given that z(q) = 0.
1
Let m(r) be the second derivative of r**5/120 - r**4/36 + r**3/36 - 11*r. Factor m(z).
z*(z - 1)**2/6
Suppose 7*l = 10*l - 9. Solve 0*p + 0 + 2/11*p**2 - 2/11*p**l = 0.
0, 1
Factor 1/4*t**2 - 2*t + 4.
(t - 4)**2/4
Suppose -77 + 79 = 2*r. What is x in r + 1/2*x - 1/2*x**2 = 0?
-1, 2
Let y(o) = -o**3 - o**2 + o. Let b(l) = 2*l**4 - 7*l**3 + 29*l**2 - 21*l. Let c(a) = b(a) + 5*y(a). Factor c(x).
2*x*(x - 2)**3
Let i be -2 + ((-67)/(-18) - 6/4). Solve 0 + i*c**3 + 2/9*c - 4/9*c**2 = 0.
0, 1
Let t(k) be the first derivative of -8*k**4/21 - 8*k**3/21 - k**2/7 + 3*k + 2. Let o(f) be the first derivative of t(f). Find p such that o(p) = 0.
-1/4
Let x(r) be the second derivative of -r**7/105 - r**6/15 - 9*r**5/50 - 7*r**4/30 - 2*r**3/15 + 6*r. Factor x(y).
-2*y*(y + 1)**3*(y + 2)/5
Suppose -x**2 + 4*x**3 - x**3 + 0*x**2 - 4*x**3 = 0. Calculate x.
-1, 0
Let s be (0 - 0)/(7 + (-10 - -7)). Find t, given that -4/9*t**4 + 4/9*t**2 + s + 2/9*t**3 - 2/9*t = 0.
-1, 0, 1/2, 1
Let n = -96 - -68. Let h be 2 + -4 - n/12. Find c, given that 0 - 1/3*c**3 + 0*c - h*c**4 + 0*c**2 = 0.
-1, 0
Let x = 24 + -21. Suppose -20 = 4*k, -5*k = 4*v - 2 + 15. Suppose -z**v + 0*z**x + 0*z**3 + z = 0. Calculate z.
-1, 0, 1
Suppose -15*z = -18*z. Let r(j) be the second derivative of 0 + z*j**3 + j + 1/24*j**4 + 0*j**2. Let r(y) = 0. Calculate y.
0
Let g(f) = -18*f - 16. Let s be g(-1). Let 4/5 - 2/5*z**4 + 6/5*z**s + 2/5*z**3 - 2*z = 0. Calculate z.
-2, 1
Let s(u) be the first derivative of 1/6*u**4 + 0*u**3 - 4*u - 4/3*u**2 - 1/30*u**5 + 2. Let n(a) be the first derivative of s(a). Factor n(l).
-2*(l - 2)**2*(l + 1)/3
Suppose 5*f - 4*k - 37 = 0, -4*f - k = -5 - 12. Let h = 25 - 25. Factor 2/7*s**f + 4/7*s**4 - 2/7*s - 4/7*s**2 + h + 0*s**3.
2*s*(s - 1)*(s + 1)**3/7
Suppose v + 3*f + 2 = -0, 50 = 5*v - 5*f. Determine k, given that -k**2 - 5 - 1 - v - 6*k + 4 = 0.
-3
Find s such that -s**4 - 6*s**3 - 2*s**4 + s**3 + 8*s**4 = 0.
0, 1
Suppose 5*p - 1 = 59. Let o be 0/(4 + p/(-4)). Factor o - a**3 + 1/3*a**5 - 2/3*a**4 + 4/3*a + 4/3*a**2.
a*(a - 2)**2*(a + 1)**2/3
Factor 7/8*b**2 + 1/4*b + 9/8*b**3 + 0 + 5/8*b**4 + 1/8*b**5.
b*(b + 1)**3*(b + 2)/8
Let f = 10 - 7. Suppose 2*l**4 - 2*l**3 - f*l**3 + 3*l**3 = 0. What is l?
0, 1
Let r = 68 - 64. Let d(v) be the first derivative of 5/8*v**r + 1/6*v**3 + 2 + 0*v - 1/4*v**2 + 3/10*v**5. Let d(f) = 0. Calculate f.
-1, 0, 1/3
Let l(m) be the second derivative of -m**7/357 + 2*m**6/255 + m**5/85 - 4*m**4/51 + 7*m**3/51 - 2*m**2/17 - 4*m. Let l(w) = 0. Calculate w.
-2, 1
Factor -80/3*d**2 + 2/3*d**5 + 32/3*d + 22*d**3 + 0 - 20/3*d**4.
2*d*(d - 4)**2*(d - 1)**2/3
Let o be (2 + -1)/((-2)/(-6)). Let z = -8 + 11. What is h in 2*h**o - 3*h**3 - h**3 + z*h**2 - h**2 = 0?
0, 1
Let h = -8/7 - -199/168. Let t(w) be the third derivative of 0 + 1/210*w**7 - h*w**4 + 0*w + 1/60*w**6 + w**2 - 1/30*w**5 + 1/6*w**3 - 1/336*w**8. Factor t(x).
-(x - 1)**3*(x + 1)**2
Suppose -3*f = 2*f. Let u be (f - (-13)/3) + -1. Let 0 - u*y**3 + 4/3*y**2 + 0*y + 2*y**4 = 0. Calculate y.
0, 2/3, 1
Let s(a) = a**2 - 3*a + 4. Let x be s(3). Factor -6*b - 48*b**3 + 6*b**2 - 20*b**2 - 19*b**2 - 21*b**x + 0*b.
-3*b*(b + 1)**2*(7*b + 2)
Let p(y) = 5*y**3 - 9*y**2 + 6*y. Let o(j) = -9*j**3 + 17*j**2 - 11*j. Suppose 5*c - 4*c + 6 = 0. Let a(m) = c*o(m) - 11*p(m). Factor a(r).
-r**2*(r + 3)
Let j(k) = -k**2 + 10*k - 2. Let r be j(9). Suppose -1 = -f + r. Factor f*l**2 - 6*l**2 - 1 + 9 - 8*l.
2*(l - 2)**2
Factor 8/3 + 4/3*d + 1/6*d**2.
(d + 4)**2/6
Let q(s) be the second derivative of -5*s**4/12 - 5*s**3/3 - 21*s. Factor q(k).
-5*k*(k + 2)
Determine v, given that -2/3*v**2 + 2/3*v**4 + 2/3*v**3 + 0 - 2/3*v = 0.
-1, 0, 1
Let r = 311/581 + 3/83. Factor r*v**3 + 2/7*v**4 + 0 + 0*v + 2/7*v**2.
2*v**2*(v + 1)**2/7
Let t(g) be the third derivative of 4*g**2 + 0*g**3 - 1/15*g**5 + 0*g - 1/3*g**4 + 0. Factor t(v).
-4*v*(v + 2)
Let p(k) be the third derivative of k**5/300 + k**4/40 + k**3/15 - 4*k**2. Determine q so that p(q) = 0.
-2, -1
Suppose 7*t - 5*t - 3*j + 9 = 0, 0 = 2*t + 5*j - 31. Factor -1/5*y**t + 4/5*y**2 + 0 - 4/5*y.
-y*(y - 2)**2/5
Let z(u) be the third derivative of -u**6/420 + u**4/84 - 5*u**2. Factor z(m).
-2*m*(m - 1)*(m + 1)/7
Let n be 2/9 - 98/(-126). Let o be (-28)/(-42)*(n + 0). Factor -1/3*q + 7/3*q**3 + 0 + 4/3*q**4 + o*q**2.
q*(q + 1)**2*(4*q - 1)/3
Let w(f) be the third derivative of -f**6/120 - f**5/30 - f**4/24 + f**2. Find z such that w(z) = 0.
-1, 0
Determine g so that -140*g - 4*g**2 + 140*g + 16 = 0.
-2, 2
Suppose 0*f - 5*f = 0. Let g(d) be the first derivative of d**3 + f*d - 3/2*d**2 + 2. Suppose g(j) = 0. What is j?
0, 1
Let z(g) be the second derivative of g**7/126 + 7*g**6/90 + g**5/4 + 13*g**4/36 + 2*g**3/9 - g + 1. Factor z(m).
m*(m + 1)**3*(m + 4)/3
Let j(h) be the second derivative of -h**6/420 - h**5/70 - h**4/42 + 3*h**2 + 4*h. Let v(w) be the first derivative of j(w). Factor v(c).
-2*c*(c + 1)*(c + 2)/7
Suppose -14*s**4 + 2*s**4 - 2*s**2 + 5*s**4 - 9*s**3 = 0. What is s?
-1, -2/7, 0
Factor 0*s + 5 + 5*s**3 - 75*s**2 - 5*s + 70*s**2.
5*(s - 1)**2*(s + 1)
Suppose -3*k = -8*k + 35. Let o = k - -3. What is g in -o*g**2 + 2 + 6*g + 0 + 2 = 0?
-2/5, 1
Suppose 5*t - 6 = j, 5*t = j - 6*j + 30. Factor -6*b**t + 3*b**3 - 6*b**2 + b**3 + 8*b.
4*b*(b - 2)*(b - 1)
Let r(s) be the first derivative of -s**3/12 - s**2/2 - 3*s/4 + 46. Factor r(a).
-(a + 1)*(a + 3)/4
Let a(n) be the second derivative of -4*n + 0 + 4/15*n**3 - 4/5*n**2 - 1/30*n**4. Factor a(h).
-2*(h - 2)**2/5
Let m(i) be the third derivative of 0*i + 1/2*i**3 + i**2 + 0 - 3/16*i**4 + 1/40*i**5. Determine j, given that m(j) = 0.
1, 2
Let s = 34 + -164/5. Solve -4/5*c**3 - 2/5*c**5 + 6/5*c**4 - 2/5 - 4/5*c**2 + s*c = 0.
-1, 1
Let f(z) = 11*z**2 - 8*z + 7. Let b(s) be the first derivative of 2*s**3 - 2*s**2 + 4*s - 1. Let h(g) = -7*b(g) + 4*f(g). Factor h(r).
2*r*(r - 2)
Let n = 28 + -25. Find w such that -4/9*w**2 + 0 + 2/9*w + 2/9*w**n = 0.
0, 1
Let v = 3/10 - 2/15. Let r(n) be the second derivative of -n**2 + 1/2*n**3 - 4*n + v*n**4 - 3/20*n**5 + 0. Factor r(q).
-(q - 1)*(q + 1)*(3*q - 2)
Let z be 4/(-4*3/(-6)). What is k in -4*k + k**2 - 2*k**z + 3*k**2 = 0?
0, 2
Let o(m) be the first derivative of m**5/15 + m**4/6 - m**2/3 - m/3 - 1. Find x such that o(x) = 0.
-1, 1
Let c(d) = 4 - 3*d**2 + 1 + 0*d**2. Let o = -24 - -29. Let r(h) = -h**2 + 2. Let g(z) = o*r(z) - 2*c(z). Find q such that g(q) = 0.
0
Let g(m) be the first derivative of 5*m**4/4 - 5*m**3 - 5*m**2/2 + 15*m + 6. Factor g(h).
5*(h - 3)*(h - 1)*(h + 1)
Solve -x**4 - 16*x + 6*x**3 - 24*x - 12 + 4*x**4 - 9*x**2 + 16*x = 0 for x.
-2, -1, 2
Suppose -3*h - 3 = -12. Suppose -i = -h - 2. Factor 2/9*u**i + 0*u**4 + 0*u**2 + 0 - 2/9*u**3 + 0*u.
2*u**3*(u - 1)*(u + 1)/9
Suppose 7*s - 5*s - 4 = 0. Let t(a) be the second derivative of -1/15*a**3 - 1/10*a**4 + 0 - a + 0*a**s - 1/75*a**6 - 3/50*a**5. Suppose t(j) = 0. Calculate j.
-1, 0
Factor 1/4*t**2 + 1/4*t**3 - 1/4*t**4 - 1/4*t + 0.
-t*(t - 1)**2*(t + 1)/4
Let y(m) = 5*m**4 - 26*m**3 + 26*m**2 + 6*m - 11. Let c(b) = b**4 - 5*b**3 + 5*b**2 + b - 2. Let x(z) = 11*c(z) - 2*y(z). Factor x(u).
u*(u - 1)**3
Suppose 6 - 3 + 4*y - 5 - 2*y**2 = 0. What is y?
1
Let i = 536 - 13398/25. Let x = i - -8/25. Factor x*p - 8/5*p**2 - 6/5*p**3 + 4/5.
-2*(p + 1)**2*(3*p - 2)/5
Factor -3/2*u**4 + u + 5*u**3 - 9/2*u**2 + 0.
-u*(u - 2)*(u - 1)*(3*u - 1)/2
Let f(w) be the first derivative of w**5/5 + 7*w**4/4 + 6*w**3 + 10*w**2 + 8*w - 5. Factor f(x).
(x + 1)*(x + 2)**3
Let o = -54 - -243. Let a = -1699/9 + o. Suppose -a*z + 0 + 0*z**2 + 2/9*z**3 = 0. What is z?
-1, 0, 1
Factor -4*s**3 - 4*s**4 + 57 - 57.
-4*s**3*(s + 1)
Let x be (5 + 5 + -9)*0. Let l(k) be the third derivative of 1/12*k**3 + 1/8*k**4 + 1/60*k**6 + 3/40*k**5 + 5*k**2 + x + 0*k. Factor l(s).
(s + 1)**2*(4*s + 1)/2
Suppose u = -0 + 3. Factor m - 3*m**u + 0*m - 2*m**4 + 0*m**3 + 0*m**3.
-m*(m + 1)**2*(2*m - 1)
Suppose t + 5*t = 12. Let c(i) be the first derivative of 1/3*i**t + 2/15*i**5 + 1/2*i**4 + 2/3*i**3 + 0*i + 2. Factor c(u).
2*u*(u + 1)**3/3
Let g(i) be the third derivative of i**2 - 1/900*i**6 + 0 + 0*i + 1/100*i**5 - 1/30*i**4 - 1/2*i**3. Let j(q) be the first derivative of g(q). Factor j(t).
-2*(t - 2)*(t - 1)/5
Find t such t