 given that j(t) = 0.
-1/2, -1/3, 0, 1
Factor b**4 + 0*b + 1/4*b**2 + 0 - 5/4*b**3.
b**2*(b - 1)*(4*b - 1)/4
Suppose h + 4 = -3*h. Let w(z) = z + 1. Let n be w(h). Find b such that 0*b**2 - 1/3*b**3 + 0 + n*b = 0.
0
Let u(y) = -y**3 - y**2 - y - 1. Let d(t) = 12*t**5 - 38*t**4 + 32*t**3 - 12*t**2 - 16*t - 2. Let s(f) = -d(f) + 6*u(f). Determine c, given that s(c) = 0.
-1/2, 2/3, 1
Let m(q) = -11*q**2 + 13*q + 9. Let r(n) be the second derivative of -5/12*n**4 + 4*n + 0 + 2*n**2 + n**3. Let x(y) = 4*m(y) - 9*r(y). Factor x(a).
a*(a - 2)
Let n be (-270)/20 + 2/2. Let d = -12 - n. Factor 2*w**3 - d + 2*w - 1/2*w**4 - 3*w**2.
-(w - 1)**4/2
Suppose t - 3*t = 0. Let i(g) be the second derivative of 2*g - 1/24*g**3 + t*g**2 - 1/48*g**4 + 0. Factor i(w).
-w*(w + 1)/4
Let d(j) = j**2 + 6*j - 3. Let k be d(1). Let p(m) be the third derivative of 4*m**2 + 1/18*m**k + 0*m + 0 + 1/180*m**5 + 2/9*m**3. Factor p(f).
(f + 2)**2/3
Suppose 0*d - 14 = -c - 5*d, -10 = -5*d. Let n be 2/5 - 2/5. Factor -32/3*r**c + 0*r + n - 2/3*r**2 + 16/3*r**3.
-2*r**2*(4*r - 1)**2/3
Suppose 4*i**2 + 2*i - 5*i**2 - 4 + 3*i**2 = 0. What is i?
-2, 1
Let j(d) = d**4 + 2*d**2 - 3. Let l(y) = y**3 + y**2 - y - 1. Suppose 6 = -z + k, -3*z + 6 = z + 2*k. Let c(w) = z*j(w) + 2*l(w). Factor c(o).
-(o - 1)**3*(o + 1)
Let n be 5/((-75)/6) + 48/45. Let w(o) be the second derivative of -n*o**3 + 1/5*o**5 + 0*o**2 + 0 + 1/15*o**6 - 1/6*o**4 - o. Solve w(j) = 0.
-2, -1, 0, 1
Let w = -1 + 2. Let v(h) = -4*h**2 + 2*h. Let p(n) = -n**2 + n. Suppose -4*c + 3 = -5*c. Let j(l) = c*p(l) + w*v(l). Find q, given that j(q) = 0.
-1, 0
Let t(v) be the first derivative of -v**4/4 - v**3/2 - v - 1. Let f(c) be the first derivative of t(c). Factor f(i).
-3*i*(i + 1)
Let q be -3*6/18 + 3. Factor 0*f**3 - 2/3*f**4 + 2*f**q + 0 - 4/3*f.
-2*f*(f - 1)**2*(f + 2)/3
Let o(u) = -u**2 + 11*u - 7. Let i be o(9). Suppose -6*a = -i*a + 10. Factor -1/2*v**3 + 3/2*v**a - v + 0.
-v*(v - 2)*(v - 1)/2
Let b(s) = -2937*s**4 - 4257*s**3 + 81*s**2 + 1119*s - 216. Let x(z) = -367*z**4 - 532*z**3 + 10*z**2 + 140*z - 27. Let i(n) = -4*b(n) + 33*x(n). Factor i(d).
-3*(d + 1)**2*(11*d - 3)**2
Let a be (-9)/(-15) + (-12)/(-5). Suppose 0 = -5*k + a*k. Factor -1/4 + 1/4*u**2 + k*u.
(u - 1)*(u + 1)/4
Let t be 0 + 1 + -24 + 23. Factor 0 + 1/4*y**3 - 1/4*y + t*y**2.
y*(y - 1)*(y + 1)/4
Let d(o) be the third derivative of 1/45*o**6 + 0 + 0*o - 2/63*o**7 + 0*o**4 + 0*o**5 + 1/84*o**8 + 4*o**2 + 0*o**3. Factor d(t).
4*t**3*(t - 1)*(3*t - 2)/3
Let y(w) = 15*w**4 - 15*w**3 + 5*w**2 - 5*w. Let a(n) = n**5 - n. Let x(l) = -5*a(l) + y(l). What is b in x(b) = 0?
0, 1
Let n be (-8)/(-5) + (-3 - -2). Factor 0 - 3/5*s**2 + 0*s + n*s**3.
3*s**2*(s - 1)/5
Suppose -2*h - f = -2 + 4, -h - 2*f - 4 = 0. Suppose h + 1/3*p**3 - 2/3*p - 1/3*p**2 = 0. What is p?
-1, 0, 2
Suppose -h = -4*z + 12, -4*z = -z - 3*h - 18. Factor o**5 + 3*o + 1 + 2*o**z - 4*o**3 - 3*o**4 + 2*o**3 - 2*o**5.
-(o - 1)*(o + 1)**4
Let b(d) be the first derivative of -d**5/20 + 8. Factor b(z).
-z**4/4
Let c = -7 + 21. Let d = 2 - 0. Factor 2*j - 2*j - 10*j**4 - 3*j**d + c*j**3 - j**2.
-2*j**2*(j - 1)*(5*j - 2)
Let y(a) be the second derivative of 10/49*a**7 - 8*a - 1/7*a**4 - 4/21*a**3 + 0*a**2 + 62/105*a**6 + 3/7*a**5 + 0. Suppose y(f) = 0. What is f?
-1, -2/5, 0, 1/3
Let m(j) = 3*j**2 - 7*j + 5. Let p(v) = 7*v**2 - 15*v + 11. Let u(k) = -9*m(k) + 4*p(k). Let g be u(-4). Factor 4*d + 5*d**2 + 0*d**2 - g*d**2.
2*d*(d + 2)
Factor -f + 1/2*f**2 - 3/2.
(f - 3)*(f + 1)/2
Let i(o) = 3*o**4 + 2 + 3*o**4 - 6*o**3 + 3*o**2 - 5*o**4 - 2*o**4. Let f(q) = 2*q**4 + 19*q**3 - 8*q**2 + q - 7. Let u(x) = 2*f(x) + 7*i(x). Factor u(s).
-s*(s - 1)*(s + 2)*(3*s + 1)
Let k(m) be the third derivative of -m**8/1344 + m**6/480 - 4*m**2. What is v in k(v) = 0?
-1, 0, 1
Suppose 0 = -2*b + 1 + 5. Let z(k) be the first derivative of -1/5*k**5 + 1/4*k**2 + 2 + 0*k - 1/12*k**6 + 0*k**4 + 1/3*k**b. Solve z(x) = 0 for x.
-1, 0, 1
Let q(h) = h**2 + 7*h - 5. Let o(y) = -8 - 3*y + 8 + 3. Let a(d) = 11*o(d) + 6*q(d). Factor a(i).
3*(i + 1)*(2*i + 1)
Let -8/7*w**3 + 8/7 - 4/7*w - 20/7*w**2 = 0. What is w?
-2, -1, 1/2
Let o(s) be the first derivative of -s**8/2520 - s**7/630 - s**6/540 - s**3/3 - 1. Let t(q) be the third derivative of o(q). Factor t(r).
-2*r**2*(r + 1)**2/3
Let a(j) = -j**3 + 6*j**2 - 5*j. Let i be a(5). Suppose i*p + 9 = 3*p. Factor 3*z**2 - z**p + 2*z**2 + 2*z**3 + 4 + 8*z.
(z + 1)*(z + 2)**2
Let u(m) be the third derivative of 4/105*m**7 + 0 + 0*m + 2*m**2 - 1/30*m**6 + 0*m**3 - 2/15*m**5 + 1/6*m**4. Factor u(k).
4*k*(k - 1)*(k + 1)*(2*k - 1)
Let u(i) be the third derivative of i**10/211680 - i**9/105840 - i**4/12 + 4*i**2. Let f(j) be the second derivative of u(j). Find y, given that f(y) = 0.
0, 1
Factor -6/5*j**2 - 4/5*j - 4/5*j**3 - 1/5 - 1/5*j**4.
-(j + 1)**4/5
Let 2*p**3 + 621*p - 621*p - 2*p**2 = 0. What is p?
0, 1
Solve 0 - 2/5*h**4 + 0*h + 0*h**2 + 4/5*h**3 = 0 for h.
0, 2
Let z be (8/(-4) - 6/(-4))*0. Let c(s) be the third derivative of z*s + 2*s**2 + 1/12*s**4 + 0*s**3 + 0 - 1/30*s**5. What is w in c(w) = 0?
0, 1
Let o(s) be the first derivative of s**5 + 25*s**4/4 + 15*s**3 + 35*s**2/2 + 10*s + 9. Factor o(m).
5*(m + 1)**3*(m + 2)
Let b(u) be the first derivative of 1/12*u**4 - 1/3*u**5 + 4 + 2/9*u**6 + 0*u + 0*u**2 + 0*u**3. Factor b(c).
c**3*(c - 1)*(4*c - 1)/3
Let o(a) be the first derivative of -3*a**4/14 + 8*a**3/21 + 4*a**2/7 - 18. Solve o(u) = 0 for u.
-2/3, 0, 2
Factor -13/4*y - y**2 + 3/4*y**3 - 3/2.
(y - 3)*(y + 1)*(3*y + 2)/4
Let -27*g - 4*g**3 - 28*g - 5 + 30*g**2 - 10*g**4 + 47*g - 3 = 0. What is g?
-2, -2/5, 1
Let z(t) be the third derivative of t**11/10395 - t**10/9450 - t**9/4320 - t**8/10080 + t**5/30 + 4*t**2. Let g(c) be the third derivative of z(c). Factor g(m).
2*m**2*(m - 1)*(4*m + 1)**2
Let o(c) be the third derivative of 0 + 1/35*c**7 + c**2 + 0*c**3 + 0*c - 1/60*c**5 + 1/80*c**6 + 0*c**4 + 1/96*c**8. Factor o(z).
z**2*(z + 1)**2*(7*z - 2)/2
Let k(m) = 3*m**2 - 4*m - 3. Let u(y) = -3*y**2 + 3*y + 3. Let a(z) = 3*k(z) + 4*u(z). Factor a(r).
-3*(r - 1)*(r + 1)
Let f = -133 - -133. Suppose -4/3*p**4 + f*p**3 - 2/3*p + 4/3*p**2 + 0 + 2/3*p**5 = 0. What is p?
-1, 0, 1
Let w(a) be the third derivative of -a**8/840 + a**7/105 - 3*a**6/100 + 7*a**5/150 - a**4/30 + 13*a**2. Solve w(m) = 0 for m.
0, 1, 2
Let h be ((-4)/(0 - 12))/1. Let m(v) be the first derivative of -h*v**2 - 2/9*v**3 + 0*v + 2. Factor m(x).
-2*x*(x + 1)/3
Let l(r) = -r**4 + r**2 + r. Let v(x) = 12*x**4 + 3*x - x - 15*x**3 + 2*x**2 - 2*x**4. Let o(m) = l(m) + v(m). Factor o(h).
3*h*(h - 1)**2*(3*h + 1)
Let t = -4 - -5. Factor -4*o**2 + o**2 + t + 2.
-3*(o - 1)*(o + 1)
Solve 3/2*o**4 - o + 1/2*o**5 + 1/2*o**3 + 0 - 3/2*o**2 = 0 for o.
-2, -1, 0, 1
Let w(u) = u**2 - 1. Let y(x) = 3*x**2 + x - 2. Let f(s) = 4*w(s) - y(s). Factor f(a).
(a - 2)*(a + 1)
Let c be 3*5/15*2/6. Factor 0 - 1/3*l**2 + c*l.
-l*(l - 1)/3
Let a be ((61/(-7) - -5) + 4)*14. Determine r, given that 0 + 3/4*r**5 - 3/4*r**3 + 0*r + 0*r**a + 0*r**2 = 0.
-1, 0, 1
Let p(y) be the first derivative of -3 - 1/12*y**3 - 1/4*y - 1/4*y**2. Determine f so that p(f) = 0.
-1
Factor 11*y**2 + 8 + 9*y**2 - 20*y - 4*y**3 + 0*y - 4*y**2.
-4*(y - 2)*(y - 1)**2
Suppose -d - 42 = -5*c + 3*d, d - 15 = -3*c. Let a be (c/18)/((-2)/(-12)). Solve 5*h + a*h**2 - 5*h = 0.
0
Let j(r) = -8*r**2 - 76*r. Suppose -5*p + 5*l = 20, -17 = 3*p + p - 5*l. Let m(s) = s**2 + 11*s. Let z(k) = p*j(k) - 20*m(k). Find a such that z(a) = 0.
-2, 0
Let f = -153/14 + 27/2. Determine c so that f*c**3 - 18/7*c - 4/7*c**2 + 4/7 = 0.
-1, 2/9, 1
Suppose -3*a + 20 = 5*z, -3*z = -a + 11 + 5. Factor 8*g**3 + 8*g**5 - a*g**4 + 6*g**3 - 12*g**3 + 0*g**4.
2*g**3*(g - 1)*(4*g - 1)
Let l(s) be the second derivative of 2*s**5/45 + 2*s**4/9 - s**3/27 - s**2/3 + 24*s. Determine c, given that l(c) = 0.
-3, -1/2, 1/2
Let l(y) be the second derivative of -y**4/60 + 7*y**3/15 + 3*y**2/2 + 43*y - 2. Factor l(f).
-(f - 15)*(f + 1)/5
Let f(p) be the second derivative of -p**6/30 - 11*p**5/20 - 19*p**4/12 - 3*p**3/2 + p + 12. Factor f(n).
-n*(n + 1)**2*(n + 9)
Factor c**3 - 16*c**4 - 25*c**3 + 4*c**3 - 4*c**5 - 8*c**2.
-4*c**2*(c + 1)**2*(c + 2)
Let j = -2 + 3. Let w(s) be the first derivative of s**3/3 + s**2/2 +