7*a**2 - 2/7 + k*a = 0 for a.
-1, 1
Factor v**3 - 7*v**4 - 8*v**3 - 5*v**3 + 3*v**4.
-4*v**3*(v + 3)
Suppose -4*d + 8*w = 5*w - 11, 2*d + 1 = -5*w. Let r be d/(-4) + (-8)/(-16). Determine n, given that -4/3*n**2 - 2/3*n**3 + r - 2/3*n = 0.
-1, 0
Factor 0*c**2 - 3/4*c + 1/4*c**3 + 1/2.
(c - 1)**2*(c + 2)/4
Determine c so that 594*c**5 - 32 - 2*c**4 - 1186*c**5 - 64*c**3 + 128*c + 16*c**2 + 600*c**5 = 0.
-2, 1/4, 2
What is v in -2*v + 2/7*v**2 + 12/7 = 0?
1, 6
Suppose 0*q**2 + 0*q**3 + 0*q + 1/4*q**5 + 0 - 1/4*q**4 = 0. Calculate q.
0, 1
Let w(d) be the third derivative of d**8/6720 + d**7/1680 + d**6/1440 - d**3/3 - 3*d**2. Let b(j) be the first derivative of w(j). Factor b(v).
v**2*(v + 1)**2/4
Let n(q) = -q**3 + 11*q**2 + 20*q + 8. Let z(t) = -3*t**3 + 45*t**2 + 81*t + 33. Let i be 5*3/((-15)/4). Let y(x) = i*z(x) + 15*n(x). Factor y(g).
-3*(g + 1)*(g + 2)**2
Let n = 13 + -16. Let l be (3/2)/(-2 - n). Let 0 + 9/2*w**3 - 3*w**2 - l*w = 0. What is w?
-1/3, 0, 1
Factor -4/9*n + 2/9 + 2/9*n**2.
2*(n - 1)**2/9
Let s(i) be the third derivative of 0*i**3 + 1/84*i**4 - i**2 - 1/735*i**7 + 1/140*i**6 - 1/70*i**5 + 0*i + 0. Factor s(q).
-2*q*(q - 1)**3/7
Let d(i) be the second derivative of i**6/10 + 2*i**5/5 + i**4/3 - 7*i. Solve d(c) = 0.
-2, -2/3, 0
Let -4 - 6*x**5 + 16*x**4 + 14*x - 7*x**2 - 12*x**2 - 8*x**3 + 7*x**2 = 0. Calculate x.
-1, 2/3, 1
Suppose 0 = -7*c + 4*c + 9. Let v(q) be the second derivative of -q**2 + 1/2*q**c + 5/12*q**4 + 2*q + 0. Factor v(d).
(d + 1)*(5*d - 2)
Let l(o) be the third derivative of 0*o**3 - 1/84*o**8 + 3*o**2 + 0*o**6 + 0 + 0*o - 2/15*o**5 + 4/105*o**7 + 1/6*o**4. Determine a, given that l(a) = 0.
-1, 0, 1
Let d(p) = -5*p**2 + 13*p - 17. Let v be 1/(-3 - 14/(-4)). Let f(q) = q**2 - 3*q + 4. Let j(z) = v*d(z) + 9*f(z). Factor j(t).
-(t - 1)*(t + 2)
Suppose -2*f + 8 = -3*a - 0*a, 5*a = 5*f - 15. Let g be (-65)/39*f/(-5). Factor -1/6*v**2 + g*v - 1/6.
-(v - 1)**2/6
Let b be (5 - 0) + 2/(-1). Suppose 0 = 3*i - 2*i - b. Factor -4*s - 3*s**3 + 4*s + 7*s**2 - i*s - 5*s**4 - 2 + 6*s.
-(s - 1)*(s + 1)**2*(5*s - 2)
Let r be (-6)/(-33) + 1646/22. Let k be 30/r + (-16)/(-10). Factor 2/7 + 0*d - 2/7*d**k.
-2*(d - 1)*(d + 1)/7
Let b(w) be the first derivative of 0*w + 0*w**2 - 2 - 1/24*w**4 - 1/60*w**5 + 1/3*w**3 - 1/360*w**6. Let l(p) be the third derivative of b(p). Factor l(u).
-(u + 1)**2
Suppose q = 4*c - 4, -2 = 2*q + 2*c - 4. Suppose 0*g - 2*g**4 + q*g**3 + 2/3*g**2 - 4/3*g**5 + 0 = 0. Calculate g.
-1, 0, 1/2
Let m = -1/772 + 413/20844. Let b(x) be the second derivative of -m*x**4 - 2*x - 2/9*x**2 - 1/9*x**3 + 0. Find w, given that b(w) = 0.
-2, -1
Let k(w) be the third derivative of 0*w**3 + 1/20*w**5 + 1/210*w**7 + 0 - 1/24*w**4 - 3*w**2 + 0*w - 1/40*w**6. Factor k(m).
m*(m - 1)**3
Let z(d) be the first derivative of -d**7/21 - 3*d**6/35 - d**5/35 + 3*d - 2. Let g(m) be the first derivative of z(m). Factor g(p).
-2*p**3*(p + 1)*(7*p + 2)/7
Let v be (3 + 49/(-14))/(-3 + 1). Let v*u + 0*u**3 + 1/2*u**4 + 0 - 1/4*u**5 - 1/2*u**2 = 0. What is u?
-1, 0, 1
Let -6*y**3 - 45*y**2 - 8 + 15*y**4 + 4*y - 4 + 44*y = 0. What is y?
-2, 2/5, 1
Let v(h) = -5*h - 3. Let f(d) = -d**3 + 2*d**2 + 3*d - 1. Let a be f(3). Let x be v(a). Suppose -x*y - 1/2*y**2 - 2 = 0. Calculate y.
-2
Let w(z) be the third derivative of z**8/1176 - 2*z**7/735 + z**5/105 - z**4/84 + 7*z**2. Factor w(f).
2*f*(f - 1)**3*(f + 1)/7
Let f(j) be the third derivative of -j**6/300 - 2*j**5/75 - j**4/12 - 2*j**3/15 - j**2. Factor f(i).
-2*(i + 1)**2*(i + 2)/5
Let p = 4 - 2. Determine s so that -2 + 3*s**2 + s + s**2 - s**p + 4*s = 0.
-2, 1/3
Suppose a + 3*a = 8. Suppose -5*s**2 + 2*s**a + 0*s**4 + 3*s**4 = 0. What is s?
-1, 0, 1
Let f be ((-4)/70)/((-74)/370). Solve 6/7 + 8/7*v + f*v**2 = 0 for v.
-3, -1
Let n(u) be the first derivative of 1/3*u**2 - 8/15*u**5 + 1/9*u**6 + 0*u + u**4 - 8/9*u**3 + 4. Suppose n(s) = 0. Calculate s.
0, 1
Suppose 5*c = 20 + 10. Factor 2*g**4 - 6 - 2*g**3 - 2*g**2 + 2*g**5 + c.
2*g**2*(g - 1)*(g + 1)**2
Let o = 9 + -10. Let f be 2 - (-4 + 2)*o. Factor 0 + f*j + 0*j**2 + 0*j**4 + 1/2*j**3 - 1/2*j**5.
-j**3*(j - 1)*(j + 1)/2
Determine s so that -112*s + 136*s**4 - 2*s**3 - 142*s**5 + 178*s**5 + 32 + 45*s**3 - 168*s**2 + 33*s**3 = 0.
-2, -1, 2/9, 1
Let z = 4 + -2. Factor -17 + 3*w + 10*w**2 - 12*w - 3*w**3 + 5*w**z - 10.
-3*(w - 3)**2*(w + 1)
Suppose 0 = -3*y + 11 + 4. Let t = y - -3. Solve -7*o**3 - 5*o**3 + 3*o**4 - 2*o - 5*o**4 - 2*o**5 + t*o**2 + 10*o**4 = 0.
0, 1
Suppose 11 = -7*p + 39. Factor -42/5*o**3 + 0 - 22/5*o**2 - 2*o**5 - 4/5*o - 34/5*o**p.
-2*o*(o + 1)**3*(5*o + 2)/5
Suppose -1/6*n**3 - 1/2*n + 1/2*n**2 + 1/6 = 0. Calculate n.
1
Let o(w) = -12*w**3 - 252*w**2 - 276*w - 164. Let g(r) = -r**3 - 23*r**2 - 25*r - 15. Let t(l) = 32*g(l) - 3*o(l). Factor t(y).
4*(y + 1)**2*(y + 3)
Suppose -5*i = -0*r - 2*r - 9, 2*r - 18 = -4*i. Suppose 13*u**3 + u + 0*u - 14*u**r = 0. What is u?
-1, 0, 1
Let o(d) be the first derivative of -2*d**5/15 - d**4/3 + 2*d**2/3 + 2*d/3 + 6. Factor o(l).
-2*(l - 1)*(l + 1)**3/3
Find c, given that -c + 7/4*c**4 + 19/4*c**3 + 2*c**2 + 0 = 0.
-2, -1, 0, 2/7
Suppose 3*l - 3 = 3*s, 0 = -3*l - 0*l - 2*s + 8. Let a(m) be the third derivative of 0*m + 0 + 0*m**3 + m**l - 1/60*m**5 - 1/24*m**4. Factor a(y).
-y*(y + 1)
Let l be 47/9 - (-4)/(-18). Suppose 3 = -i + l. Factor 0*z**i + 0 + 2/5*z - 2/5*z**3.
-2*z*(z - 1)*(z + 1)/5
Let r(h) be the third derivative of -h**5/180 - 5*h**4/72 - 2*h**3/9 - 12*h**2. Factor r(v).
-(v + 1)*(v + 4)/3
Suppose 0 = k - 4*a + 2, -3*a + 5 = -0*k + k. What is r in -2 - 4*r**2 + 3*r**4 - 4*r + 3*r**4 - k*r**5 - 4*r**3 + 10*r = 0?
-1, 1
Factor -1 + 1/2*r**2 - 1/2*r.
(r - 2)*(r + 1)/2
Let c(r) be the third derivative of r**7/105 - r**6/60 - r**5/30 + r**4/12 + 3*r**2. Solve c(n) = 0.
-1, 0, 1
Let k(u) = -99*u**3 + 399*u**2 - 345*u - 105. Let w(f) = -25*f**3 + 100*f**2 - 86*f - 26. Let y(d) = 2*k(d) - 9*w(d). Factor y(h).
3*(h - 2)**2*(9*h + 2)
Let f(z) be the third derivative of 0*z**3 - 2*z**2 - 1/480*z**6 + 1/96*z**4 + 0*z**5 + 0*z + 0. Factor f(w).
-w*(w - 1)*(w + 1)/4
Let m(r) = 28*r**3 - 36*r**2 - 216*r + 118. Let g(f) = -3*f**3 + 4*f**2 + 24*f - 13. Let x(d) = 52*g(d) + 6*m(d). Factor x(l).
4*(l - 2)*(l + 2)*(3*l - 2)
Suppose 8*b - 88 = -14*b. Let -3/5*m**3 + 2/5*m**b + 0 - 3/5*m**2 + 2/5*m = 0. Calculate m.
-1, 0, 1/2, 2
Suppose -l + 4*c = 1 - 16, -4*l - 4*c = 0. Factor 0 - 6/5*p**l - 8/5*p + 12/5*p**2 + 1/5*p**4.
p*(p - 2)**3/5
Let u be 7/(-4) - (-1 - 1). Let o(j) be the first derivative of 0*j - 1/3*j**3 + 0*j**2 + u*j**4 + 2 + 1/5*j**5 - 1/6*j**6. Determine h, given that o(h) = 0.
-1, 0, 1
Let s(o) = 7*o - 1 - 4*o + 2 - 2. Let j be s(1). Determine n so that 4/5*n - 2/5*n**j - 2/5 = 0.
1
Let p(c) be the third derivative of 0*c - 343/90*c**7 + 343/45*c**6 + 28/9*c**4 - 98/15*c**5 + 0 - 6*c**2 - 8/9*c**3. Factor p(f).
-(7*f - 2)**4/3
Suppose 1/7*b**2 - 2/7*b - 3/7 = 0. Calculate b.
-1, 3
Let l be ((-3)/2)/(1/(-1 - 1)). Let t(b) be the second derivative of 0 + 0*b**4 + 0*b**l + 2*b - 1/80*b**5 + 0*b**2 - 1/120*b**6. Factor t(a).
-a**3*(a + 1)/4
Factor -94*b**3 + 212*b + 38*b**3 + 2*b**4 + 2*b**4 + 256 + 236*b + 132*b**2.
4*(b - 8)**2*(b + 1)**2
Let o = -9 + 13. Let n(d) be the first derivative of -o + 1/3*d**3 - 9/4*d**2 + 9/8*d**4 - d. Factor n(t).
(t - 1)*(t + 1)*(9*t + 2)/2
Let a(m) = 33*m**2 + 9*m + 15 + 0*m - 39*m**2. Let d(b) = -b**2 - b - 1. Let x(r) = -a(r) - 15*d(r). Solve x(l) = 0 for l.
-2/7, 0
Suppose 5*a - 5 = 3*k + 5, -5*a + 5*k = -10. Factor -2/5*q**3 + 0 + 2/5*q**5 + 2/5*q**4 + 0*q - 2/5*q**a.
2*q**2*(q - 1)*(q + 1)**2/5
Let j be -5 - ((-264)/64 - (-1)/(-1)). Suppose 0*v**4 + 0*v**2 + 0 + 1/8*v**5 + 0*v - j*v**3 = 0. What is v?
-1, 0, 1
Let i(d) be the first derivative of 0*d**3 - 3*d + 3/4*d**2 + 4 - 1/8*d**4. Let s(y) be the first derivative of i(y). Find c such that s(c) = 0.
-1, 1
Let s be (-2)/21*(9 + -12). Let -2/7*g**2 - s - 4/7*g = 0. What is g?
-1
Let l(q) = q + 7. Let p be l(7). Suppose p - 4 = 5*u. Factor 5*o**u - 3*o**2 + 8*o**3 + 0*o**3.
2*o**2*(4*o + 1)
Factor 12 - 56*u + 100/3*u**2 - 16/3*u**3.
-4*(u - 3)**2*(4*u - 1)/3
What is a in -15/4*a**2 + 9/2 + 39/4*a = 0?
-2/5, 3
Let f(n) be the third derivative of -n**6/480 + n**5/240 + n**4/48 - 9*n**2. Find 