- 1)**3/5
Let f(b) be the first derivative of -4*b**3/3 - 2*b**2 + 24*b + 3. Factor f(q).
-4*(q - 2)*(q + 3)
Let -6 + 3*t**2 + 16*t - 5*t - 8*t = 0. What is t?
-2, 1
Let 8/3*x**3 + 0 - 4/3*x**2 + 5/3*x**4 + 0*x = 0. What is x?
-2, 0, 2/5
Let r = 409 - 404. Factor -1/4*u**r + 1/4*u**4 + 0*u + 0*u**3 + 0*u**2 + 0.
-u**4*(u - 1)/4
Suppose 2*z + z + k + 1 = 0, -z - 4 = 4*k. Let m be ((-3)/6)/(35/(-60)). Solve -2/7*d**2 + 0 - 2/7*d**5 - 6/7*d**4 - m*d**3 + z*d = 0.
-1, 0
Let k be (-1 - 0)/(1 + -7). Let b(y) be the first derivative of k*y**6 + 1/4*y**4 + 0*y**2 - 2/5*y**5 + 0*y**3 + 1 + 0*y. Suppose b(o) = 0. What is o?
0, 1
Suppose 2*u = 4*u - 7*u. Factor 8/3*w**3 + u - 2/3*w**2 + 0*w.
2*w**2*(4*w - 1)/3
Let g = -6 - -8. Factor 3*v**3 - 4*v**2 + 2*v**4 + g*v - 2*v**5 + 2*v**4 - 3*v**3.
-2*v*(v - 1)**3*(v + 1)
Let w(u) be the second derivative of -u**5/60 + u**4/6 - u**3/2 - 5*u**2/2 + 5*u. Let j(x) be the first derivative of w(x). Factor j(s).
-(s - 3)*(s - 1)
Let u(d) = d**2 - d + 2. Let v be u(2). Suppose v*t - 5*t = 0. Find z such that 1/2*z**3 + 1/4*z**4 + t + 1/4*z**2 + 0*z = 0.
-1, 0
Solve -2*m**2 + 0*m**2 + 4 + 0*m - m - m = 0.
-2, 1
Let f(d) be the second derivative of 0 - 3/10*d**5 + 0*d**2 + 1/2*d**6 + 0*d**3 - 3*d + 1/2*d**7 + 0*d**4. Find b, given that f(b) = 0.
-1, 0, 2/7
Let s = -72 + 76. Let m(d) be the second derivative of 0*d**2 - 1/48*d**s + 0 - 1/24*d**3 + 2*d. Factor m(t).
-t*(t + 1)/4
Let a = 23 - 18. Let i = a + -2. Suppose 1/3 - 2/3*f**i + 1/3*f**4 + 1/3*f**5 - 2/3*f**2 + 1/3*f = 0. Calculate f.
-1, 1
Let h(a) be the second derivative of -225*a**4/8 + 15*a**3/2 - 3*a**2/4 - 24*a. Factor h(k).
-3*(15*k - 1)**2/2
Suppose 0*w = -0*w - 4*w. Suppose -1/4*v**2 - 1/4*v**3 + w*v + 0 = 0. Calculate v.
-1, 0
Let h(u) = u**3 + 4*u**2 + 2*u - 4. Let s(p) = -3*p**3 - 11*p**2 - 5*p + 11. Let t(b) = -8*h(b) - 3*s(b). Factor t(d).
(d - 1)*(d + 1)**2
Suppose 0 = -6*a + 7*a - 2. Suppose a*k - 10 = -3*k. Factor 6*d**4 - 8/5*d**5 + 0*d - 2/5 - 8*d**3 + 4*d**k.
-2*(d - 1)**4*(4*d + 1)/5
Determine k, given that 3*k**3 + k + 3*k**2 - 4*k + 3*k + k**4 + k = 0.
-1, 0
Let z(u) = u**2 + u - 2. Let c be z(2). Let m be 57/21 + (-4)/(-14). Solve -5*x + 5*x**3 - 5*x**m + 2 - x**3 + c*x**2 = 0.
1, 2
Let f(d) be the first derivative of 7*d**6/10 + 6*d**5/25 + 32. Factor f(t).
3*t**4*(7*t + 2)/5
Let p(k) = -k + 2. Let m be p(2). Suppose -f + i + 7 - 3 = m, 5*i + 8 = f. Factor 2/7*o**2 - 2/7*o**4 + 2/7*o**f - 2/7*o + 0.
-2*o*(o - 1)**2*(o + 1)/7
Let h(n) = n**2 + 17*n + 44. Let l be h(-14). Factor -2/3 - 2/9*i**l + 8/9*i.
-2*(i - 3)*(i - 1)/9
Find i, given that -3/7*i**4 + 6/7*i**3 - 6/7*i - 9/7 + 12/7*i**2 = 0.
-1, 1, 3
Suppose -3*t + 2*u + 4 = -6, 3*u + 14 = 4*t. Let g(h) be the first derivative of -2 + h - 1/3*h**3 + 0*h**t. Let g(w) = 0. Calculate w.
-1, 1
Suppose 0*w**2 + 6/5*w**3 - 3/5*w**5 + 3/5*w**4 + 0 + 0*w = 0. Calculate w.
-1, 0, 2
Let i(v) be the second derivative of 2*v - 1/36*v**4 + 1/3*v**2 + 0 + 1/18*v**3. Factor i(d).
-(d - 2)*(d + 1)/3
Let b(n) be the first derivative of n**6/12 + n**5/10 - n**4/4 - n**3/3 + n**2/4 + n/2 + 4. Factor b(x).
(x - 1)**2*(x + 1)**3/2
Let v(y) be the third derivative of -y**9/90720 + y**8/30240 - y**5/20 + 2*y**2. Let k(c) be the third derivative of v(c). Determine w so that k(w) = 0.
0, 1
Let a = 8 + -14. Let c = -4 - a. Factor -c*f + f - f - 2*f**2.
-2*f*(f + 1)
Let s(j) be the first derivative of 2*j**5/45 - j**4/18 + 26. Factor s(t).
2*t**3*(t - 1)/9
Let f = 16 - 16. Let n be (1/2)/((-3)/(-8)). Find s, given that 0*s + f + 2/3*s**3 - n*s**2 = 0.
0, 2
Solve 3 + 15/2*t + 3/2*t**3 + 6*t**2 = 0 for t.
-2, -1
Factor 10*h**5 + 111*h**2 - 8*h**3 + 8*h**5 - 8*h**3 + 6*h**4 - 119*h**2.
2*h**2*(h - 1)*(3*h + 2)**2
Let b(u) be the third derivative of u**8/112 + u**7/35 - u**6/20 - u**5/5 + u**4/8 + u**3 - 7*u**2. Suppose b(c) = 0. Calculate c.
-2, -1, 1
Let h = -6 + 7. Let l be (-2 - -3)*h/4. Factor l*t**4 + 0*t**3 + 0*t**2 - 1/4*t**5 + 0*t + 0.
-t**4*(t - 1)/4
Determine a, given that a**3 - 1/6*a**4 + 2*a - 13/6*a**2 - 2/3 = 0.
1, 2
Let a(s) = 5*s**2 + 7*s + 2. Let n(d) = 4*d**2 + 6*d + 2. Let j(h) = h**2 - 2. Let z be j(3). Let y(u) = z*n(u) - 6*a(u). Factor y(w).
-2*(w - 1)*(w + 1)
Let t(i) = i**3 + i**2. Let d(y) = -3*y**3 - 3*y**2. Let x(r) = 4*d(r) + 14*t(r). Factor x(p).
2*p**2*(p + 1)
Let u be 1070/50 + (-4)/10. Let l = -18 + u. Factor 0 + 8/7*d**5 + 0*d**4 - 6/7*d**l + 2/7*d**2 + 0*d.
2*d**2*(d + 1)*(2*d - 1)**2/7
Let a be 720/2025 + 2/(-15). Determine k, given that 0 + 2/9*k**3 + 0*k**2 - a*k = 0.
-1, 0, 1
Let y(h) = 3*h**2 - h + 1. Let o be y(1). Suppose -o*j + 6 = -0*j. Find s, given that -2*s**2 + 2 - s + s**3 - 2 + j*s = 0.
0, 1
Let s be ((-119)/(-14) - 8) + 0. Determine c so that -1/2*c**2 + c**3 + 0 - s*c**4 + 0*c = 0.
0, 1
Let r(a) = a**2 - 9*a - 8. Let s be r(10). Suppose -s*f = 2*f - 36. Factor -10*k**2 + 4*k + 10*k**3 - 4 - f*k**2 + 14*k - 5*k**2.
2*(k - 1)**2*(5*k - 2)
Let i(a) = -a**3 + 3*a**2 - 2*a. Let q be i(2). Let r(v) be the second derivative of 0*v**2 + 1/27*v**3 + q - 2*v - 1/54*v**4. Solve r(g) = 0.
0, 1
Let n(p) be the third derivative of -p**6/660 - p**5/165 + p**4/132 + 2*p**3/33 + p**2 + 18*p. Factor n(q).
-2*(q - 1)*(q + 1)*(q + 2)/11
Let t(m) be the third derivative of -1/36*m**4 - 2/9*m**3 + 1/90*m**5 + 0 + 0*m + m**2. What is l in t(l) = 0?
-1, 2
Let u(t) be the second derivative of 2/5*t**5 + 2/3*t**4 + 1/3*t**3 + 0 + 0*t**2 - 2*t. Factor u(v).
2*v*(2*v + 1)**2
Let s = 144/55 - 20/11. Factor 6/5*x + 0 - s*x**2 - 2/5*x**3.
-2*x*(x - 1)*(x + 3)/5
Let r = -4 - -6. Suppose 2*g - 3*a = 2*a + 14, -r*g + 10 = -3*a. Factor t**5 + 2*t**4 - 2*t**5 + t**5 - g*t**5.
-2*t**4*(t - 1)
Let h = 34 - 98/3. Factor 8/3*n + h*n**2 + 4/3.
4*(n + 1)**2/3
Let l(m) be the first derivative of -m**4/8 - 3*m**3/2 + 44. Suppose l(t) = 0. Calculate t.
-9, 0
Let g(r) be the third derivative of 0 - 1/105*r**7 + 4*r**2 - 1/6*r**4 + 1/30*r**6 + 0*r**5 + 0*r + 1/3*r**3. Factor g(a).
-2*(a - 1)**3*(a + 1)
Let n(w) be the second derivative of 0 + w + 0*w**2 + 2/9*w**3 + 1/6*w**4. Solve n(r) = 0.
-2/3, 0
Let w(y) be the third derivative of y**6/40 + 11*y**5/50 - 17*y**4/40 - y**3 - 42*y**2. Factor w(u).
3*(u - 1)*(u + 5)*(5*u + 2)/5
Let a(b) be the third derivative of 1/36*b**5 - 1/144*b**4 + b**2 + 2/63*b**7 - 1/126*b**8 + 0*b**3 + 0*b + 0 - 11/240*b**6. Factor a(p).
-p*(p - 1)**2*(4*p - 1)**2/6
Let a(v) be the third derivative of v**6/420 + v**5/70 + v**4/28 + v**3/21 - 2*v**2. Factor a(m).
2*(m + 1)**3/7
Let w(f) = f**3 + f**2 + f + 2. Let l = 3 + -3. Let u be w(l). Determine q so that -2/3*q + 0 + 2/3*q**u = 0.
0, 1
Let i(k) = -2*k - 10. Let u be i(-6). Factor -2/11*f**u + 4/11*f**3 - 2/11*f**4 + 0*f + 0.
-2*f**2*(f - 1)**2/11
Let t(b) = -4*b**3 - 56*b**2 + 60*b. Let a(l) = l**3 + 11*l**2 - 12*l. Let f(x) = -16*a(x) - 3*t(x). Factor f(w).
-4*w*(w - 1)*(w + 3)
Factor 0 + 2/7*s - 2/7*s**3 + 0*s**2.
-2*s*(s - 1)*(s + 1)/7
Let t(k) = k**3 + k**2 - k - 2. Let x(c) = -2*c**3 - 184*c**2 - 1110*c + 276. Let n(r) = 6*t(r) - x(r). Solve n(v) = 0.
-12, 1/4
Let x(c) be the third derivative of c**6/1080 - c**4/216 + 2*c**2. Solve x(m) = 0 for m.
-1, 0, 1
Let l(z) be the second derivative of z**7/1260 - z**6/360 - z**4/6 + 4*z. Let v(d) be the third derivative of l(d). Solve v(m) = 0 for m.
0, 1
Let k(r) = -r - 1. Let n(x) = -12*x**2 + 12. Let v(j) = 8*k(j) + n(j). Solve v(w) = 0.
-1, 1/3
Factor 1/6*v**2 + 0 + 1/3*v.
v*(v + 2)/6
Let t(p) = -4*p**4 - 6*p**3 + 20*p**2 - 30*p + 2. Let n(z) = 9*z**4 + 11*z**3 - 39*z**2 + 61*z - 3. Let h(r) = 6*n(r) + 13*t(r). Suppose h(v) = 0. Calculate v.
1, 2
Let b = 167/15 + -49/5. Let m(i) = -i**2 - 5*i + 16. Let y be m(-7). Factor -b*p**y + 1/3 + p.
-(p - 1)*(4*p + 1)/3
Let s(z) = -z**4 - 3*z**3 + 3*z**2 - 5*z + 5. Let p(x) be the second derivative of x**4/12 - x**3/6 + x**2/2 + 4*x. Let c(q) = 5*p(q) - s(q). Solve c(d) = 0.
-2, -1, 0
Determine o, given that 8/9*o**4 + 2/9*o - 2/9*o**3 + 0 - 8/9*o**2 = 0.
-1, 0, 1/4, 1
Let t = 157/228 - 5/228. Factor -5/3*j**3 - 4*j**2 - t - 3*j.
-(j + 1)**2*(5*j + 2)/3
Let t be 5 - (3 - (-2)/2*-1). Let j(y) be the second derivative of 0*y**2 + 0 - y + 0*y**t + 1/30*y**5 + 0*y**4 + 1/45*y**6. Factor j(v).
2*v**3*(v + 1)/3
Let t be (6 - 8) + (1 - -1). Suppo