*y - 4*y = 0, 2*a = -3*y. Find t, given that 2/9*t**5 + a*t + 4/9*t**4 + 0*t**2 + 2/9*t**3 + 0 = 0.
-1, 0
Let l(q) be the first derivative of q**6/6 - q**4/4 - 4. Factor l(z).
z**3*(z - 1)*(z + 1)
Let z = 344/5 - 673/10. Factor 0 - z*q + 1/2*q**2.
q*(q - 3)/2
Suppose 4*x - 12 - 4*x**2 - 6*x + 18*x = 0. Calculate x.
1, 3
Let x(n) be the second derivative of n**4/7 + 34*n**3/21 - 12*n**2/7 - 56*n. Solve x(b) = 0 for b.
-6, 1/3
Let w = 31/54 - 2/27. Let j = 13/2 + -6. Factor 1/2*f**3 + 0 + w*f**2 - j*f**4 - 1/2*f.
-f*(f - 1)**2*(f + 1)/2
Let g(p) be the third derivative of p**7/1260 + p**6/180 + p**5/60 + p**4/8 + 2*p**2. Let v(o) be the second derivative of g(o). Suppose v(k) = 0. What is k?
-1
Suppose -5*i = 3*m, -i - 5 = -m + 3. Find k, given that -4/5*k**m + 2/5*k**4 + 0*k + 4/5*k**3 + 0 - 2/5*k**2 = 0.
-1, 0, 1/2, 1
Suppose 6 + 38 = 2*i + 3*s, -2*s + 88 = 5*i. Suppose 0 = 2*j - 6*j + i. Let 5/4*y**5 + 1/4*y**3 + 2*y**j - 1/2*y**2 + 0*y + 0 = 0. What is y?
-1, 0, 2/5
Let y = 77 + -74. Let i(a) be the second derivative of -1/54*a**4 + y*a + 0*a**2 + 1/27*a**3 + 0. Suppose i(v) = 0. Calculate v.
0, 1
Let p(m) be the third derivative of m**7/7560 - m**4/8 - m**2. Let k(s) be the second derivative of p(s). Suppose k(l) = 0. Calculate l.
0
Suppose -4*a = 4*q - 24, a = 1 + 1. Let f(s) = -s**3 + s - 1. Let v(g) = -856*g**2 + 856*g**2 - 2*g + g**3 - 3*g**3. Let m(k) = q*f(k) - v(k). Factor m(w).
-2*(w - 1)**2*(w + 2)
Let z be (-132)/55*(-6)/8*1. Let -6/5 + z*q - 12/5*q**3 + 0*q**4 + 6/5*q**2 + 3/5*q**5 = 0. What is q?
-2, -1, 1
Suppose 7*x - 10*x - 6 = 0. Let s(a) = a + 1. Let r(q) = 5*q**3 + 2*q**2 + 2*q + 2. Let j(t) = x*s(t) + r(t). Factor j(k).
k**2*(5*k + 2)
Let l be 4/(15/9 + -1). Factor -3*x - x + l*x + x**2 - x.
x*(x + 1)
Let p be (-1)/((-176)/76) + 12/(-48). Factor 16/11*n + 10/11*n**2 + 8/11 + p*n**3.
2*(n + 1)*(n + 2)**2/11
Let u be 50/(-13) + 6/(-39). Let s = 8 + u. Factor -2*r + s*r - 2*r**3 + 0*r**3.
-2*r*(r - 1)*(r + 1)
Factor 24*f - 216 - 2/3*f**2.
-2*(f - 18)**2/3
Let c(w) = -12*w**5 - 7*w**4 + 5*w**3 - 5*w**2 - 5*w + 5. Let p(u) = u**5 + u**4 - u**3 + u**2 + u - 1. Let v(g) = -c(g) - 5*p(g). Factor v(x).
x**4*(7*x + 2)
Suppose 3*h + 4*p + 5 = -6, -h + 4*p + 23 = 0. Suppose -h*d + 8 = -i + 1, 0 = i + 4*d - 14. Let -1/2*m**5 + m**4 - m**i + 1/2*m**3 + 0*m + 0 = 0. What is m?
-1, 0, 1, 2
Find z, given that z**3 + 105*z**2 + 21*z + 79*z**3 + 20*z**4 + 10 + 34*z = 0.
-2, -1, -1/2
Let y(b) be the third derivative of -b**6/180 - b**5/30 - b**4/12 - b**3 - b**2. Let g(d) be the first derivative of y(d). Find k such that g(k) = 0.
-1
Let x(f) be the first derivative of 5*f**6/33 - 16*f**5/55 + f**4/22 + 4*f**3/33 + 49. Find a such that x(a) = 0.
-2/5, 0, 1
Let t(r) = -r + 7. Let j be t(5). Factor 3*s**2 - s - 1 - j*s**2 + 1.
s*(s - 1)
Suppose -19*o**4 - 10*o**5 - 18*o**3 - 5*o**4 - 2*o**2 - 2*o**2 = 0. What is o?
-1, -2/5, 0
Let f(l) = 3*l**2 + l. Let z be f(-1). Factor -3*i**z - 2 + 4*i**2 - 3*i**2 + 4*i.
-2*(i - 1)**2
Let y(s) = 9*s**4 + 27*s**3 + 45*s**2 + 24*s + 6. Let j(u) = -10*u**4 - 27*u**3 - 46*u**2 - 23*u - 6. Let w(v) = 3*j(v) + 4*y(v). Factor w(z).
3*(z + 1)**2*(z + 2)*(2*z + 1)
Let i be 148/6 + (-4)/(-12). Suppose -l + 0*l = -3*j - 15, -4*l + 5*j = -i. Factor 2*b - 2*b**3 + l*b + 0*b**3.
-2*b*(b - 1)*(b + 1)
Let c(o) be the second derivative of o**10/120960 + o**9/60480 - o**8/26880 - o**7/10080 - o**4/12 + 3*o. Let y(z) be the third derivative of c(z). Factor y(n).
n**2*(n - 1)*(n + 1)**2/4
Let j = 10 + -9. Let s(w) be the third derivative of -w**5/20 - w**4/6 - 2*w**2. Let z(m) = m**2 + m. Let n(g) = j*s(g) + 4*z(g). Factor n(r).
r**2
Factor -20/3*u**4 - 80/9*u**2 - 14/9*u**5 - 10/3*u - 4/9 - 100/9*u**3.
-2*(u + 1)**4*(7*u + 2)/9
Suppose -20/3*g**3 + 0 - 25/3*g**2 - 5/3*g**4 - 10/3*g = 0. What is g?
-2, -1, 0
Let t = 251/1880 + -2/235. Solve -t*o**2 + 1/8*o**4 + 0 + 0*o + 0*o**3 = 0.
-1, 0, 1
Let m(d) be the first derivative of d**4/6 + 8*d**3/9 + 33. Factor m(z).
2*z**2*(z + 4)/3
Let g(s) be the second derivative of -s**4/6 - s**3/3 + 2*s**2 + 2*s. Factor g(u).
-2*(u - 1)*(u + 2)
Let k(l) be the first derivative of -l**5 + 15*l**4/4 - 5*l**3/3 - 15*l**2/2 + 10*l + 24. Find x, given that k(x) = 0.
-1, 1, 2
Let o = 11 + -7. Solve 4*u**2 + 4*u**2 - o + 5*u**2 + 6*u - 3*u**2 = 0.
-1, 2/5
Suppose -31 - 41 = c. Let u be 27/c*4/(-6). Factor u*t**5 - 1/4 + 5/2*t**3 - 5/2*t**2 - 5/4*t**4 + 5/4*t.
(t - 1)**5/4
Let l = -18 - -22. Let t(i) be the second derivative of 1/54*i**l + 2*i - 2/9*i**2 + 0 - 1/27*i**3. Determine m, given that t(m) = 0.
-1, 2
Let j be 6/18 + 0 + 1. Solve -j*p**4 + 0*p**2 - 2*p**3 + 0 + 2/3*p = 0.
-1, 0, 1/2
Factor -4/3*l + 0 + 4/3*l**2.
4*l*(l - 1)/3
Let y(l) be the first derivative of -l**4/4 + 5*l**3/3 - 2*l**2 + 2*l + 2. Let r be y(3). Determine k, given that 2*k**2 + 13 - r*k - 5 + 0*k**2 = 0.
2
Suppose 0 = -u + 4*g + 3 - 23, -5*u - 5*g = 50. Let f be (0*(-3)/u)/2. Factor -12/7*r**3 + f - 2/7*r + 8/7*r**2 + 8/7*r**4 - 2/7*r**5.
-2*r*(r - 1)**4/7
Let z = 19 - 7. Factor 8*l - 52*l**3 - 9*l**4 + 30*l**4 + z*l**2 + 2*l**3.
l*(l - 2)*(3*l - 2)*(7*l + 2)
Factor 5*h**2 + h**5 + 3*h**4 + 5*h**2 - 3*h - 1 + 2*h**3 - 14*h**2 + 2*h**2.
(h - 1)*(h + 1)**4
Suppose 3*n - 5*r = 12, n + 2*r = 7*r + 4. Let f(l) be the first derivative of 4/7*l**2 - 2/7*l**n - 2/21*l**3 + 2/7*l - 1. Factor f(b).
-2*(b - 1)*(b + 1)*(4*b + 1)/7
Let z = -33/2 - -17. Suppose 0*u - 1/4*u**4 - z*u**3 + 0 - 1/4*u**2 = 0. What is u?
-1, 0
Suppose -2*k + 11 - 3 = 0. Suppose i - k = 2. Let -14*r**3 - 6*r**2 + 4*r**5 + 9*r**4 - 3*r**4 + 4*r + i*r**5 = 0. What is r?
-1, 0, 2/5, 1
Suppose 4*s = w + 2, -3*w + 2*s = w - 6. Solve -5*v**w + 4*v**2 - 5*v**4 + 4*v**2 + 2*v**4 = 0.
-1, 0, 1
Let r be -1 + (4 - (4 + -2)). Suppose -8 = -5*d + z - 1, 4*d + r = 3*z. Factor 0 + 0*y**d - 2/13*y**5 + 0*y - 2/13*y**3 + 4/13*y**4.
-2*y**3*(y - 1)**2/13
Suppose 3*v + 440 = v. Let g be (-4)/34 + v/(-425). Factor g*l**2 + 0*l + 0.
2*l**2/5
Let i be (388/(-64) + 6)/((-2)/8). Factor 0 - i*l**3 - 1/4*l**2 + 1/2*l.
-l*(l - 1)*(l + 2)/4
Let t(l) be the third derivative of l**8/1512 - l**6/540 + 23*l**2. Let t(b) = 0. What is b?
-1, 0, 1
Suppose -4*v + v + 2*c + 4 = 0, -12 = -3*c. Suppose -t - 8 - 3 = 5*r, v*t - 44 = 2*r. Solve 41*w + t*w**3 - 3 - 7 - 30*w**2 + 2 - 13*w = 0 for w.
2/3, 2
Let d(t) = t**3 - 8*t**2 + 7*t - 6. Let m be d(7). Let s be (-2)/6 + (-2)/m. Solve s + 2/7*y + 2/7*y**2 = 0 for y.
-1, 0
Factor -6*r - 15*r**3 - 3*r**4 + 20*r**2 - 6*r - 27*r**2 - 17*r**2.
-3*r*(r + 1)*(r + 2)**2
Let b(i) be the second derivative of i**7 - 13*i**6/15 - 33*i**5/10 + 17*i**4/6 + 4*i**3 - 4*i**2 + 14*i. Suppose b(d) = 0. What is d?
-1, -2/3, 2/7, 1
Let n = 8 + -14. Let m(k) = 2*k**4 - 14*k**3 + 6*k**2 - 2*k + 8. Let j(d) = 2*d**4 - 15*d**3 + 5*d**2 - d + 9. Let q(f) = n*j(f) + 7*m(f). Factor q(b).
2*(b - 1)**4
Suppose p + 6 = -4*k + 29, -21 = -4*k - 3*p. Suppose 2*o - 10 + 4 = 0. Let i**3 - 5*i**3 - 5*i**3 - k*i**4 + o*i**5 = 0. What is i?
-1, 0, 3
Let 2*l**3 - 1 - 4 - 2*l**5 + 5 = 0. What is l?
-1, 0, 1
Let r(o) be the second derivative of o**9/68040 + o**8/15120 + o**7/11340 + o**4/3 + 4*o. Let f(x) be the third derivative of r(x). Factor f(a).
2*a**2*(a + 1)**2/9
Factor 0 + 0*j**2 - 1/3*j**3 + 1/3*j.
-j*(j - 1)*(j + 1)/3
Suppose 5*m + 0 - 5 = 0. Determine t so that -3*t + 4*t**2 - 3*t + m + 0 + 2*t = 0.
1/2
Let h = 52 - 50. Let m(n) be the third derivative of 0*n**3 + 1/36*n**4 + 0*n + 0 + 1/180*n**6 + h*n**2 - 1/45*n**5. Factor m(p).
2*p*(p - 1)**2/3
Let t = -235/21 + 83/7. Determine i so that -2*i**2 + 0 + t*i**3 + 4/3*i = 0.
0, 1, 2
Factor -3/2*s**3 + 0*s + 0*s**4 + 1/2*s**5 + 0 + s**2.
s**2*(s - 1)**2*(s + 2)/2
Let z(m) = -m**2 + 4*m + 7. Let r be z(5). Suppose -r*k = -k. Suppose k*n - 1/3*n**2 + 1/3 = 0. Calculate n.
-1, 1
Let w(j) = -j**2 - 6*j + 5. Let f(r) = -2*r**2 - 13*r + 11. Let m(n) = -6*f(n) + 13*w(n). Let z(s) = -4*s**2 + 4*s - 7. Let v(u) = 6*m(u) - 2*z(u). Factor v(o).
2*(o - 2)**2
Let z(q) be the first derivative of -2*q**3/3 + 14*q**2 - 98*q + 49. Factor z(d).
-2*(d - 7)**2
Solve 1/3*z**2 + 5/3*z**4 + 0 - 2/3*z + 8/3*z**3 = 0 for z.
-1, 0, 2/5
Let c(v) be the third derivative of -v**6/360 + v**5/60 - v**3/2 - 2*v**2. Let r(i) be the first derivative of c(i). 