f - 4)**2
Let y = 296 - 1478/5. Factor -14/15*j**3 + 8/5*j**2 - 4/15 - y*j.
-2*(j - 1)**2*(7*j + 2)/15
Suppose 10*t = 15*t. Let x(s) be the third derivative of 0*s**3 + 0*s**4 + t*s**5 + 1/300*s**6 + 2*s**2 + 0*s + 0. Suppose x(a) = 0. What is a?
0
Factor 1/2 + 1/4*s**4 - 3/4*s**2 - 1/4*s + 1/4*s**3.
(s - 1)**2*(s + 1)*(s + 2)/4
Let p = 6 + -3. Suppose -28*t + 25*t + 6 = 0. Factor -21/5*l**5 - 30*l**p - 24*l**t - 9*l - 18*l**4 - 6/5.
-3*(l + 1)**4*(7*l + 2)/5
Let x(o) be the second derivative of -9*o**4/4 - 3*o**3 - 3*o**2/2 - 6*o. Factor x(t).
-3*(3*t + 1)**2
Let i be (4/40*-2)/(-5 + 1). Let g(c) be the second derivative of 1/12*c**4 + 0 + 1/90*c**6 - 3*c - i*c**5 - 1/18*c**3 + 0*c**2. Let g(j) = 0. Calculate j.
0, 1
Let r be 18/8 + (-2)/8. Let j be 1/(-1) + (-22)/(-18). What is q in 2/9*q + 2/9 - 2/9*q**3 - j*q**r = 0?
-1, 1
Suppose -81*s = -75*s - 18. Suppose 12/7*g**4 + 0*g - 3/7*g**5 + 6/7*g**2 + 0 - 15/7*g**s = 0. What is g?
0, 1, 2
Let g(a) = -1. Let y(t) = t**3 + t**2 + 8. Let v(k) = 24*g(k) + 3*y(k). Factor v(o).
3*o**2*(o + 1)
What is x in -12/7*x**2 - 48/7 + 2/7*x**4 + 8*x - 6/7*x**3 = 0?
-3, 2
Let n = 715 - 2144/3. Factor -n*o + 1/3 + 1/3*o**3 - 1/3*o**2.
(o - 1)**2*(o + 1)/3
Determine a, given that 0 + 0*a + 1/3*a**3 - 1/3*a**2 = 0.
0, 1
Let t(l) be the first derivative of 14*l**5/5 + 23*l**4/2 + 18*l**3 + 13*l**2 + 4*l - 2. Factor t(u).
2*(u + 1)**3*(7*u + 2)
Find t such that -44/13*t + 242/13 + 2/13*t**2 = 0.
11
Let t(k) be the third derivative of k**6/120 + k**5/40 - k**3/6 - 4*k**2. Let w(l) be the first derivative of t(l). Solve w(u) = 0 for u.
-1, 0
Let r be (16/7)/(10/35). Let y = 11 - r. Find c such that -1/3*c**y + 0 - 1/3*c + 2/3*c**2 = 0.
0, 1
Let a(p) = -p**5 + 9*p**4 + 5*p**3 - 3*p**2 - 7*p. Let t(m) = 8*m**4 + 4*m**3 - 4*m**2 - 6*m. Let v(o) = 4*a(o) - 6*t(o). Find y, given that v(y) = 0.
-2, -1, 0, 1
Let j(l) = l**2 + 5*l + 3. Let n be j(-4). Let r be ((-1)/(n/(-8)))/(-2). Let -2*z - r*z**2 - z**3 + z**3 - 2*z**3 = 0. What is z?
-1, 0
Let f(i) = -2*i + 2. Let c(m) = m + 1. Let p(l) = 3*c(l) + f(l). Let a be p(-5). Determine y so that 0*y**3 + 0 + 1/3*y**4 - 1/3*y**2 + a*y = 0.
-1, 0, 1
Let y(s) = 0*s - 4*s**3 - s + 2*s + 7*s**3 - 2*s**2. Let i be y(1). Let 0*t - 1/4*t**3 - 1/4*t**i + 0 = 0. What is t?
-1, 0
Let j(c) = -12*c**4 + 39*c**2 - 9*c - 3. Let s(x) = -13*x**4 - x**3 + 40*x**2 - 8*x - 4. Let m(r) = 4*j(r) - 3*s(r). Suppose m(b) = 0. Calculate b.
-2, 0, 1/3, 2
Factor 12*w**2 - 8*w**3 + 78*w**4 + 2*w**5 + 34*w**3 - 62*w**4.
2*w**2*(w + 1)**2*(w + 6)
Suppose 9*g - 116 = 28. Let b be (-18)/g*(-16)/12. Find m such that 0*m**2 + 3/4*m**5 + 0*m - b*m**4 + 0 + 3/4*m**3 = 0.
0, 1
Let b = -94/3 - -284/9. Factor b*h + 0 - 2/9*h**2.
-2*h*(h - 1)/9
Let b(r) be the third derivative of r**5/90 - r**4/18 + r**3/9 - 3*r**2. Factor b(y).
2*(y - 1)**2/3
Let x(a) be the first derivative of a**6/42 - a**5/35 - 3*a**4/28 + a**3/21 + a**2/7 + 34. Solve x(u) = 0.
-1, 0, 1, 2
Let q be 8 + -2 + (-32)/8. What is n in -2/9*n**5 + 0*n**q + 0 + 2/9*n**3 + 0*n**4 + 0*n = 0?
-1, 0, 1
Let p(q) be the first derivative of q**6/120 - q**4/24 - 7*q**2/2 - 5. Let u(j) be the second derivative of p(j). Factor u(l).
l*(l - 1)*(l + 1)
Let p(u) = -u - 4. Let b be p(-6). Suppose 4*x**b - x**2 - x**2 + 2*x + 6*x + 8 = 0. Calculate x.
-2
Let c(o) be the first derivative of o**5/5 - o**4/3 - o**3/9 + o**2/3 + 6. Factor c(t).
t*(t - 1)**2*(3*t + 2)/3
Let c be -5*1/(-5)*3. Let u(q) be the second derivative of 0 - q + 1/18*q**4 + 0*q**c + 0*q**2. Factor u(l).
2*l**2/3
Let t(h) = -h**2 + 2. Let s be t(0). Determine d, given that -d**2 - d**2 + 2*d**s - 2*d**2 = 0.
0
Let y(d) = d**3 - 9*d**2 + 8*d. Let l be y(8). Find f, given that -f**2 + f**3 + 2*f**3 + l*f**3 + 4*f**2 = 0.
-1, 0
Let b(l) = -3*l**2 - 11*l - 2. Let o(d) = 3*d**2 + 10*d + 2. Suppose 4*p + 42 = -3*p. Let m(s) = p*o(s) - 5*b(s). Factor m(j).
-(j + 1)*(3*j + 2)
Let d(g) be the first derivative of -g**5/10 - g**4/2 - 2*g**3/3 - 2*g - 2. Let s(i) be the first derivative of d(i). Factor s(z).
-2*z*(z + 1)*(z + 2)
Let z(v) be the third derivative of v**7/105 - v**5/15 + v**3/3 - 25*v**2. Factor z(l).
2*(l - 1)**2*(l + 1)**2
Let g(m) be the third derivative of -m**7/5040 - m**6/2160 + m**3/2 + 6*m**2. Let j(u) be the first derivative of g(u). Factor j(s).
-s**2*(s + 1)/6
Let q(z) = 2*z**2 + 4*z + 2. Let v(r) = -r**2 - 4*r - 1. Let d be v(-5). Let w(p) = -3*p + 0 - p**2 - 1 + p. Let o(a) = d*q(a) - 13*w(a). Factor o(h).
(h + 1)**2
Let q(y) be the third derivative of -1/28*y**4 + 5*y**2 - 1/21*y**3 + 0 + 0*y + 1/210*y**6 + 1/245*y**7 - 1/105*y**5 + 1/1176*y**8. Factor q(s).
2*(s - 1)*(s + 1)**4/7
Let v(n) be the third derivative of n**8/2520 - n**6/540 - n**3/6 + 6*n**2. Let m(t) be the first derivative of v(t). Factor m(i).
2*i**2*(i - 1)*(i + 1)/3
Find m such that 2*m + 2 - 3/2*m**2 = 0.
-2/3, 2
Suppose i = -2*i. Suppose l = -i + 2. Factor 0 + 1/4*x + 1/4*x**l.
x*(x + 1)/4
Let t(w) be the first derivative of w**5/150 - w**2 + 2. Let b(s) be the second derivative of t(s). Factor b(m).
2*m**2/5
Factor 0 + 2/13*j**2 + 2/13*j.
2*j*(j + 1)/13
Factor 0*h + 2/7 - 2/7*h**2.
-2*(h - 1)*(h + 1)/7
Let b be 4 - ((-352)/12)/(-8). Solve -b*j**4 - 4/3*j**3 - 2*j**2 - 4/3*j - 1/3 = 0.
-1
Let m(o) be the second derivative of -o**8/8400 + o**6/900 - o**4/120 - 4*o**3/3 - 4*o. Let y(b) be the second derivative of m(b). Factor y(v).
-(v - 1)**2*(v + 1)**2/5
Let v be ((-50)/8)/(-5) + 72/(-96). Suppose 0 + 1/2*m**3 + v*m + m**2 = 0. Calculate m.
-1, 0
Let 6*l**5 + 16*l**3 - 21*l**3 - l**5 = 0. Calculate l.
-1, 0, 1
Let h(z) be the third derivative of -z**8/168 - z**7/210 + z**6/40 + z**5/60 - z**4/24 - 23*z**2. Solve h(m) = 0.
-1, 0, 1/2, 1
Suppose -2*v = -3*h - 212, -4*h - 5*v - 65 = -3*h. Let c be 2/7 + (-120)/h. Factor -4/3*f**4 + c*f**3 - 4/3*f**2 + 1/3*f**5 + 1/3*f + 0.
f*(f - 1)**4/3
Let h be 0 + 1 - (-2 - 1). Let s = -4 + h. Factor 0*u - 2/9*u**5 - 2/9*u**3 + s + 0*u**2 - 4/9*u**4.
-2*u**3*(u + 1)**2/9
Let y(w) = -30*w**4 + 94*w**3 - 82*w**2 + 14*w + 2. Let l(z) = 61*z**4 - 189*z**3 + 165*z**2 - 27*z - 5. Let f(i) = 2*l(i) + 5*y(i). Factor f(q).
-4*q*(q - 2)*(q - 1)*(7*q - 2)
Suppose 0 = i + i. Find x such that 1 + i + 0 - x + x**2 - x = 0.
1
Let z(a) be the third derivative of a**8/504 - a**6/180 - a**2. Factor z(i).
2*i**3*(i - 1)*(i + 1)/3
Let 2/7 + 6/7*b**2 - 2/7*b**3 - 6/7*b = 0. What is b?
1
Let z(t) be the second derivative of 3/20*t**5 + 5/2*t**3 + 0 - 3*t**2 - t**4 - 2*t. Factor z(d).
3*(d - 2)*(d - 1)**2
Let x = 1353 + -20288/15. Let h(t) be the first derivative of -x*t**5 + 1 + 8/9*t**3 - 1/3*t**2 + 2/9*t**6 - 1/3*t - 1/6*t**4. Factor h(d).
(d - 1)**3*(d + 1)*(4*d + 1)/3
Determine w so that 12/5*w + 0*w**2 - 8/5 - 4/5*w**3 = 0.
-2, 1
Let f be ((-8)/(-3))/(-1)*(-6)/4. Factor -1/2*c + 1/4*c**2 + 1/2*c**3 + 0 - 1/4*c**f.
-c*(c - 2)*(c - 1)*(c + 1)/4
Let s(n) = -n**3 + n**2 + 1. Let a(h) = -51*h**3 + 30*h**2 - 4*h + 2. Let g(i) = a(i) - 2*s(i). Factor g(t).
-t*(7*t - 2)**2
Let a = -139/3 - -47. Factor a*t**3 - 2/3*t**2 + 0 + 0*t.
2*t**2*(t - 1)/3
Let o(c) = c**3 + c**2 - c**5 + c + 0*c + 0*c + c**4. Let y(l) = 3*l**5 + 2*l**4 + 2*l**3 - 2*l**2 - 2*l. Let n(a) = -2*o(a) - y(a). Factor n(t).
-t**3*(t + 2)**2
Suppose 5*u - 2 = -2*i - 6, -3*i + 4*u = -17. Suppose 3*f + i*h = 24, f + 0*h - 20 = -5*h. Find r, given that r**3 - r - 5*r**2 + f*r**2 = 0.
-1, 0, 1
Let f(i) be the second derivative of -i**6/40 + 3*i**5/80 + 3*i**4/16 - 5*i**3/8 + 3*i**2/4 + 20*i. Factor f(j).
-3*(j - 1)**3*(j + 2)/4
Let w(j) = 2 + 24*j**4 - 23*j**4 - 3 + j**2 - j**3. Let c(h) = -14*h**4 - h**3 + 10*h**2 + 3*h + 2. Let v(q) = c(q) + 2*w(q). Let v(p) = 0. Calculate p.
-1, -1/4, 0, 1
Let z(w) be the third derivative of w**8/336 - w**7/70 + w**6/60 + w**5/30 - w**4/8 + w**3/6 + 9*w**2. Factor z(n).
(n - 1)**4*(n + 1)
Let m = -4/39 - -151/78. Let a = 13/6 - m. Factor 1/3*b**2 - 1/3*b**3 - 1/3 + a*b.
-(b - 1)**2*(b + 1)/3
Let w = -28 + 31. Let s(b) be the second derivative of -2*b + 0*b**2 + 1/36*b**4 - 1/18*b**w + 0. Factor s(c).
c*(c - 1)/3
Factor -25*n**3 - 15*n**4 - 20*n**3 + 60*n**3 - 24*n**3 + 6*n**2.
-3*n**2*(n + 1)*(5*n - 2)
Let f(o) be the first derivative of -2*o**6 + 4*o**5 - 2*o**4 - 25. Factor f(j).
-4*j**3*(j - 1)*(3*j - 2