
Let r be 2/4*(-63)/(-126). Let m(g) be the second derivative of 2*g + r*g**2 - 1/48*g**4 + 0 - 1/24*g**3. Factor m(u).
-(u - 1)*(u + 2)/4
Let r(u) = -6*u**4 + u**3 - 9*u**2 - 5*u. Suppose 2*o = -o + 15. Let n(i) = i**4 + i**3 + i. Let j(t) = o*n(t) + r(t). Factor j(q).
-q**2*(q - 3)**2
Let f = -28/23 - -863/690. Let h(n) be the second derivative of -2*n - f*n**4 - 2/15*n**3 + 0 - 1/5*n**2. Determine l so that h(l) = 0.
-1
Find m, given that -52/7 - 30/7*m - 2/7*m**2 = 0.
-13, -2
Let o = 15/34 - -23/102. Let -4/15*i - 2/5*i**3 - o*i**2 + 0 = 0. Calculate i.
-1, -2/3, 0
Let i(f) be the second derivative of -f**5/80 - 3*f**4/16 - f**3 - 5*f**2/2 + 23*f + 1. Factor i(c).
-(c + 2)**2*(c + 5)/4
Let j(c) be the third derivative of -c**7/70 + c**6/20 + 9*c**5/20 - 9*c**4/4 - 3*c**2 - 63*c. Factor j(h).
-3*h*(h - 3)*(h - 2)*(h + 3)
Find y such that 110/7*y**2 - 224 - 2/7*y**3 - 208*y = 0.
-1, 28
Let w(z) be the first derivative of -7*z**6/2 - 12*z**5 - 15*z**4/4 + 20*z**3 + 18*z**2 + 682. Let w(b) = 0. Calculate b.
-2, -1, -6/7, 0, 1
Factor d**2 + d**4 - 7*d**3 - 19*d**3 + 28*d**3.
d**2*(d + 1)**2
Suppose 112/9 - 2/9*t**3 + 2*t**2 + 44/3*t = 0. Calculate t.
-4, -1, 14
Let d(h) be the third derivative of 7*h**5/90 + h**4/18 - 21*h**2. Factor d(s).
2*s*(7*s + 2)/3
Let p(s) be the first derivative of -2/3*s**3 + 0*s**2 - 3 + 1/8*s**4 - 1/120*s**6 + 0*s**5 + 0*s. Let l(q) be the third derivative of p(q). Factor l(g).
-3*(g - 1)*(g + 1)
Let d(w) = -9*w**3 + 68*w**2 + 576*w + 1536. Let j(n) = 21*n**3 - 135*n**2 - 1152*n - 3072. Let g(f) = -9*d(f) - 4*j(f). Factor g(z).
-3*(z + 8)**3
Let -6/5*k + 6/5*k**3 - 9/5*k**4 + 24/5*k**2 - 3 = 0. Calculate k.
-1, 1, 5/3
Let s(l) be the second derivative of -l**7/105 + 4*l**6/75 + 3*l**5/10 - 3*l**4/5 + 21*l - 15. Solve s(g) = 0.
-3, 0, 1, 6
Let n = -10699 + 10708. Solve -9/4*u + n*u**4 + 69/4*u**3 - 3/4 + 27/4*u**2 = 0.
-1, -1/4, 1/3
Let n(b) be the first derivative of -b**5/25 - 17*b**4/5 + 139*b**3/15 - 7*b**2 + 795. What is h in n(h) = 0?
-70, 0, 1
Let f(j) = -3*j**3 - 3*j**2 + 8*j + 13. Let y(c) = -4*c**3 - 4*c**2 + 12*c + 20. Let i(d) = -8*f(d) + 5*y(d). Suppose i(w) = 0. What is w?
-1, 1
Let i(f) = f**3 + 2*f**2 - 6*f. Let u(t) = -35*t + 18*t + 16*t. Let v(k) = 2*i(k) - 6*u(k). Suppose v(x) = 0. Calculate x.
-3, 0, 1
Let q = -53591/30 + 1790. Let a = q - 17/6. Factor 0 + a*m**3 - 2/5*m + 0*m**4 - 2/5*m**5 + 0*m**2.
-2*m*(m - 1)**2*(m + 1)**2/5
Let z(p) be the first derivative of -p**2/2 + 4*p + 22. Let h be z(2). Find v, given that 8/9 + 8/9*v + 2/9*v**h = 0.
-2
Let k(b) be the third derivative of b**7/4200 - b**6/200 + 9*b**5/200 + b**4/24 + 12*b**2. Let i(f) be the second derivative of k(f). Factor i(a).
3*(a - 3)**2/5
Let q be -2*1/3 - 204/(-36). Let p(k) be the second derivative of 0 - 1/40*k**q - 1/12*k**4 + 4*k + 0*k**2 - 1/12*k**3. Factor p(w).
-w*(w + 1)**2/2
Let f(r) be the third derivative of r**5/20 + 8*r**4 - 65*r**3/2 - 680*r**2. Find v, given that f(v) = 0.
-65, 1
Let w be 7174/3376 + (-3)/(-8). Factor -3*z**2 - 21/4*z - 1/4*z**3 - w.
-(z + 1)**2*(z + 10)/4
Let a(s) be the second derivative of 18*s + 3*s**3 + 1/4*s**4 + 27/2*s**2 + 0. Find i, given that a(i) = 0.
-3
Let q(g) be the second derivative of -g**4/24 - 14*g**3/3 - 196*g**2 + 2*g - 7. Factor q(d).
-(d + 28)**2/2
Let v(q) be the second derivative of -q**7/6300 - q**6/900 + 11*q**4/12 - 13*q. Let w(g) be the third derivative of v(g). Factor w(a).
-2*a*(a + 2)/5
Let s(n) be the second derivative of 0*n**2 - 8/3*n**3 + 1/5*n**5 + 2/3*n**4 - 1/15*n**6 - 2*n + 0. Factor s(m).
-2*m*(m - 2)**2*(m + 2)
Factor 0*m - 1/4*m**3 + 9/4*m**2 + 0.
-m**2*(m - 9)/4
Factor -1519*n**2 - 400*n + 28*n**2 - 542*n - 124 + 78*n + 49*n**3.
(n - 31)*(7*n + 2)**2
Factor 8/3*m**2 + 0 + 1/3*m + 16/3*m**3.
m*(4*m + 1)**2/3
Let y(r) = -11*r**3 + 11*r**2 - 5*r - 3. Let b(k) = -3*k - 2 - 3*k**3 - 4*k**3 - 11*k**2 + 18*k**2 + 0*k. Let s(x) = 8*b(x) - 5*y(x). Factor s(l).
-(l - 1)**2*(l + 1)
Suppose 0 = i - 7 + 5. Let o be 7 + (-4 - 6) - (-1 - i). Solve 1/2*h**5 + o + 0*h + h**4 + 1/2*h**3 + 0*h**2 = 0 for h.
-1, 0
Factor -3/2*f**2 + 0*f - 3/2*f**4 + 0 + 3*f**3.
-3*f**2*(f - 1)**2/2
Find j such that 12 - 46/5*j**3 + 262/5*j + 34*j**2 - 14/5*j**4 = 0.
-5, -1, -2/7, 3
Let d(l) be the third derivative of 2*l**7/105 + 92*l**6/15 + 8278*l**5/15 - 2852*l**4 + 5766*l**3 + 2*l**2 + 10. Factor d(m).
4*(m - 1)**2*(m + 93)**2
Let t(v) = 4*v**4 + 49*v**3 + 147*v**2 + 203*v + 101. Let z(u) = u**3 - u**2 - u + 1. Let f(o) = t(o) - 5*z(o). Factor f(q).
4*(q + 1)*(q + 2)**2*(q + 6)
Find b such that 2/9*b**3 + 16/3 - 8/9*b - 4/3*b**2 = 0.
-2, 2, 6
Let p(v) = 3*v**5 - 6*v**4 + v**3 - 2. Let d = -56 + 53. Let h(m) = m**5 + 1. Let u be 2/(-4) + (-22)/4. Let x(o) = d*p(o) + u*h(o). Factor x(l).
-3*l**3*(l - 1)*(5*l - 1)
Let x = 59/30 - 19/30. Let m(d) be the first derivative of 6*d**2 - 3*d**4 + 4/5*d**5 + x*d**3 - 1 - 8*d. Let m(i) = 0. What is i?
-1, 1, 2
Let o(t) be the first derivative of 3/4*t**4 + 8 + 0*t + 0*t**2 - 3*t**3. Find l such that o(l) = 0.
0, 3
Let h(f) be the first derivative of 3*f**4/10 - 64*f**3/15 - 11*f**2/5 - 178. Find s, given that h(s) = 0.
-1/3, 0, 11
Let c(a) = -26 + 0*a + 25 + a + a**2. Let w(y) = 4*y**2 + 15*y - 11. Let b(s) = 21*c(s) - 3*w(s). Factor b(n).
3*(n - 2)*(3*n - 2)
Let 0 - 20/11*n**3 + 24/11*n**2 + 2/11*n**4 + 144/11*n = 0. Calculate n.
-2, 0, 6
Let v(i) = -i + 17. Let k be v(17). Suppose x - 4*x = -k*x. Suppose -2/9*z**4 + x + 0*z + 4/9*z**3 - 2/9*z**2 = 0. What is z?
0, 1
Let n(v) be the first derivative of 5*v**4 - 125*v**3/3 - 55*v**2 + 35*v + 43. Determine h so that n(h) = 0.
-1, 1/4, 7
Let f = -64/5 + 197/15. Factor f*p + 2/3 - 1/3*p**2.
-(p - 2)*(p + 1)/3
Let t(u) = -8*u**3 - 6*u**2 + 18*u - 4. Let h = -83 + 65. Let x(z) = z**3 - z. Let i(f) = h*x(f) - 2*t(f). Factor i(w).
-2*(w - 4)*(w - 1)**2
Let d = 122 - 94. Let -12*i**5 - 4 - 10*i**3 + 2*i**3 - 10*i**2 + 5*i**2 + 20*i - 19*i**2 + d*i**4 = 0. What is i?
-1, 1/3, 1
Let u(i) be the third derivative of -i**6/56 + 27*i**5/140 - 15*i**4/28 + 4*i**3/7 + 2*i**2 + 30. Factor u(m).
-3*(m - 4)*(m - 1)*(5*m - 2)/7
Let t(h) = -3*h**5 - 6*h**4 + 21*h**3 + 12*h**2 - 24*h. Let b(a) = -a**3 + a**2. Let v(u) = 6*b(u) - t(u). Let v(y) = 0. Calculate y.
-4, -1, 0, 1, 2
Suppose 11*i - 4 = 15*i. Let n be 1 + 2 + i*(2 - 4). Let -2/3*a**2 + 0 + 0*a**3 + 1/2*a**4 - 1/6*a**n + 0*a = 0. Calculate a.
-1, 0, 2
Let k(t) be the second derivative of -t**5/20 - 7*t**4/12 - 5*t**3/3 + 4*t + 12. Factor k(m).
-m*(m + 2)*(m + 5)
Suppose 13*p - 15613 - 17563 = 0. Factor -p*g - 24565 - 1783*g - 4*g**3 + 0*g**3 - g**3 - 255*g**2.
-5*(g + 17)**3
Let v = -7/2 + 4. Let h = -345/28 - -88/7. Let 3/4*a + h*a**2 + v = 0. Calculate a.
-2, -1
Let r(j) = -24*j**4 - 37*j**3 - 2*j**2 + 11*j + 9. Let k(m) = -m**4 + m**3 + m**2 - m - 1. Let w(t) = -36*k(t) - 4*r(t). What is n in w(n) = 0?
-1, -2/11, 0, 1/3
Let f(r) be the third derivative of 5/6*r**3 - 5*r**2 + 1/36*r**5 - 5/18*r**4 + 0 + 0*r. Factor f(g).
5*(g - 3)*(g - 1)/3
Suppose 6*a + 6*a - 15*a**2 + 2*a**4 - 6*a + 3*a**4 + 4*a = 0. What is a?
-2, 0, 1
Let v be 3/10 + 4681/4530. Factor 11/3*n**3 + 0 - v*n**4 + 1/6*n**5 - 4*n**2 + 3/2*n.
n*(n - 3)**2*(n - 1)**2/6
Factor 35*t - 3*t + t**3 + 6*t**2 - 23*t + 4.
(t + 1)**2*(t + 4)
Find u, given that 8/9*u**2 - 4/9 + 0*u**3 + 0*u - 4/9*u**4 = 0.
-1, 1
Suppose -46*a = -40*a - 30. Factor 32*k - 20*k**4 - 3*k**3 + 0*k**3 + 80*k**2 + a*k**3 - 10*k**3.
-4*k*(k - 2)*(k + 2)*(5*k + 2)
Let p be 5*((-65)/(-25) - 3). Let v be 3/((1 + p)*-3 + 4). Factor -v*c**2 + 6/7 - 3/7*c.
-3*(c - 1)*(c + 2)/7
Factor 4/3*p - 2/9*p**3 + 2/9*p**2 + 0.
-2*p*(p - 3)*(p + 2)/9
Let -33 + 26*t**2 + 35*t + 29*t + 9 - 6*t**3 = 0. What is t?
-2, 1/3, 6
Let j = 2 + -12. Let s = 17 + j. Factor 4*a + 9 - s - 4*a**2 - 2.
-4*a*(a - 1)
Factor 2/7*l**5 + 0*l + 0 - 576/7*l**2 - 52/7*l**4 + 384/7*l**3.
2*l**2*(l - 12)**2*(l - 2)/7
Factor 2*b**2 - 18 - 851*b + 849*b - 22.
2*(b - 5)*(b + 4)
Suppose 190 - 45 = 5*d. Factor -d*t + 9*t + 32*t**4 - 126*t**2 - 8 - 40*t + 16*t**3 - 4*t.
2*(t - 2)*(t + 2)*(4*t + 1)**2
Let w(m) be the first derivative of 1/15*m**3 + 36/5*m - 8 + 6/5*m**2. What is g in w(g) = 0?
-6
Determine z, given that -17*z**3 - 4*z**3 - 72 - 279*z**2 + 177*z - 307*z - 200*z 