9
Let k be ((-3)/9)/((-2)/36). Let s(v) be the third derivative of 0*v + 2/15*v**3 - 1/100*v**k + 0 - 7/60*v**4 + 4/75*v**5 + 2*v**2. Solve s(w) = 0 for w.
2/3, 1
Let d(h) be the second derivative of -h**4/12 - h**3/6 + 14*h. Factor d(k).
-k*(k + 1)
Let b(u) = -9*u - 6. Let n be b(-3). Factor -n*f**4 - 2*f**5 - 6*f**4 + 6*f**3 + 23*f**5.
3*f**3*(f - 1)*(7*f - 2)
Let c(r) be the second derivative of r**6/720 - r**5/360 + r**2/2 + 2*r. Let n(a) be the first derivative of c(a). Determine i, given that n(i) = 0.
0, 1
Let g(f) be the third derivative of 1/60*f**4 + 0 + 0*f**3 + 0*f - 4*f**2 - 1/150*f**5. What is x in g(x) = 0?
0, 1
Let o(s) = 2*s**5 + 3*s**4 + 3*s**3 + s + 1. Let l(x) = -x**2 + 0*x + x - x**5 + 2*x**5 + 1. Let n(g) = -2*l(g) + 2*o(g). Determine a, given that n(a) = 0.
-1, 0
Let d(k) = 5*k**3 - 2*k**2 - 11*k + 6. Let l(g) = -6*g**3 + 3*g**2 + 12*g - 6. Let v(o) = 3*d(o) + 2*l(o). Solve v(a) = 0.
-2, 1
Let v(p) be the third derivative of -p**5/30 + 3*p**2. Let u(b) = 7*b**2 - 1. Let j(s) = -2*u(s) - 6*v(s). Let j(t) = 0. What is t?
-1, 1
Let i(m) be the first derivative of -8/21*m**3 + 2/7*m - 3/7*m**2 + 4. Factor i(w).
-2*(w + 1)*(4*w - 1)/7
Let s be (-7)/(-420)*44 - 2/5. Suppose 2/3*l**4 + 2/3 - 4/3*l**2 + 1/3*l - 2/3*l**3 + s*l**5 = 0. Calculate l.
-2, -1, 1
Let j = 166/5 + -33. Let z = 3/10 + j. Find w such that -z - 3/4*w - 1/4*w**2 = 0.
-2, -1
Let n = 5/3 + -29/21. Determine k, given that -6/7*k**3 - n*k + 0 + 8/7*k**2 = 0.
0, 1/3, 1
Let i(u) be the first derivative of -1/15*u**6 - 2 - 4/25*u**5 + 0*u**4 + 4/15*u**3 + 0*u + 1/5*u**2. Factor i(z).
-2*z*(z - 1)*(z + 1)**3/5
Factor 3*k**2 + 6*k + 12*k**3 + 11*k**2 + k**2 + 3*k**4.
3*k*(k + 1)**2*(k + 2)
Let s = -642 + 3865/6. Determine h, given that 1/6 - s*h**2 - 1/6*h + 25/6*h**3 - 2*h**4 = 0.
-1/4, 1/3, 1
Suppose 4*y + 84 = 5*y. Let w be (-24)/y - 4/(-14). Factor -2/5*d**3 + 0*d + 0 + w*d**2.
-2*d**3/5
Let t(a) = -7*a**3 - 4*a**2 - 3*a - 2. Let w(b) = 15*b**3 + 7*b**2 + 5*b + 4. Let p(u) = 9*t(u) + 4*w(u). Let p(m) = 0. Calculate m.
-1, -2/3
Let n(t) be the first derivative of -t**4/4 + t**3/3 - t**2/2 - t - 8. Let i(s) = 3*s**3 - 6*s**2 + 5*s + 6. Let c(w) = -i(w) - 4*n(w). Factor c(x).
(x - 1)*(x + 1)*(x + 2)
Let z be (254/84 - 3) + 0. Let u(h) be the third derivative of -1/210*h**5 + 0 + 0*h - 1/21*h**3 - z*h**4 + 2*h**2. Solve u(c) = 0.
-1
Let q(p) = p**3 + p**2 - p. Let v(y) = -10*y**3 + 18*y**2 - 30*y. Let j(n) = -6*q(n) - v(n). What is i in j(i) = 0?
0, 3
Let w(z) be the first derivative of 7*z**6/36 - 3*z**5/10 - 19*z**4/24 + 41*z**3/18 - 2*z**2 + 2*z/3 - 8. Find m such that w(m) = 0.
-2, 2/7, 1
Factor 8*u**3 + 11*u**4 - 3*u**4 - 10*u**5 - 4*u**3 - 2*u**5.
-4*u**3*(u - 1)*(3*u + 1)
Let z(h) be the third derivative of h**6/84 + h**5/35 - h**4/28 - 4*h**3/21 + h**2. Suppose z(m) = 0. Calculate m.
-1, 4/5
Let p(n) be the third derivative of -n**5/150 + n**4/10 - 3*n**3/5 - 3*n**2. Factor p(m).
-2*(m - 3)**2/5
Let u(f) be the third derivative of -1/27*f**3 + 0 + 0*f**4 + 0*f - 2*f**2 + 1/270*f**5. Factor u(k).
2*(k - 1)*(k + 1)/9
Let y(g) be the third derivative of -g**6/135 + g**5/270 + g**4/27 - g**3/27 - 7*g**2. Factor y(s).
-2*(s - 1)*(s + 1)*(4*s - 1)/9
Let u(b) = b - 1. Let y(z) = 2*z**4 - 4*z**3 + 2*z**2 + 5*z - 5. Suppose d = 3*d - 4. Let o be -2 + -4 + d - 1. Let c(q) = o*u(q) + y(q). Factor c(s).
2*s**2*(s - 1)**2
Let b(g) = -g**3 - 15*g**2 - 5*g + 15. Let m(t) = t**3 + 30*t**2 + 10*t - 30. Let u(a) = -11*b(a) - 6*m(a). Find r, given that u(r) = 0.
-1, 1, 3
Let g = 0 + -1. Let i be 2 - 1*(g + 1). Factor 0*h**4 - h**4 + 2*h - 3*h + h**3 + h**i.
-h*(h - 1)**2*(h + 1)
Let k(t) = 7*t**3 - 7*t**2 - 6*t + 4. Let x(u) = -36*u**3 + 36*u**2 + 30*u - 21. Let b(p) = 21*k(p) + 4*x(p). Let b(m) = 0. Calculate m.
-1, 0, 2
Let u = -28692 - -143902/5. Let l = u - 88. Factor -1/5*v**2 - 3/5*v - l.
-(v + 1)*(v + 2)/5
Let s(z) be the second derivative of -z**6/90 + z**5/15 - 5*z**4/36 + z**3/9 + 4*z. Factor s(o).
-o*(o - 2)*(o - 1)**2/3
Factor 0 + 4/7*j**3 + 0*j**2 + 0*j - 10/7*j**5 + 6/7*j**4.
-2*j**3*(j - 1)*(5*j + 2)/7
Suppose 6*f = 2*f + f. Let g(y) be the first derivative of 0*y**5 + f*y + 4/9*y**3 - 1/9*y**6 + 0*y**2 + 4 + 1/2*y**4. Factor g(t).
-2*t**2*(t - 2)*(t + 1)**2/3
Let l(t) be the first derivative of 3*t**4/4 - t**3 + 7. Factor l(f).
3*f**2*(f - 1)
Let g(o) = -o**3 - 2*o. Let y be g(-3). Factor -y*r + 33*r - 2*r**3.
-2*r**3
Let k(x) be the first derivative of x**4/2 + 10*x**3/3 + 7*x**2 + 6*x - 3. Suppose k(d) = 0. What is d?
-3, -1
Let k = 106887/197800 + -3/7912. Let q = k + -1/25. Factor t**2 + q*t**3 + 0 + 1/2*t.
t*(t + 1)**2/2
Let v = -46/5 + 342/35. Find d, given that 4/7*d + 0 - v*d**2 = 0.
0, 1
Factor 372*q**2 + 20*q**4 + 350*q**3 + 5 + 11 + 78*q**4 + 93*q + 43*q.
2*(q + 1)*(q + 2)*(7*q + 2)**2
Let q(w) = -120*w**3 - 425*w**2 - 305*w - 35. Let p(f) = 7*f**3 + 25*f**2 + 18*f + 2. Let c(r) = -35*p(r) - 2*q(r). Factor c(y).
-5*y*(y + 1)*(y + 4)
Suppose 8*f - 50 = 3*f. Suppose f = -2*s - 4*x - 10, -5*s - 25 = 5*x. Solve 0*c - 2/7*c**3 + s + 2/7*c**2 = 0.
0, 1
Let i(c) = -4*c**4 - 2*c**3 - 8*c**2 - 12*c - 16. Suppose 2*m - 112 = -2*m. Let b(z) = -z**2 - z - 1. Let a(k) = m*b(k) - 2*i(k). Find y such that a(y) = 0.
-1, 1/2, 1
Let b be (-12)/(-90)*(1 - -9). Factor -b + 2*z - 2/3*z**2.
-2*(z - 2)*(z - 1)/3
Let f be (-4)/10*54/(-72). Let u(k) be the first derivative of -2 - 2/3*k**3 + f*k**4 + 2/5*k**2 + 0*k. Determine g, given that u(g) = 0.
0, 2/3, 1
Let x(u) = u + 8. Let l be x(-8). Let w(k) be the first derivative of l*k + 0*k**4 + 0*k**2 + 1 + 1/5*k**5 - 1/3*k**3. Determine j, given that w(j) = 0.
-1, 0, 1
Let a(k) = 3*k + 5*k + 5*k**2 - 5 - k - 2*k**3. Let h(w) = -6*w**3 + 14*w**2 + 20*w - 14. Let z(m) = 14*a(m) - 5*h(m). Factor z(s).
2*s*(s - 1)*(s + 1)
Let d = -2 - -4. Determine m so that 0*m + 0 + 0*m**d - 2/9*m**3 = 0.
0
Let m(g) be the third derivative of 3*g**7/70 - g**6/4 + 9*g**5/20 - g**4/4 - 4*g**2 + 2. Factor m(q).
3*q*(q - 2)*(q - 1)*(3*q - 1)
Let a(k) = -k**3 + 5*k**2 + 5*k + 8. Let f be a(6). Suppose -8 + 4 = -f*m. Factor 4/9*s - 2/9*s**4 + 0*s**m + 2/9 - 4/9*s**3.
-2*(s - 1)*(s + 1)**3/9
Let l(a) = 5*a**5 + 55*a**4 + 107*a**3 + 117*a**2 + 64*a + 12. Let z(h) = -h**5 + h**4 - h**3 + h. Let w(q) = -l(q) + 4*z(q). Find r, given that w(r) = 0.
-2, -1, -2/3
Let n(c) = 5*c**2 + 7*c + 5. Let l(d) be the second derivative of -d**4/3 - d**3 - 2*d**2 - 3*d. Let r(f) = 3*l(f) + 2*n(f). Factor r(p).
-2*(p + 1)**2
Let k(f) be the first derivative of -1 + 0*f + 2/33*f**3 - 1/22*f**4 + 1/11*f**2 - 2/55*f**5. Factor k(z).
-2*z*(z - 1)*(z + 1)**2/11
Let j(s) be the third derivative of s**5/20 - s**4/8 - s**3/3 - 3*s**2. Let y(g) = -5*g**2 + 6*g + 4. Let q(z) = -7*j(z) - 4*y(z). Find h such that q(h) = 0.
-2, -1
Let l(x) be the third derivative of -x**6/780 + x**5/39 - 17*x**4/156 + 8*x**3/39 - 3*x**2 + 12. Factor l(b).
-2*(b - 8)*(b - 1)**2/13
Let c(a) = -a**3 - 6*a**2 - 4*a + 7. Let y be c(-5). Suppose 0 = -4*q + 10 - y. Factor 5*h - h + 4 + q*h**2 - h**2.
(h + 2)**2
Let z(k) = k**3 - 8*k**2 + 9*k - 9. Let u be z(7). Let x(l) be the first derivative of 3 + 0*l**3 + 0*l - 3/4*l**4 - 1/5*l**u + 2*l**2. Solve x(t) = 0.
-2, 0, 1
Let j(s) be the second derivative of -s**6/80 - 3*s**5/80 + 3*s**4/32 + s**3/4 - 3*s**2/4 + 13*s. Suppose j(b) = 0. What is b?
-2, 1
Let z be 8/5*15/2. Suppose i**2 + 17*i**2 + z*i + 4 + 5*i**3 - 2 + 3*i**3 = 0. What is i?
-1, -1/4
Let i(l) be the third derivative of 0*l**5 + 4*l**2 + 0 + 0*l + 0*l**3 + 0*l**7 + 0*l**4 - 1/2352*l**8 + 1/840*l**6. Suppose i(h) = 0. What is h?
-1, 0, 1
Let t(a) = -a**2 + 9*a - 15. Let l be t(4). Let d(j) be the third derivative of -9/10*j**3 - 1/100*j**l + 3*j**2 + 0 - 3/20*j**4 + 0*j. Factor d(f).
-3*(f + 3)**2/5
Let d(o) be the third derivative of o**8/60480 - o**7/15120 - o**5/20 + o**2. Let r(b) be the third derivative of d(b). Factor r(l).
l*(l - 1)/3
Let j(z) = -4*z**5 + 6*z**4 + 4*z**3 - 6*z**2. Let i(t) = -t**5 + t**4 + t**3 - t**2. Let k(v) = 5*i(v) - j(v). Factor k(p).
-p**2*(p - 1)*(p + 1)**2
Let j be 2 - (-395*5 - -2). Suppose -5*g - 200 + j = 0. Factor 201*l**2 + 4 + 70*l**5 + 234*l**4 + g*l**3 + 48*l + 11*l**5 + 45*l**4.
(l + 1)**3*(9*l + 2)**2
Let v = 39 + -39. Let r(g) be the second derivati