. Factor u(p).
2*p*(p - 1)*(p + 1)**3
Suppose -r + 4*o = -15 - 5, 0 = -4*r - 3*o - 15. Solve -u**2 + u**2 + u**2 - 2 + r*u + u = 0 for u.
-2, 1
Let t(o) be the third derivative of o**6/300 + o**5/150 - o**2. Factor t(l).
2*l**2*(l + 1)/5
Let y(u) be the second derivative of 49*u**5/50 - 7*u**4/10 - 8*u**3/5 - 4*u**2/5 + 3*u. Determine x so that y(x) = 0.
-2/7, 1
Let i be 98/(-308) + 2/4. Determine c, given that -2/11 - 2/11*c**3 + 2/11*c + i*c**2 = 0.
-1, 1
Let f be (-6 - 296/(-48))*(-1 + 5). Factor -f*n + 2/3*n**4 + 2/3 - 2/3*n**5 + 4/3*n**3 - 4/3*n**2.
-2*(n - 1)**3*(n + 1)**2/3
Let j(l) be the first derivative of -l**8/2352 + l**7/1470 + 3*l**2/2 - 5. Let h(y) be the second derivative of j(y). Suppose h(c) = 0. Calculate c.
0, 1
Let d(w) = -w**5 + w**4 - w**3 - w - 1. Let u(x) = 8*x**5 + 34*x**4 + 80*x**3 + 40*x**2 - 12*x - 10. Let z(t) = -4*d(t) - u(t). Solve z(l) = 0.
-7, -1, 1/2
Suppose 8 - 2 = 3*l. Suppose 0 = 3*b + b - 16. Factor -h**3 + b*h**3 - l*h**3 - 4*h**4 + 4*h**5.
h**3*(2*h - 1)**2
Let f(x) be the first derivative of -20*x**3/9 - 35*x**2/6 + 10*x/3 + 27. Factor f(t).
-5*(t + 2)*(4*t - 1)/3
Let v(n) be the second derivative of -n**6/25 - 7*n**5/50 + 3*n**4/10 + 7*n**3/15 - 6*n**2/5 + 26*n. Suppose v(h) = 0. Calculate h.
-3, -1, 2/3, 1
Let b(r) be the second derivative of -r**5/50 + r**3/5 - 2*r**2/5 - 14*r. Factor b(c).
-2*(c - 1)**2*(c + 2)/5
Suppose 4*h - 3*q + 12 = 0, -5*h - 91 + 75 = -4*q. Factor 1/3*c**2 + h + c.
c*(c + 3)/3
Let f(p) = -p**3 - 6*p**2 - 5*p + 1. Let k be f(-5). Factor -o + 0*o + k + o**2 - 3.
(o - 2)*(o + 1)
Let z(n) be the first derivative of -n**4/7 + 4*n**3/7 + 2*n**2/7 - 12*n/7 - 28. Solve z(b) = 0.
-1, 1, 3
Let r(w) be the second derivative of 2/3*w**3 + 1/15*w**6 - 1/5*w**5 - 1/6*w**4 - 7*w + 0 + 0*w**2. Factor r(o).
2*o*(o - 2)*(o - 1)*(o + 1)
Suppose -2*u + 0 = -z - 3, -u + 6 = -2*z. Let t(k) be the second derivative of 0*k**2 + 1/6*k**4 + u*k**3 - 1/10*k**5 + 1/60*k**6 - 2*k + 0. Solve t(g) = 0.
0, 2
Let v be 18/24 + 2*(-2)/8. Let u(r) be the second derivative of 1/12*r**3 + v*r**4 + 2*r + 0 + 9/40*r**5 + 1/15*r**6 + 0*r**2. Factor u(x).
x*(x + 1)**2*(4*x + 1)/2
Let 2/5*y + 6/5*y**3 + 0 + 6/5*y**2 + 2/5*y**4 = 0. Calculate y.
-1, 0
Let y be 4/(-14)*(-3 + 4/6). Suppose 1/3*p - 1/3*p**5 - 2/3*p**2 + 0*p**3 + y*p**4 + 0 = 0. Calculate p.
-1, 0, 1
Let f(u) = -u**3 - 6*u**2 + 17*u + 10. Let d be f(-8). Let 2/3*i**d + 0 + 2/3*i = 0. Calculate i.
-1, 0
Let j = -4 + 6. Suppose 0 = -4*o + j*o + 4. Factor 8*d + 9*d**4 - 1 + o + 2*d**2 + 20*d**2 + 24*d**3.
(d + 1)**2*(3*d + 1)**2
Let j be ((-4)/(-5))/((-2)/(-5)). Factor 6*h**3 + 6*h + 9*h**5 + 10*h**j - 11*h**5 - 3*h + h - 2*h**4.
-2*h*(h - 2)*(h + 1)**3
Find v, given that -3/2*v**4 - 3/2*v**5 + 0*v + 0*v**3 + 0 + 0*v**2 = 0.
-1, 0
Suppose 1/5*t**2 + 32/5*t + 256/5 = 0. Calculate t.
-16
What is n in 0 - 3/2*n**3 - 1/3*n**2 - 1/2*n**5 + 0*n - 5/3*n**4 = 0?
-2, -1, -1/3, 0
Factor 0*w**2 - 3/2*w + 0 + 3/2*w**3.
3*w*(w - 1)*(w + 1)/2
Determine g so that 2 - 3*g**4 + 3*g**3 - 2 + 3*g**2 - 3*g = 0.
-1, 0, 1
Factor 0*b + 0 - 2/3*b**4 + 4/3*b**3 - 2/3*b**2.
-2*b**2*(b - 1)**2/3
Let i(b) be the third derivative of 0*b + 1/2*b**3 - 1/20*b**5 + 1/8*b**4 - 1/40*b**6 - 2*b**2 + 0. Suppose i(m) = 0. What is m?
-1, 1
Solve 87*j**2 - 67*j**2 - 8*j - 8*j**3 + 0*j**3 = 0.
0, 1/2, 2
Suppose -4*z = k + k - 12, 3*z - 5*k = 9. Suppose 5 = 4*s - z. Factor l**s - 3*l**2 + 4*l + 0*l**2.
-2*l*(l - 2)
Let r(z) = -2*z - 11. Let l be (1 + -9)*1 - 0. Let m be r(l). Determine i, given that -5*i**2 - 5/2*i - 5*i**3 - 5/2*i**4 - 1/2 - 1/2*i**m = 0.
-1
Let s = -31 - -33. Let y(g) be the second derivative of 0 + 0*g**2 + s*g + 0*g**3 + 9/40*g**5 + 1/12*g**4 + 7/60*g**6. Factor y(i).
i**2*(i + 1)*(7*i + 2)/2
Let t be 155/(-15) + 12 + (-35)/(-6). Determine p, given that -6*p**2 + 3/2*p**3 - 3 + t*p = 0.
1, 2
Let w(q) be the third derivative of 1/30*q**6 - 1/105*q**7 + 0 + 0*q**4 - 2*q**2 - 1/30*q**5 + 0*q**3 + 0*q. Factor w(c).
-2*c**2*(c - 1)**2
Suppose 20*u - 23 = -4*f + 17*u, 2*f - 4*u = -16. Let -2/9 + 0*k + 2/9*k**f = 0. What is k?
-1, 1
Let s(t) be the second derivative of -3*t**6/35 + 6*t**5/35 - 2*t**4/21 + 8*t. Factor s(x).
-2*x**2*(3*x - 2)**2/7
Suppose q + 5*d = -1, 4*q - 4*d + 3 + 1 = 0. Let i be q/(-1 - -1 - 3). Factor 4/3*y**2 + i + 4/3*y.
(2*y + 1)**2/3
Let l(b) be the third derivative of 0*b + 1/12*b**4 + 1/60*b**5 + 1/6*b**3 + 3*b**2 + 0. Factor l(q).
(q + 1)**2
Suppose 2*i - 6 = -v, 0*i = -i + 3. Let p(y) be the second derivative of 2*y + 1/18*y**4 + 0 + 0*y**2 + v*y**3 - 1/60*y**5. Let p(b) = 0. Calculate b.
0, 2
Let b = 8 - 3. Suppose 0 = 4*v - b - 3. Factor -5*t**2 + v*t**2 - 2 + 0 + 5*t.
-(t - 1)*(3*t - 2)
Let d(q) be the second derivative of q**5/10 + q**4/3 - 15*q. Let d(z) = 0. What is z?
-2, 0
Let v(s) = -6*s**4 + s**3 + 5. Let t(c) = -c**4 + 1. Suppose 0 = 5*q - 10. Let g(j) = q*v(j) - 10*t(j). Factor g(l).
-2*l**3*(l - 1)
Determine p, given that -2/7*p**3 + 0 - 4/7*p - 6/7*p**2 = 0.
-2, -1, 0
Suppose 0 = -3*p - 6 + 18. Let y(i) be the third derivative of 1/96*i**p + 1/240*i**5 - 1/12*i**3 + 0 + 0*i - 2*i**2. Factor y(k).
(k - 1)*(k + 2)/4
Let a(s) = -s**3 - 4*s**2 - 4*s. Let l be a(-3). Let i(o) be the third derivative of 0 + 1/24*o**4 + 0*o**l + o**2 + 0*o - 1/60*o**5. What is c in i(c) = 0?
0, 1
Let j(b) = b**3 - b**2 + 1. Let g(q) = q**2 + 1. Let m(y) = 2*y**3 + 4*y**2 + 6. Let w(u) = -5*g(u) + m(u). Let r(h) = -j(h) + w(h). What is l in r(l) = 0?
0
Let 0*l + 2/13*l**3 + 0*l**2 + 2/13*l**4 + 0 = 0. What is l?
-1, 0
Let n(q) be the third derivative of -q**8/252 + 2*q**7/315 + q**6/90 - q**5/45 + 7*q**2. Factor n(p).
-4*p**2*(p - 1)**2*(p + 1)/3
Let b(p) = -p + 5 - 1 + 3*p**4 + 3*p + 3*p**3 + 2*p. Let t(r) = 3*r**4 + 4*r**3 + 5*r + 5. Let v(q) = 5*b(q) - 4*t(q). Factor v(o).
o**3*(3*o - 1)
Let y = 26 + -24. Let k(n) be the first derivative of -n**3/3 + n**2/2 + n - 1. Let a(b) = -2*b**2 - 4*b - 2. Let p(r) = y*k(r) + a(r). What is w in p(w) = 0?
-1/2, 0
Determine d, given that 2 - 20/11*d - 2/11*d**2 = 0.
-11, 1
Find u such that -4*u**5 + 29*u**2 - 36*u - 56*u**3 + 213*u**4 + 8 + 35*u**2 - 189*u**4 = 0.
1, 2
Let j(q) = -4*q**3 - 26*q**2 - 94*q - 126. Let s(k) = 9*k**3 + 53*k**2 + 187*k + 251. Let g(t) = -10*j(t) - 4*s(t). What is x in g(x) = 0?
-4
Let 8/13 + 18/13*t**3 + 0*t - 4/13*t**4 - 22/13*t**2 = 0. Calculate t.
-1/2, 1, 2
Suppose -10*u = -6*u - 8. Suppose 0 - 2/7*o**u - 4/7*o = 0. What is o?
-2, 0
What is p in 2/7*p + 0 - 15/7*p**2 = 0?
0, 2/15
Suppose 0 = 3*l - 404 - 121. Let z = -1223/7 + l. Factor 0*r - 2/7 + z*r**2.
2*(r - 1)*(r + 1)/7
Factor 2*v - 2/7*v**2 - 20/7.
-2*(v - 5)*(v - 2)/7
Let p be 1/20 + 9/12. Factor -2/5*s**2 + 3/5*s**5 + p*s**4 + 0 - 1/5*s**3 + 0*s.
s**2*(s + 1)**2*(3*s - 2)/5
Determine i, given that 2*i**3 + i**4 - 10*i**2 + 21*i**2 - 11*i**2 = 0.
-2, 0
Let b(m) be the third derivative of -m**8/84 - 2*m**7/105 + m**6/5 - 2*m**5/15 - 5*m**4/6 + 2*m**3 - 3*m**2. Factor b(h).
-4*(h - 1)**3*(h + 1)*(h + 3)
Factor -40*g + 3*g**2 - 43 + 8*g**2 - 2 - 6*g**2.
5*(g - 9)*(g + 1)
Let l(s) be the third derivative of s**6/200 - s**5/25 - s**4/8 - 46*s**2. Factor l(g).
3*g*(g - 5)*(g + 1)/5
Let j(l) be the first derivative of -l**8/840 - l**7/210 + l**5/30 + l**4/12 + 5*l**3/3 + 6. Let r(t) be the third derivative of j(t). Factor r(g).
-2*(g - 1)*(g + 1)**3
Let f(q) = -q**3 - 5*q**2 - 2*q - 7. Let v be f(-5). Factor -51*c - v + 10 + 50*c**2 - 9*c + 11.
2*(5*c - 3)**2
Let z(i) be the second derivative of -11/21*i**3 - 2/7*i**2 + 5*i - 1/10*i**5 - 8/21*i**4 + 0. Factor z(k).
-2*(k + 1)**2*(7*k + 2)/7
Let c be (10 + -18)*6/(-16). Let d(a) be the third derivative of 0 - 1/150*a**5 - 1/300*a**6 + 2*a**2 + 0*a**4 + 0*a + 0*a**c. What is o in d(o) = 0?
-1, 0
Let z = -1/614 + -10429/5526. Let m = -11/9 - z. Factor 0*o + 2/3 - m*o**2.
-2*(o - 1)*(o + 1)/3
Suppose 4*v + v - 75 = 0. Suppose -25*g - g - 15*g**3 + 4 + 52*g**2 - v*g**3 = 0. What is g?
1/3, 2/5, 1
Let j(q) be the first derivative of -4*q**3/3 + 6*q**2 - 8*q - 3. Factor j(y).
-4*(y - 2)*(y - 1)
Let s(n) be the third derivative of -n**6/30 - 2*n**5/15 + 4*n**2. Find h, given that s(h) = 0.
-2, 0
Let t be 2/28 + (234/(-42) - -6). Determine f so that 1/4*f + 0 - t*f**4 + 1/2*f**2 - 1/4*f**5 + 0*f**3 = 