(a - 1)**3
Let p = -1 - -4. Let t(g) be the first derivative of 2/5*g + 2/15*g**p + 1 - 2/5*g**2. Suppose t(o) = 0. Calculate o.
1
Let j(q) be the second derivative of q**3/3 - 5*q**2/2 - q. Let m be j(4). Determine h, given that h**5 + 3*h**3 - h**3 - m*h**3 = 0.
-1, 0, 1
Let v(c) = 36*c + 288. Let s be v(-8). Factor 6/7*w + 2/7*w**2 + s.
2*w*(w + 3)/7
Suppose 4*h + 2*h = 0. Let v(t) be the second derivative of 0 - 3/50*t**5 + h*t**2 + 2*t + 2/15*t**3 + 1/30*t**4. Factor v(w).
-2*w*(w - 1)*(3*w + 2)/5
Determine y, given that 1/5*y**2 - 3/5*y**3 + 0 - 1/5*y**4 + 3/5*y = 0.
-3, -1, 0, 1
Let s(h) be the second derivative of -h**4/60 - h**3/30 + 11*h. Factor s(l).
-l*(l + 1)/5
Let p(v) be the first derivative of v**7/3780 - v**6/1620 - v**5/540 + v**4/108 + v**3/3 - 2. Let i(y) be the third derivative of p(y). Solve i(x) = 0.
-1, 1
Suppose -1/4*n + 1/4*n**2 - 1/2 = 0. Calculate n.
-1, 2
Let l be (39 - 40) + 1 + 4/10. Find g such that l*g + 6/5*g**3 - 2*g**2 - 8/5*g**5 + 2*g**4 + 0 = 0.
-1, 0, 1/4, 1
Let k(w) be the first derivative of w**4/12 - w**3/4 - w + 3. Let t(f) be the first derivative of k(f). Find i such that t(i) = 0.
0, 3/2
Let l(g) = g - 3. Let m(s) = -s**2 - 10*s - 10. Let f be m(-8). Let u be l(f). Solve -5 + 9 + u*a - a - 2*a**2 = 0.
-1, 2
Let g(x) be the first derivative of -x**6/480 - x**5/240 - 3*x**2/2 + 4. Let v(c) be the second derivative of g(c). Factor v(n).
-n**2*(n + 1)/4
Find n such that -70/9*n + 22/9*n**2 - 2/9*n**3 + 50/9 = 0.
1, 5
Let n(m) be the third derivative of -m**7/245 + m**6/40 - m**5/140 - m**4/8 + 3*m**3/14 - 20*m**2. Solve n(v) = 0.
-1, 1/2, 1, 3
Let o(z) = z + 9. Let w be o(-5). Suppose -w*j**3 - 24*j + 0 + 8 + 16*j**2 + 4*j = 0. What is j?
1, 2
Let q(r) be the first derivative of -2*r**3/39 - 2*r**2/13 + 6*r/13 + 26. Factor q(g).
-2*(g - 1)*(g + 3)/13
Let p(w) be the first derivative of -w**4/14 + 4*w**3/21 + 5*w**2/7 - 12*w/7 - 25. Factor p(s).
-2*(s - 3)*(s - 1)*(s + 2)/7
Let o(s) be the third derivative of 1/360*s**5 - 1/720*s**6 + 0*s + 9*s**2 + 5/144*s**4 + 0 + 1/12*s**3. Suppose o(y) = 0. What is y?
-1, 3
Let s be (-10)/4 - (-3)/(-6). Let r be (-8)/(-6)*s/(-2). Factor j + j**2 + r - 5*j + j**2.
2*(j - 1)**2
Let w(v) be the first derivative of -4*v**6/15 + 14*v**5/25 + v**4/10 - 14*v**3/15 + 3*v**2/5 - 32. Solve w(z) = 0.
-1, 0, 3/4, 1
Suppose 28*h = 36*h. Suppose -2/3*v + 2/3*v**3 - 1/3*v**4 + h*v**2 + 1/3 = 0. What is v?
-1, 1
Let d(n) = 2*n**5 + n**4 + 7*n**3 + 5*n**2. Let r(u) = u**5 + u**4 + 4*u**3 + 3*u**2. Let y(v) = 3*d(v) - 5*r(v). Suppose y(g) = 0. What is g?
0, 1
Let d(v) be the third derivative of v**5/300 + v**4/24 - v**3/5 - 20*v**2. Factor d(u).
(u - 1)*(u + 6)/5
Solve 9/2*j**2 + 1/2*j**3 + 8 + 12*j = 0.
-4, -1
Let x(c) be the second derivative of c**5/20 - c**3/2 - c**2 - 12*c. Suppose x(r) = 0. What is r?
-1, 2
Let g be (-4)/6 - (-78)/(-18). Let q = 5 + g. Factor -2*v**3 + q*v**3 + 2*v**2 + 0*v**2.
-2*v**2*(v - 1)
Let h(z) = 8*z**4 + 7*z**3 + 13*z**2 + 17*z - 2. Let r(w) = -w**4 + w**3 + w**2 - w + 1. Let k(y) = h(y) + 5*r(y). Solve k(o) = 0 for o.
-1
Suppose -2*t + 6 = t. Let v(j) be the first derivative of 17/15*j**3 + 49/30*j**6 + 1 + 12/5*j**t + 4/5*j - 21/25*j**5 - 73/20*j**4. Solve v(h) = 0 for h.
-1, -2/7, 1
Let w = 110 - 108. Suppose -2*h = -4*h + 2. Factor -h - 49/4*b**w - 7*b.
-(7*b + 2)**2/4
Let o = 3 + 6. Let d = 9 - o. Factor -1/4*a**4 - 1/4*a**3 + d + 1/4*a**2 + 1/4*a.
-a*(a - 1)*(a + 1)**2/4
Let t = -25831/16 - -1612. Let l = -131/80 - t. Determine a, given that 0*a - l*a**2 + 0 + 2/5*a**3 = 0.
0, 2
Let 115*s**4 + 91*s**2 + 3 + 88*s**2 + 295*s**3 + 190*s + 166*s**2 + 37 + 15*s**5 = 0. Calculate s.
-4, -1, -2/3
Let a(l) be the second derivative of -l**6/75 - l**5/25 + l**4/30 + 2*l**3/15 + 39*l. Suppose a(i) = 0. Calculate i.
-2, -1, 0, 1
Let 22/3*p + 26/3*p**2 + 2 + 10/3*p**3 = 0. Calculate p.
-1, -3/5
Let f(v) = v. Let y be f(-3). Let a be (2/(-6))/(1/y). Factor 2*c - 5*c - a + c - c**2.
-(c + 1)**2
Let s(d) be the first derivative of -d**6/18 + d**4/4 - 2*d**3/9 - 18. Factor s(o).
-o**2*(o - 1)**2*(o + 2)/3
Suppose -4*l + 2 + 6 = 0. Solve 7*s**3 + 4 + 5*s**l - 4*s**3 - 6*s - 4*s**3 - 2*s = 0.
1, 2
Let m(v) be the first derivative of v**7/42 - v**6/30 - v**5/10 + v**4/6 + v**3/6 - v**2/2 - 3*v + 5. Let f(z) be the first derivative of m(z). Factor f(i).
(i - 1)**3*(i + 1)**2
Suppose -2*w = -3*l + 8, -2*l + 0 = 2*w + 8. Suppose 0*q = -4*q - 3*x + 8, 5*q + x - 10 = l. Factor -5*i**3 - q*i**2 + i**5 + 3*i**3 - i**3.
i**2*(i - 2)*(i + 1)**2
Factor -r**4 + r**3 + 0*r**3 + 3*r - 2*r**3 - 2*r + r**2.
-r*(r - 1)*(r + 1)**2
Let r be ((-10 - -10) + 1*3)/2. Factor 3/2*n**4 + 3/2*n**5 + r*n - 3*n**2 + 3/2 - 3*n**3.
3*(n - 1)**2*(n + 1)**3/2
Let o be 2/13 - (-24)/13. Let u be (2/9 + 0)/1. Factor u*j**3 + 0 - 2/9*j**o + 0*j.
2*j**2*(j - 1)/9
Let u(c) = -21*c - 13. Let o be u(-13). Let y be 143/o + (-2)/(-8). Determine h so that 0*h**3 - y*h**4 + 2/5*h + 4/5*h**2 - 2/5*h**5 + 0 = 0.
-1, 0, 1
Factor 0*n**2 + 4/11 - 2/11*n**3 + 6/11*n.
-2*(n - 2)*(n + 1)**2/11
Let o(v) = -4*v**2 + 3*v + 2. Let h(f) = 5*f**2 - 3*f - 2. Let j(u) = 5*h(u) + 6*o(u). Factor j(w).
(w + 1)*(w + 2)
Solve -1/4*k**3 + 0 + 1/4*k - 1/4*k**4 + 1/4*k**2 = 0.
-1, 0, 1
Let z(j) be the first derivative of -j**5/40 + j**4/8 - 5*j**3/24 + j**2/8 - 24. Solve z(b) = 0 for b.
0, 1, 2
Let j(o) = -o**2 + o + 2. Let q be j(0). Let p(m) be the second derivative of 0*m**4 + 1/3*m**3 + 0 - m + 0*m**q - 1/10*m**5. Let p(b) = 0. Calculate b.
-1, 0, 1
Let k(l) be the second derivative of -l**7/63 + 2*l**6/45 - l**4/9 + l**3/9 + 3*l. Find s such that k(s) = 0.
-1, 0, 1
Factor 0 + 0*d**2 + d**3 + 1/3*d**4 - 4/3*d.
d*(d - 1)*(d + 2)**2/3
Let g be (3/2)/(3/4). Suppose g*u - 8 = -0*u + d, 26 = 5*u - 4*d. Determine c so that 0*c**2 - 4*c**2 - 2*c**5 - 2*c - u*c**3 + 2 + 2*c**4 + 6*c**3 = 0.
-1, 1
Let d(w) be the second derivative of w**7/1365 - w**6/780 - w**5/195 + w**2/2 + w. Let i(p) be the first derivative of d(p). Factor i(m).
2*m**2*(m - 2)*(m + 1)/13
Suppose -2*r + 5*j + 8 = j, 4*r - j - 9 = 0. Let w(q) be the first derivative of r + 0*q**2 + 0*q + 2/33*q**3. Factor w(p).
2*p**2/11
Let y(k) be the second derivative of -k**6/15 + k**5/5 + k**4/6 - 2*k**3/3 - 3*k. Let y(r) = 0. What is r?
-1, 0, 1, 2
Suppose -8 + 4 = u. Let t = u - -8. Factor t*i**3 + i**2 - 5*i**3 - i**4 + 0*i**4 + i.
-i*(i - 1)*(i + 1)**2
Let x(n) be the first derivative of 0*n + 0*n**2 + 3 + 1/6*n**3. Suppose x(s) = 0. What is s?
0
Let h(t) be the first derivative of 1/3*t**6 + 0*t**5 + 0*t**3 + 0*t**2 + 0*t + 2 - 1/2*t**4. Let h(o) = 0. What is o?
-1, 0, 1
Factor 2/3 + 4/9*y - 2/9*y**2.
-2*(y - 3)*(y + 1)/9
Let r(v) be the first derivative of v**7/60 - v**6/120 - 7*v**5/120 + v**4/24 + 3*v**2/2 - 4. Let j(i) be the second derivative of r(i). Factor j(h).
h*(h - 1)*(h + 1)*(7*h - 2)/2
Let r(k) be the second derivative of -7*k**6/75 - k**5/25 + 7*k**4/10 + 4*k**3/3 + 4*k**2/5 + 3*k. Determine d, given that r(d) = 0.
-1, -2/7, 2
Let n be 12/(-182)*(-34 - -13). Let l = n + -23/26. Solve -1 - 1/2*c + l*c**2 = 0.
-1, 2
Let s(k) be the third derivative of k**5/12 + 35*k**4/8 - 55*k**3/3 - 7*k**2. Determine n, given that s(n) = 0.
-22, 1
Let o = 13/3 + -127/30. Let q(f) be the second derivative of o*f**5 + 0*f**2 - 3*f + 2/3*f**3 + 1/2*f**4 + 0. Factor q(s).
2*s*(s + 1)*(s + 2)
Factor 8/5*s**2 + 4/5 - 2/5*s**3 - 2*s.
-2*(s - 2)*(s - 1)**2/5
Let o(n) = -n**3 - 5*n**2 + 6*n + 4. Let r be o(-6). Find f such that -34*f**3 + r + 165*f**2 - 32*f**3 - 48*f - 55*f**3 = 0.
2/11, 1
Let w = 5 - 2. Let u(j) = -2*j + 6. Let n be u(w). Factor n*k - 2/5*k**3 - 2/5*k**2 + 0.
-2*k**2*(k + 1)/5
Let j(l) be the first derivative of -l**7/42 + l**6/6 - 2*l**5/5 + l**4/3 + 4*l + 4. Let k(b) be the first derivative of j(b). Factor k(h).
-h**2*(h - 2)**2*(h - 1)
Let 7 + 1 - 5*w - 5*w**2 + 2 = 0. Calculate w.
-2, 1
Let 4/7 - 6/7*k + 2/7*k**3 + 0*k**2 = 0. What is k?
-2, 1
Let s(b) be the third derivative of -b**9/30240 + b**7/2520 - b**5/240 - b**4/12 - 8*b**2. Let k(l) be the second derivative of s(l). What is a in k(a) = 0?
-1, 1
Let l(c) be the first derivative of -c**6/60 - 2*c**5/15 - c**4/3 - 3*c**2/2 + 3. Let a(s) be the second derivative of l(s). Factor a(f).
-2*f*(f + 2)**2
Let i(