2
Let o be (-2*1/4)/((-10)/4). Factor -2/5*s**2 + 0 + o*s**5 + 0*s + 2/5*s**4 - 1/5*s**3.
s**2*(s - 1)*(s + 1)*(s + 2)/5
Let r be (3/(-42))/((-3)/9054). Let h = r + -215. Determine k so that -h - 10/7*k**2 - 2*k = 0.
-1, -2/5
Let h(f) be the third derivative of 1/35*f**7 + 0*f**3 - f**2 + 0*f - 1/10*f**5 + 0 + 1/30*f**6 - 1/6*f**4. Factor h(u).
2*u*(u - 1)*(u + 1)*(3*u + 2)
Let z = 23/3 - 7. Let w(y) = -y**2 + 11*y + 14. Let a be w(12). Solve -2/3*u + 2/3 - z*u**a + 2/3*u**3 = 0.
-1, 1
Suppose -c = -6*c - 15. Let r(y) = -y**2 - 4*y - 3. Let g be r(c). Factor 3*h**3 + g*h**3 + h**4 + 3*h**2 + h + 0*h**3.
h*(h + 1)**3
Let p = 11 + -6. Factor -8*j - 1 - 2 - j**3 + p*j**2 + 7.
-(j - 2)**2*(j - 1)
Let 1/2*i**3 - 2*i - 1/2*i**2 + 2 = 0. What is i?
-2, 1, 2
Let g(m) be the second derivative of m**7/168 + m**6/60 - m**5/40 - m**4/6 - 7*m**3/24 - m**2/4 - 57*m. Factor g(p).
(p - 2)*(p + 1)**4/4
Suppose -3*c + 36 = -3*h, -3*h + 6 = c + 2. Suppose -4*f = n - c, -4 = f - 3*f - n. What is a in 2*a + 4/7 - 2*a**f - 4/7*a**2 = 0?
-1, -2/7, 1
Let m(q) be the third derivative of q**5/30 + q**4/2 + 5*q**3/3 - 44*q**2. Solve m(n) = 0.
-5, -1
Let o(x) be the third derivative of -x**6/900 - x**5/300 + x**4/30 + 2*x**3/3 + 2*x**2. Let b(a) be the first derivative of o(a). Factor b(n).
-2*(n - 1)*(n + 2)/5
Let p(r) = 4*r**2 + 2*r + 4. Let n(s) = -s**2. Let y be (-8)/(2 + -3) + -2. Let a(k) = y*n(k) + p(k). Solve a(c) = 0.
-1, 2
Suppose -5*k = -k - 48. Suppose n - 4*n = -k. Factor -6*c**2 - 3*c**4 + 2*c**5 + c**n + 6*c**2.
2*c**4*(c - 1)
Let j(m) = m**2 - 8*m - 7. Let i be j(9). Determine d, given that 0*d + i*d + 2*d**2 + 12 - 16 - 4*d = 0.
-1, 2
Let f(b) = 2*b**3 - b**2 - 2*b + 1. Let r be f(2). Determine q, given that 8 - 3*q**3 - 2 + 0*q**4 + 4*q - r*q**2 - q + 3*q**4 = 0.
-1, 1, 2
Let d(q) be the first derivative of -3/5*q**2 - 4/15*q**3 + 4 + 3/10*q**4 + 4/5*q. Factor d(m).
2*(m - 1)*(m + 1)*(3*m - 2)/5
Let d = 1209/8 - 151. Solve -1/4*o**4 - d*o + 1/2*o**2 - 1/8*o**5 - 1/4 + 1/4*o**3 = 0.
-2, -1, 1
Let a(w) = -w**4 - w**3 + w - 1. Let n(d) = 6*d**4 + 8*d**3 + 3*d**2 - 8*d + 5. Let m = 18 + -20. Let z(x) = m*n(x) - 14*a(x). Factor z(s).
2*(s - 2)*(s - 1)*(s + 1)**2
Let s(l) = -l**3 - 2*l**2 + 2*l + 1. Let d be s(-3). Let g(u) = u**3 + 6*u**2 + 6*u + 7. Let i be g(-5). Factor 2 - d*y - i*y + y**2 + 3*y.
(y - 2)*(y - 1)
Let w = -37 - -39. Let t(q) be the first derivative of 8/5*q**5 - 2*q + 2*q**4 - w - 4*q**2 - 2*q**3. Let t(i) = 0. What is i?
-1, -1/2, 1
Let k(w) be the second derivative of -w**8/2520 + w**7/1260 + w**6/1080 - w**4/4 - 8*w. Let i(d) be the third derivative of k(d). Factor i(n).
-2*n*(n - 1)*(4*n + 1)/3
Let f = 4/13 - 3/52. Let i(a) be the first derivative of 1/8*a**4 + f*a**2 - 3 + 1/3*a**3 + 0*a. Factor i(v).
v*(v + 1)**2/2
Let d(h) be the second derivative of 5*h**4/108 - 2*h**3/27 - 2*h**2/3 + 38*h. Factor d(t).
(t - 2)*(5*t + 6)/9
Let g(t) be the first derivative of t**4/18 - t**2/9 + 11. Factor g(n).
2*n*(n - 1)*(n + 1)/9
Let n be (-2)/(-18)*-2 + (-120)/(-54). Suppose 0*g - g + 4 = 0. Let 0*l + 3/2*l**g + 0 + 3/2*l**3 + 1/2*l**5 + 1/2*l**n = 0. Calculate l.
-1, 0
Let 2*u**4 + 2*u**4 + 6*u**3 - u**3 - u**3 = 0. Calculate u.
-1, 0
Let j = -1184 - -1189. Suppose -3/2*x + 0 + 3*x**3 + 0*x**2 + 0*x**4 - 3/2*x**j = 0. What is x?
-1, 0, 1
Let w be 10/(-8)*(-8 + 39/5). Let l(b) be the first derivative of -1/6*b**3 + 1/24*b**6 - 3/8*b**2 + 2 - w*b + 1/8*b**4 + 3/20*b**5. Let l(h) = 0. What is h?
-1, 1
Let q(z) be the second derivative of 3*z**5/20 + 3*z**4/4 + z**3 - 4*z. Factor q(a).
3*a*(a + 1)*(a + 2)
Suppose 6*b - 15 = b. Let k be b*(3 + (-37)/15). Factor -8/5*q - 2/5*q**2 - k.
-2*(q + 2)**2/5
Suppose 0 = y + 3 - 7, 11 = s + 2*y. Factor 2/3*c + 5/3*c**2 + c**s + 0.
c*(c + 1)*(3*c + 2)/3
Let c(v) be the third derivative of 1/300*v**6 - 1/50*v**5 - 2*v**2 + 1/30*v**4 + 0 + 0*v**3 + 0*v. Factor c(o).
2*o*(o - 2)*(o - 1)/5
Let g(y) = y**2 + 10*y + 9. Let q be g(-9). Suppose q = -4*x + 3*o + 10, x = -4*x + 5*o + 10. Factor -2/9*t**2 + 0*t + 0 + 2/9*t**x + 0*t**3.
2*t**2*(t - 1)*(t + 1)/9
Let i(j) be the third derivative of 5/448*j**8 + 0 - 1/60*j**5 + 7*j**2 + 0*j**4 + 0*j + 0*j**3 - 31/840*j**7 + 1/24*j**6. What is r in i(r) = 0?
0, 2/5, 2/3, 1
Let l(r) = -r**3 - 7*r**2 + 2. Let n be l(-7). Find b, given that -8/3*b**3 - 1/3*b + 0 - 7/3*b**n + 16/3*b**4 = 0.
-1/4, 0, 1
Let h = 62059/244962 - -1/878. Let t = h - 1/31. Factor 2/9*g**5 + t*g + 4/9*g**2 - 2/9*g**4 - 4/9*g**3 - 2/9.
2*(g - 1)**3*(g + 1)**2/9
Factor -4*g**4 + 20 - 15*g**2 + 20*g - 7*g**4 - 5*g**3 + 6*g**4 - 15*g**3.
-5*(g - 1)*(g + 1)*(g + 2)**2
Let k be (-1)/1*(-2 - 1). Factor 1 - 2*t**k - t - 3*t - t**4 + 6*t.
-(t - 1)*(t + 1)**3
Let x(h) = h**2 - 4*h - 4. Let f(i) = -3*i**2 + 9*i + 10. Let p(y) = 2*f(y) + 5*x(y). Solve p(s) = 0 for s.
-2, 0
Let b(q) be the third derivative of q**5/20 + q**4/4 + 11*q**2. Let b(n) = 0. Calculate n.
-2, 0
Let b(s) = -s**2 - 10*s - 24. Let r be b(-6). Factor 5/2*j**5 + r + 1/2*j**3 + j**2 - 4*j**4 + 0*j.
j**2*(j - 1)**2*(5*j + 2)/2
Suppose 5*z - 8 = 3*z. Let -z*b**2 + 0*b**3 - 3*b**2 - 6 - 3 + b**3 + 15*b = 0. What is b?
1, 3
Let f(g) be the second derivative of -g**4/15 - 4*g**3/15 - 2*g**2/5 - 13*g. Let f(m) = 0. What is m?
-1
Let n(h) be the second derivative of -7/2*h**3 + 0 - 4*h - 1/56*h**7 + 19/8*h**4 + 1/5*h**6 - 15/16*h**5 + 3*h**2. Factor n(d).
-3*(d - 2)**3*(d - 1)**2/4
Suppose -17*n + 50 = -1. Find g such that -26/7*g**2 - 2/7*g**4 + 12/7*g**n - 8/7 + 24/7*g = 0.
1, 2
Let l(i) be the second derivative of i**7/231 + 2*i**6/165 - i**4/33 - i**3/33 + 7*i. Find c such that l(c) = 0.
-1, 0, 1
Let -6 - 9*h - 3*h**3 - h**3 + 7*h**3 + 0 = 0. Calculate h.
-1, 2
Let g(t) be the first derivative of -t**5/30 + t**4/18 + 2*t - 2. Let a(r) be the first derivative of g(r). Suppose a(j) = 0. Calculate j.
0, 1
Let l = 6 - 2. Suppose -4*v**3 + 11*v**4 + 2*v + 2 - 6*v**2 - 15*v**l - 6*v**3 = 0. What is v?
-1, 1/2
Let m be 2/6 - (-42)/36. Let c be ((-7)/3 - -2)/((-8)/36). Suppose c*f**2 + 1/2 + m*f + 1/2*f**3 = 0. What is f?
-1
Let y be (12/30)/((-2)/(-60)). Let j be -2 + (9525/y)/5. Suppose 90*q**4 + 45*q + 249/2*q**2 + 75/4*q**5 + j*q**3 + 6 = 0. Calculate q.
-2, -1, -2/5
Let m(i) be the first derivative of 2*i**5/15 + 3*i**4/14 + 4*i**3/63 + 11. Suppose m(f) = 0. Calculate f.
-1, -2/7, 0
Suppose -4*f = n - 59, 5*f + 6*n - n - 85 = 0. Let t(i) = 8*i**2 + 12*i. Let q(h) = -3*h**2 - 4*h. Let l(x) = f*q(x) + 5*t(x). Factor l(s).
-2*s*(s - 2)
Let z(j) = j**3 + 11*j**2 - j - 8. Let p be z(-11). Let d(q) be the first derivative of -2 - 1/6*q**4 - 1/3*q**2 - 4/9*q**p + 0*q. Factor d(u).
-2*u*(u + 1)**2/3
Find p, given that -6/7*p + 2/7*p**2 + 4/7 = 0.
1, 2
Determine u so that -40/11*u**2 + 128/11 - 50/11*u**3 + 20/11*u**4 + 160/11*u - 2/11*u**5 = 0.
-1, 4
Let p(s) be the second derivative of s**4/3 + 2*s**3/3 - 8*s. Factor p(h).
4*h*(h + 1)
Let z = -8 - -13. Suppose -c = 2*c, -z*h + 4*c + 10 = 0. Suppose -3*m**2 - 2*m**3 + 2 + 0*m**2 + 5*m**h + 2*m - 4*m**2 = 0. What is m?
-1, 1
Let y(a) = 14*a**3 - 15*a**2 - 13*a. Let q be 2/(3/(-3)*1). Let p(c) = c**3 + c**2 + 1. Let w(r) = q*p(r) + y(r). Find n, given that w(n) = 0.
-1/3, -1/4, 2
Factor -6/5*h**3 - 2*h + 14/5*h**2 + 2/5.
-2*(h - 1)**2*(3*h - 1)/5
Let m = 9 + -6. Factor -6*k**4 - 3*k**2 - 3*k**3 + m*k + 13*k**4 - 4*k**4.
3*k*(k - 1)**2*(k + 1)
Let j(l) be the first derivative of l**8/6720 + l**7/1120 + l**6/480 + l**5/480 - 2*l**3 - 2. Let c(p) be the third derivative of j(p). Factor c(b).
b*(b + 1)**3/4
Let i(z) be the first derivative of 0*z + 4/5*z**5 - 4 - 4/3*z**3 + z**2 - 1/3*z**6 + 0*z**4. Let i(a) = 0. What is a?
-1, 0, 1
Let d(l) be the first derivative of -l**8/280 - 3*l**7/350 + l**5/100 + l**2/2 + 3. Let k(c) be the second derivative of d(c). Factor k(s).
-3*s**2*(s + 1)**2*(2*s - 1)/5
Suppose 0 = j + 3*p + 4, 0 + 6 = 2*j - p. Find f, given that f**4 + 3*f + 7*f**j - 8*f**3 - 2 + 5*f**3 - 6*f**4 = 0.
-1, 2/5, 1
Let m(y) be the second derivative of y**6/10 - 3*y**5/10 + y**3 - 3*y**2/2 - 4*y. Solve m(b) = 0.
-1, 1
Let a(l) be the second derivative of l**7/42 - l**6/15 + l**5/20 - 22*l. Factor a(z).
z**3*(z - 1)**2
Let n be ((-4)/5)/(32/(-80)). Let c be 2 - (2/(-9) + n). Factor -c + 4/9*z**2 + 2/9*z.
