b - 1)**2*(b + 1)
Suppose 5*z = -4*u - 5 + 19, -z + 4*u + 22 = 0. Factor -3*q**5 + 7*q**5 - 6*q**5 - 4*q**3 + z*q**4.
-2*q**3*(q - 2)*(q - 1)
Let g(k) be the second derivative of -3*k + 1/9*k**2 - 2/27*k**3 - 7/54*k**4 - 2/45*k**5 + 0. Find w, given that g(w) = 0.
-1, 1/4
Suppose 2*s + 15 = 4*n - 15, -4*s + 2*n = 42. Let h = -9 - s. Let 0*z**2 + h + 4/3*z**4 + 2/3*z**5 + 0*z + 2/3*z**3 = 0. What is z?
-1, 0
Let i(m) be the third derivative of m**6/420 + m**5/210 - m**4/42 + 3*m**2. Solve i(w) = 0 for w.
-2, 0, 1
Let i(m) = -4*m**3 + 3*m**2 - 16*m. Let l(s) = -s**3 + s**2 - 4*s. Let q(d) = 6*i(d) - 26*l(d). Suppose q(t) = 0. Calculate t.
0, 2
Let t(s) be the second derivative of -s**6/270 + s**5/36 - s**4/12 + 7*s**3/54 - s**2/9 + 3*s. Factor t(o).
-(o - 2)*(o - 1)**3/9
Let n be 140/8 + (-2)/(-4). Suppose 5*i = 2*i + n. Factor -x**2 - x**2 - 4*x**5 - 6*x**4 + 6*x**5 + i*x**3 + 0*x**5.
2*x**2*(x - 1)**3
Let d = 2/1069 + 1065/2138. Find n such that 1/6*n**2 + d*n + 1/3 = 0.
-2, -1
Let f(d) be the second derivative of 0 + 0*d**5 + 0*d**2 - 1/48*d**4 - 2*d + 0*d**3 + 1/120*d**6. Factor f(h).
h**2*(h - 1)*(h + 1)/4
Let n = -9699/52 + 373/2. Let g = 205/156 - n. Solve -2/3*i**3 + 0 - 2*i**2 - g*i = 0.
-2, -1, 0
Suppose 4*p = 0, a + 0*p - 4*p - 5 = 0. Let z be (-3 + 0)/(9/(-6)). Suppose t**2 + 2*t**z - 4*t**a + 0*t**4 - t + 5*t**3 - 3*t**4 = 0. Calculate t.
-1, 0, 1/4, 1
Let l = -1896/5 + 380. Determine i so that 2/5*i**4 + 2*i**3 + 18/5*i**2 + 14/5*i + l = 0.
-2, -1
Suppose -3*y - y = 4*m, 5*y - 4*m = 27. Let d(h) be the third derivative of 1/240*h**5 + 0*h + 0*h**y - 1/48*h**4 + 0 - 2*h**2. Factor d(t).
t*(t - 2)/4
Let o(d) = 2*d. Let a be o(-2). Let h = a - -6. What is n in 3*n**5 - h*n**3 + n - n**5 + 0*n - n**5 = 0?
-1, 0, 1
Factor 151*t**3 - 8*t + 5*t**2 + 38*t - 146*t**3 + 20*t**2.
5*t*(t + 2)*(t + 3)
Let 2/7*i**2 - 2/7 - 2/7*i**3 + 2/7*i = 0. What is i?
-1, 1
Let a(m) be the first derivative of -m**3 + m**2/2 + 1. Let y = -8 - -6. Let x(z) = -16*z**2 + 6*z. Let o(f) = y*x(f) + 11*a(f). Suppose o(c) = 0. What is c?
-1, 0
Let q(y) be the second derivative of y**6/360 - y**5/360 - y**4/72 + y**3/36 + 3*y**2 + 5*y. Let c(t) be the first derivative of q(t). Factor c(d).
(d - 1)*(d + 1)*(2*d - 1)/6
Let r(f) be the first derivative of -3/4*f**4 - 6 + f**3 + 0*f**2 + 0*f. Factor r(u).
-3*u**2*(u - 1)
Suppose -5*j + 1 = -j - 3*c, -3*j = -4*c + 8. Factor -3/2*u**3 - 1/2*u**j + 1/2*u**5 + u + 0 + 1/2*u**2.
u*(u - 2)*(u - 1)*(u + 1)**2/2
Let y(u) be the third derivative of u**8/840 + u**7/420 - u**3/6 - 2*u**2. Let l(r) be the first derivative of y(r). Factor l(f).
2*f**3*(f + 1)
Let z(r) be the first derivative of -r**3/3 - r**2/2 - r + 2. Let i(t) = -4*t**3 - 6*t**2 - 6*t - 16. Let j(p) = -i(p) + 12*z(p). Find m, given that j(m) = 0.
-1, 1/2, 2
Let b be 14 + -13 - 2/(-2). Factor -1/3 - 1/3*o**b - 2/3*o.
-(o + 1)**2/3
Let a(v) be the third derivative of -v**7/350 + v**6/50 - v**5/25 + 8*v**2. Let a(s) = 0. What is s?
0, 2
Let r = 8 + -5. Factor k**4 + k**4 - r*k**5 + 0*k**5.
-k**4*(3*k - 2)
Let u(k) be the first derivative of -3*k**4/20 - k**3/5 + 3*k**2/2 - 9*k/5 - 22. Factor u(p).
-3*(p - 1)**2*(p + 3)/5
Let w(g) = 21*g**2 + 225*g + 783. Let c(h) = -3*h**2 - 32*h - 112. Let r(d) = -27*c(d) - 4*w(d). What is m in r(m) = 0?
-6
Let y(k) be the first derivative of -2*k**3/21 - 2*k**2/7 - 2*k/7 - 7. Factor y(s).
-2*(s + 1)**2/7
Let r be 1 + 4*2/8. Let t(d) be the first derivative of -4 + 4/5*d - 3/5*d**r + 2/15*d**3. Factor t(x).
2*(x - 2)*(x - 1)/5
Let m(s) be the first derivative of -s**4/6 - s**3 - 2*s**2 + 4*s - 2. Let n(w) be the first derivative of m(w). Factor n(c).
-2*(c + 1)*(c + 2)
Let s be 0/(1 - 5 - -2). Suppose -6*t + t = s. Factor -1/3*i**2 + 0 - 1/3*i**4 - 2/3*i**3 + t*i.
-i**2*(i + 1)**2/3
Let p(o) = 15*o**2 + 365*o + 85. Let u(x) = -x**2 - 26*x - 6. Let h(l) = 6*p(l) + 85*u(l). Factor h(k).
5*k*(k - 4)
Let 2/3*v + 8/9 - 2/9*v**2 = 0. What is v?
-1, 4
Let t(h) = h + 1. Let a(y) = 2*y**2 + 14*y + 8. Let u(x) = x + 1. Let l be u(7). Let w(k) = l*t(k) - a(k). Factor w(f).
-2*f*(f + 3)
Let q = -585885786/7015 - -83519. Let h = 113644/7015 + q. Factor -27/5*u**2 - h*u - 3/5*u**3 - 81/5.
-3*(u + 3)**3/5
Let u(h) be the second derivative of 1/15*h**6 + h + 0*h**3 + 1/6*h**4 + 0 + 1/5*h**5 + 0*h**2. Factor u(b).
2*b**2*(b + 1)**2
Let c(a) be the third derivative of a**9/22680 + a**8/2520 + a**7/756 + a**6/540 + a**4/4 + 6*a**2. Let q(g) be the second derivative of c(g). Factor q(i).
2*i*(i + 1)**2*(i + 2)/3
Let a(k) = 7*k**2 + 8*k + 3. Let w be a(-1). Factor -1/2*z + 1/2*z**4 - 1/2*z**w + 1/2*z**3 + 0.
z*(z - 1)*(z + 1)**2/2
Let p(d) = -9*d**2 - 70*d - 249. Let t(z) = 8*z**2 + 70*z + 248. Let v(w) = 3*p(w) + 4*t(w). Let v(f) = 0. What is f?
-7
Let s(j) be the second derivative of -7*j**6/120 - 4*j**5/15 - j**4/6 + 3*j**2/2 + j. Let g(o) be the first derivative of s(o). Factor g(b).
-b*(b + 2)*(7*b + 2)
Let b(q) be the third derivative of q**5/15 - 5*q**4/6 + 4*q**3 - 5*q**2. Factor b(p).
4*(p - 3)*(p - 2)
Let f = -316 - -319. Find r, given that 0 + 27/4*r**4 + 18*r**f + 39/4*r**2 + 3/2*r = 0.
-2, -1/3, 0
Suppose -5*w + 4*j = 2, -2*j + 9 + 7 = 5*w. Factor -k - 5*k**2 + 2*k**2 + w + 2*k**2 + 0*k**2.
-(k - 1)*(k + 2)
Factor 0*h**2 - 2/5*h + 0 + 0*h**4 - 2/5*h**5 + 4/5*h**3.
-2*h*(h - 1)**2*(h + 1)**2/5
Let m(y) = y**2 + 20*y + 101. Let l be m(-9). Let -3/7*x**3 + 6/7*x - 3/7*x**l + 0 = 0. Calculate x.
-2, 0, 1
Determine t, given that -6/5*t + 18/5 + 2*t**4 + 4/5*t**3 + 2/5*t**5 - 28/5*t**2 = 0.
-3, -1, 1
Factor -3/2*a**2 + 1/2 + a.
-(a - 1)*(3*a + 1)/2
Let g = -30 - -21. Let m(s) = -25*s**2 - 16*s + 41. Let p(b) = 6*b**2 + 4*b - 10. Let l(f) = g*p(f) - 2*m(f). Factor l(a).
-4*(a - 1)*(a + 2)
Let n(h) = 2*h**2 + 5*h + 5. Let s be n(-2). Factor -7*m - m**3 + s*m**3 + m - 4.
2*(m - 2)*(m + 1)**2
Let v = 11 + -16. Let x(d) = 20*d**4 + 32*d**3 - 2*d**2 + 14. Let c(y) = -7*y**4 - 11*y**3 + y**2 - 5. Let i(u) = v*x(u) - 14*c(u). Factor i(b).
-2*b**2*(b + 1)*(b + 2)
Let b = 17/39 - -3/13. Let k be 9/12 + 1/(-12). Find p, given that -k*p + b*p**2 + 0 = 0.
0, 1
Let b be (-9)/(-2)*8/12. Let f be b - (-1 - -2 - -2). Factor -2/3*l**5 + 0*l + 2/3*l**3 + f + 2/3*l**2 - 2/3*l**4.
-2*l**2*(l - 1)*(l + 1)**2/3
Let x = 1088/11 + -103. Let m = x - -257/44. Factor 0*t**2 - m*t**4 + 0*t + 0 + 1/2*t**3.
-t**3*(7*t - 2)/4
Let y(s) be the second derivative of -s**5/110 + s**4/66 - 6*s. Let y(q) = 0. What is q?
0, 1
Let t(m) = -15*m**5 + 29*m**4 - 32*m**3 + 3*m**2 - 5. Let b(x) = -8*x**5 + 14*x**4 - 16*x**3 + x**2 - 3. Let f(l) = 5*b(l) - 3*t(l). Factor f(j).
j**2*(j - 2)*(j - 1)*(5*j - 2)
Let g(v) be the first derivative of -v**5/150 + v**4/60 - 9*v**2/2 - 8. Let u(j) be the second derivative of g(j). Determine s so that u(s) = 0.
0, 1
Let j(h) be the third derivative of h**5/60 - h**4/3 + 3*h**3/2 + 2*h**2. Let b be j(7). Suppose i + i**b + i**2 + i = 0. What is i?
-1, 0
Let y(h) be the third derivative of h**5/210 - 5*h**2. Factor y(u).
2*u**2/7
Determine c, given that -98/3*c**5 + 154/3*c**4 - 8/3 + 34/3*c**3 - 146/3*c**2 + 64/3*c = 0.
-1, 2/7, 1
Let i(x) be the third derivative of -5*x**7/63 + 2*x**6/3 - 92*x**5/45 + 8*x**4/3 - 16*x**3/9 - 5*x**2. Factor i(j).
-2*(j - 2)**2*(5*j - 2)**2/3
Let f be 3/2*5/9. Determine q, given that -1/6 - 5/3*q**2 - 1/6*q**5 - 5/3*q**3 - 5/6*q - f*q**4 = 0.
-1
Let r(f) be the first derivative of -2*f**6/3 - 12*f**5/5 - 3*f**4 - 4*f**3/3 - 24. What is s in r(s) = 0?
-1, 0
Let b(v) be the second derivative of v**6/360 - v**5/90 + v**4/72 - 3*v**2 + 4*v. Let x(t) be the first derivative of b(t). Suppose x(q) = 0. What is q?
0, 1
Let n be (0 - -2)*(0 + 1). Factor 0*q**2 - 4*q**2 + 0 + 0 - n*q**3.
-2*q**2*(q + 2)
Let m(o) = -2. Let h(v) = -v - 2. Let t(u) = -2*h(u) + 3*m(u). Let y be t(3). Determine d, given that 6/5*d**y + 4/5*d**3 + 2/5 - 4/5*d - 8/5*d**2 = 0.
-1, 1/3, 1
Let z = 2/1379 + 4133/2758. Factor 1/2*t**2 + 2*t + z.
(t + 1)*(t + 3)/2
Let l = -4 - -6. Factor -18*w**2 + 3 - l - 1 - 4*w.
-2*w*(9*w + 2)
Suppose -3*b + 13 = 2*j, j + b + 6 = 11. Solve -3/5*m + 0 - 1/5*m**j = 0.
-3, 0
Suppose -2*u - 2 = -8. Let a(f) be the second derivative of 0*f**4 - f + 0*f**2 + 0 + 1/8*f**u - 3/80*f**5. Factor a(p).
-3*p*(p - 1)*(p + 1)/4
Let r(f) = 