 - 9*v**2 - 41 + 0*v**2 + 11. Let z(h) = 5*c(h) + 24*t(h). Factor z(g).
3*(g - 1)*(g + 2)
Let u**3 + 4*u**5 - 4*u**4 + 9*u**3 - 10*u**3 = 0. What is u?
0, 1
Let v(f) be the second derivative of -f**6/10 + 9*f**5/20 - f**4/2 + 12*f - 1. Let v(t) = 0. Calculate t.
0, 1, 2
Let 2*m + 2 - m**3 - 3/2*m**2 + 1/2*m**4 = 0. What is m?
-1, 2
Let p(c) be the second derivative of -c**6/15 + c**5/20 + c**4/6 - c**3/6 - 25*c. Factor p(m).
-m*(m - 1)*(m + 1)*(2*m - 1)
Suppose 2*p = -2*p + 24. Suppose -p*o + 20 = -o. Let 1/2*t - 1/2*t**3 + 1/2*t**2 + 0 - 1/2*t**o = 0. What is t?
-1, 0, 1
Let k(j) be the second derivative of j**6/50 + 9*j**5/100 + j**4/20 - 3*j**3/10 - 3*j**2/5 - 4*j. Factor k(t).
3*(t - 1)*(t + 1)**2*(t + 2)/5
Let u(n) be the first derivative of n**5/60 - n**4/8 + n**3/3 - 3*n**2/2 + 3. Let d(k) be the second derivative of u(k). Factor d(x).
(x - 2)*(x - 1)
Let p = -1 - -5. Suppose -q = -p*q. Suppose q*o + 0 + 2/7*o**2 = 0. What is o?
0
Let q be ((-4)/24)/((-2)/354). Let z = q + -29. Factor z + 0*g - 1/2*g**2.
-(g - 1)*(g + 1)/2
Let s(v) be the second derivative of -v**6/45 - v**5/15 + v**4/6 + 4*v**3/9 - 4*v**2/3 - 3*v. Suppose s(h) = 0. Calculate h.
-2, 1
Let w(f) = -1. Let o(l) be the second derivative of l**4/12 - l**3/6 - 2*l. Let h(c) = -o(c) - 2*w(c). Factor h(j).
-(j - 2)*(j + 1)
Let m(k) be the first derivative of -4/3*k**2 + 2/45*k**5 - 1/3*k**4 + 26/27*k**3 + 8/9*k - 2. Let m(g) = 0. What is g?
1, 2
Let v(i) = -19*i**3 + 79*i**2 - 80*i + 23. Let z(b) = -b**3 + b**2 - 1. Let n(a) = 2*v(a) - 2*z(a). Factor n(m).
-4*(m - 3)*(3*m - 2)**2
Let i(y) be the third derivative of -y**3 + 4*y**2 + 0*y + 1/14*y**7 + 7/40*y**6 - 7/8*y**4 + 0 - 3/20*y**5. Solve i(q) = 0 for q.
-1, -2/5, 1
Suppose -25 = 5*o, -4*f + f + 5 = -o. Factor 2/7*w**2 + f*w + 0.
2*w**2/7
Solve -1/5*g**3 + 0*g - 1/5*g**2 + 0 = 0 for g.
-1, 0
Let m(a) be the first derivative of 2*a**6/3 - 3. What is l in m(l) = 0?
0
Let a be 2/2 - (-148)/6. Let g = a - 24. Factor 0 + m**4 + 1/3*m + 1/3*m**2 - g*m**3.
m*(m - 1)**2*(3*m + 1)/3
Let f(k) be the third derivative of -k**6/30 + k**5/15 + 5*k**4/6 + 2*k**3 + 49*k**2. Let f(d) = 0. Calculate d.
-1, 3
Find t such that 6*t**2 - 10/13*t**4 - 14/13*t - 20/13 - 34/13*t**3 = 0.
-5, -2/5, 1
Let d(p) = -12*p**3 - 20*p**2 - 13*p + 9. Suppose -2 = -5*f + 3. Let l(o) = o**3 - o - f + 5 - 3. Let x(w) = 2*d(w) - 18*l(w). Solve x(g) = 0 for g.
-2/3, -2/7, 0
Let a(u) = -u**3 - 6*u**2 - 7*u - 5. Let d be a(-4). Let q be (-3)/d*(8 + 1). Let -4*b - q - b**2 + 1 - b**2 = 0. Calculate b.
-1
Suppose -j = j + 88. Let f be 6/(-4)*j/33. Suppose 0 - 9/5*v**3 + f*v**4 + 2/5*v**2 + 0*v - 3/5*v**5 = 0. What is v?
0, 1/3, 1, 2
Let l = -7 - -8. Let m be 1/(9/3*l). Factor -u + 4/3*u**2 - m.
(u - 1)*(4*u + 1)/3
Let p(z) = 1 + z**3 - z - 2*z - 3*z**2 + 7*z**2. Let q be p(-4). Solve 2*x**2 - 2*x - 13 + q = 0.
0, 1
Let s(u) be the third derivative of 0*u**4 + 0*u**6 + 0 - 1/20*u**5 - 4*u**2 + 1/70*u**7 + 0*u**3 + 0*u. Suppose s(z) = 0. Calculate z.
-1, 0, 1
Let l(z) be the second derivative of -5*z**4/48 + 5*z**3/3 - 10*z**2 + 9*z. Factor l(y).
-5*(y - 4)**2/4
Let u(z) be the second derivative of -z**7/105 - z**6/30 - z**5/30 - z**2/2 - 3*z. Let j(v) be the first derivative of u(v). Suppose j(m) = 0. Calculate m.
-1, 0
Let v(i) be the first derivative of i**5/5 - 2*i**4/15 - 2*i**3/5 + 5*i - 3. Let t(d) be the first derivative of v(d). Factor t(a).
4*a*(a - 1)*(5*a + 3)/5
Suppose -10*m**4 + 94*m**2 - 100*m**3 - 5*m**4 + 91*m**2 - 120*m**3 - 20 + 70*m**5 = 0. What is m?
-2, -2/7, 1/2, 1
Let i(k) be the third derivative of 0*k - 1/1344*k**8 - 3*k**2 + 1/420*k**7 + 0*k**4 + 0 + 0*k**3 - 1/120*k**5 + 1/480*k**6. Determine d so that i(d) = 0.
-1, 0, 1, 2
Let a(p) be the second derivative of 0 - 1/50*p**6 + 1/20*p**4 + 2*p + 3/100*p**5 - 1/10*p**3 + 0*p**2. Factor a(h).
-3*h*(h - 1)**2*(h + 1)/5
Let u = -21 + 24. Let x(q) be the third derivative of 0*q**7 + 1/336*q**8 - u*q**2 + 0*q**3 + 0*q**5 + 1/24*q**4 - 1/60*q**6 + 0*q + 0. Factor x(v).
v*(v - 1)**2*(v + 1)**2
Suppose -2*k + 16 = 3*o + 2*k, 0 = 3*k - 12. Factor l - 5*l**3 + o*l**3 + 4*l**3.
-l*(l - 1)*(l + 1)
Suppose -5*w + 31 = 2*s, -s + 4*w = 2*s + 11. Let l(o) be the first derivative of 2 + o + 9/4*o**2 + 5/2*o**s + 3/10*o**5 + 11/8*o**4. Factor l(n).
(n + 1)**3*(3*n + 2)/2
Let s = 263 + -3947/15. Let v = s + 7/15. What is o in -4/3*o**2 + 0 + 4/3*o + v*o**3 = 0?
0, 2
Let v(y) = -y**3 + 2*y**2 - 3*y + 6. Let j(u) = -u**3 + 3*u**2 - 4*u + 7. Let p(f) = -4*j(f) + 5*v(f). Factor p(w).
-(w - 1)*(w + 1)*(w + 2)
Let f(a) be the second derivative of -a**7/5040 + a**5/240 - a**4/6 + 3*a. Let j(c) be the third derivative of f(c). Factor j(k).
-(k - 1)*(k + 1)/2
Let a(y) be the third derivative of 0*y + 1/20*y**5 + 0 - y**3 + 1/8*y**4 - y**2. Factor a(s).
3*(s - 1)*(s + 2)
Let g(l) = l**2 - 2*l + 6. Let c be g(5). Suppose 4*k - c = -5. Let -1 + 53*m**4 + 36*m**3 + k*m**2 + 63*m**5 + 42*m**4 + 1 = 0. Calculate m.
-1, -2/7, -2/9, 0
Let t(o) be the third derivative of o**7/140 + o**6/40 + o**5/40 - 9*o**2. Solve t(a) = 0.
-1, 0
Suppose -m = -3*m + 22. Suppose -3*s + j + m = 0, 2*j - 3*j = -4*s + 14. Factor -3*o**5 + s*o**5 + o**5 - o**4.
o**4*(o - 1)
Let s(l) = -l**2 + 8. Let j be s(0). Suppose 0 = -a + 3*a - j. Factor -16*n**2 + 3 - 7*n**5 + n - 1 - 12*n**4 - 14*n**a - 34*n**3.
-(n + 1)**4*(7*n - 2)
Let b(o) = o**2 - 5*o + 4. Let x be b(5). Let v(c) = c**2 - 4*c + 5. Let g be v(4). Factor -1/2*u**x + 0*u - 1/2*u**g + 0 + 1/2*u**2 + 1/2*u**3.
-u**2*(u - 1)*(u + 1)**2/2
Suppose 2*a + 10 = -2*x, a = 5*a + 3*x + 15. Solve a*u + 0 + 2/3*u**2 = 0 for u.
0
Let i = -63 + 127/2. Factor 0 + 0*n**2 - i*n + 1/2*n**3.
n*(n - 1)*(n + 1)/2
Let g(v) = 8*v**2 + 5*v - 2. Let y(s) = 7*s**2 + 6*s - 1. Let n(i) = -4*g(i) + 5*y(i). Factor n(h).
(h + 3)*(3*h + 1)
Let i(j) = j**5 + j**4 + 5*j**3 - j**2 - 6*j. Let v(o) = -4*o**5 - 5*o**4 - 19*o**3 + 5*o**2 + 23*o. Let r(q) = -22*i(q) - 6*v(q). Factor r(k).
2*k*(k - 1)*(k + 1)**2*(k + 3)
Determine f, given that -6*f**3 + 20*f**3 - 15*f**3 + f = 0.
-1, 0, 1
Let n(k) be the first derivative of -k**6/18 + k**4/12 + 9. Factor n(v).
-v**3*(v - 1)*(v + 1)/3
Let p = -1 + -1. Let i = 0 - p. Factor 9*b - 9*b - 3*b**i - 3*b**4 + 6*b**3.
-3*b**2*(b - 1)**2
Factor 20/7*f**2 - 4/7*f**3 + 12/7 - 4*f.
-4*(f - 3)*(f - 1)**2/7
Suppose 50 = 18*f - 16*f. Determine i, given that -2*i**4 - 27*i**3 + 3*i**4 + f*i**3 + i**2 = 0.
0, 1
Factor -5/3*s - 7/3*s**2 + 2/3.
-(s + 1)*(7*s - 2)/3
Factor 8/9 + 8/9*t + 2/9*t**2.
2*(t + 2)**2/9
Let k be 2/3 - (-2)/6 - -2. Factor -3/4*s**4 + 0*s + 0 + 0*s**2 - 3/4*s**k.
-3*s**3*(s + 1)/4
Let z(g) = -g**2 - 4*g. Let c be z(-4). Find s, given that 11*s**3 + 4*s**2 + c + 0 - 2*s - 5*s**3 = 0.
-1, 0, 1/3
Let z be (-6)/(-14) + 485/(-14). Let g = z - -69/2. Factor 0 - 2/7*f**2 + g*f.
-2*f*(f - 1)/7
Let p be (-40)/(-35) - (1 - 0). Let a(f) be the second derivative of -1/14*f**4 - 1/7*f**3 + f + 0 - 1/70*f**5 - p*f**2. Factor a(j).
-2*(j + 1)**3/7
Let o(d) = -4*d**3 - 42*d**2 - 114*d - 114. Let c(h) = 4*h**3 + 43*h**2 + 115*h + 115. Let b(i) = -6*c(i) - 7*o(i). Factor b(k).
4*(k + 3)**3
Let a(h) be the second derivative of 7*h**4/60 - 3*h**3/10 + h**2/5 - 14*h. Determine m, given that a(m) = 0.
2/7, 1
Suppose -32/13*a - 2/13*a**3 - 16/13*a**2 + 0 = 0. Calculate a.
-4, 0
Let q(p) be the second derivative of p**4/24 + p**3 + 9*p**2 - 13*p. Find n, given that q(n) = 0.
-6
Let i(x) be the first derivative of 2*x**3/15 + 3*x**2/5 + 4*x/5 - 8. Factor i(f).
2*(f + 1)*(f + 2)/5
Let r(u) be the third derivative of 0*u + 0*u**7 - 4/5*u**3 + 1/2*u**4 - 9/40*u**6 + 1/10*u**5 + 4*u**2 + 0 + 27/560*u**8. Suppose r(h) = 0. Calculate h.
-1, 2/3
Let f(c) = -c**2 + c - 1. Let h(i) = 4*i**2 + 4*i - 3. Let m(r) = -r**2 - 6*r + 6. Let j be m(-7). Let o(z) = j*f(z) + h(z). Factor o(k).
(k + 1)*(5*k - 2)
Let a(p) be the second derivative of p**9/1512 - p**8/420 + p**7/420 + p**3/6 + 7*p. Let x(z) be the second derivative of a(z). Factor x(j).
2*j**3*(j - 1)**2
Let j(p) be the third derivative of p**5/35 - 4*p**4/21 + 8*p**3/21 - 13*p**2. Factor j(i).
4*(i - 2)*(3*i - 2)/7
Let s(z) be the first derivative of 0*z**4 + 1/18*z**6 + 2/9*z**3 - 2 - 1/6*z**2 + 0*z - 2/15*z**5. Factor s(v).
v*(v - 1)**3*(v + 1)/3
Let v(z) b