/10*s**5 + 0*s + 2 - 1/4*s**6 - 1/2*s**3 - 3/8*s**4 + w*s**2. Factor r(x).
-x*(x - 1)**3*(3*x + 2)/2
Let t(l) be the first derivative of -l**4/24 - 5*l**3/6 - 21*l**2/4 - 27*l/2 + 382. Suppose t(j) = 0. What is j?
-9, -3
Let q(k) be the first derivative of k**6/18 + 8*k**5/15 + k**4 - 2*k**3/9 - 13*k**2/6 - 2*k + 1. Factor q(w).
(w - 1)*(w + 1)**3*(w + 6)/3
Let m(c) be the first derivative of -47 - 5/4*c**4 - c**5 + 0*c**2 + 5/6*c**6 + 0*c + 5/3*c**3. Factor m(r).
5*r**2*(r - 1)**2*(r + 1)
Let g = 40 - 38. Suppose -30*f + 30*f - 3*f**3 + 3*f**g = 0. Calculate f.
0, 1
Let r(a) = -a - 16. Let b be r(-16). Let k(i) be the second derivative of -6*i**2 + i + b - 2*i**3 - 1/4*i**4. Factor k(u).
-3*(u + 2)**2
Let f = 55 - 51. Suppose -f*o = -8*o. Factor -n + 3/2*n**4 + o + n**3 - 3/2*n**2.
n*(n - 1)*(n + 1)*(3*n + 2)/2
Solve 76/3*a - 4/3*a**2 + 80/3 = 0.
-1, 20
Suppose g - 63 = 5*n, 4*n + 3*g + 15 = -24. Let i be 3*5*n/(-165). Factor 26/11*j + 10/11*j**2 - i.
2*(j + 3)*(5*j - 2)/11
Let s(t) be the third derivative of -1/210*t**5 - 1/84*t**4 + 2/7*t**3 + 0*t - 20*t**2 + 0. What is l in s(l) = 0?
-3, 2
Suppose 0 = -2*p + 7*p - 2*x - 42, -5*p + 3*x = -43. Let d = -4 + p. Find s, given that 0*s - 11*s**4 + 3*s**d + 2*s + 6*s**2 - 10*s**3 + 8*s + 2 = 0.
-1, -1/4, 1
Let j(n) = n**2 + 8*n + 11. Let o be j(-6). Let q be (-22 - o)*((-8)/60)/2. Factor l**2 - q*l + 2/5.
(l - 1)*(5*l - 2)/5
Let k(u) = -81*u**2 + 510*u - 432. Let j(o) = -o**3 + 241*o**2 - 1528*o + 1296. Let q(v) = 3*j(v) + 8*k(v). Factor q(c).
-3*(c - 12)**2*(c - 1)
Let b(m) be the first derivative of -2*m**6/21 + m**5/5 - 2*m**4/21 + 5*m + 12. Let y(u) be the first derivative of b(u). Determine s, given that y(s) = 0.
0, 2/5, 1
Let w(b) be the third derivative of -42*b**2 - 1/900*b**6 + 0*b + 1/225*b**5 + 0 + 1/180*b**4 - 2/45*b**3. Find x, given that w(x) = 0.
-1, 1, 2
Let d(z) be the third derivative of -z**7/210 + z**6/60 + 38*z**2 + 3. Solve d(w) = 0 for w.
0, 2
Let u = 0 - 0. Let z(w) = w