(t) = 6*t**2 - 8*t + 6. Let q(i) = n*g(i) - 3*r(i). Factor q(p).
-2*(p - 2)*(2*p - 1)
Suppose -5*j = -j. Let c(q) be the third derivative of -1/24*q**4 + j*q + 0*q**3 + 2*q**2 + 0 - 1/60*q**5. Factor c(m).
-m*(m + 1)
Suppose -5*l + 32 = 3*l. Factor 4/7*y**3 - 2/7*y**l + 0 - 2/7*y**2 + 0*y.
-2*y**2*(y - 1)**2/7
Let k be (1/(-1) - -4) + 0. Let f = 44 - 85/2. Factor 3/2 + f*z**2 + k*z.
3*(z + 1)**2/2
Let u(d) = 5*d**3 - 7*d**2 - 6*d + 3. Let n(w) = -16*w**3 + 22*w**2 + 18*w - 10. Let f(q) = 6*n(q) + 20*u(q). Factor f(j).
4*j*(j - 3)*(j + 1)
Let r = 227887/7 + -32644. Let p = r - -89. Factor 0*o**2 - 2/7*o**3 + 0 + p*o.
-2*o*(o - 1)*(o + 1)/7
Let v(l) be the third derivative of l**8/13440 + l**7/5040 + l**4/6 - 2*l**2. Let q(n) be the second derivative of v(n). Factor q(h).
h**2*(h + 1)/2
Factor -2/3*c**4 - 1/3*c**5 + 0 + 0*c - 1/3*c**3 + 0*c**2.
-c**3*(c + 1)**2/3
Solve -5*c**4 - 5*c - 8*c + 5*c**3 + 8*c + 10*c**4 - 5*c**2 = 0 for c.
-1, 0, 1
Let a(v) be the third derivative of 4/105*v**7 + 0 + 0*v + 0*v**3 - 1/10*v**6 - 1/168*v**8 + 2/15*v**5 - 3*v**2 - 1/12*v**4. Factor a(z).
-2*z*(z - 1)**4
Let y(s) be the third derivative of s**8/840 - s**7/105 + 7*s**6/300 + s**5/150 - 2*s**4/15 + 4*s**3/15 + 10*s**2. Determine x so that y(x) = 0.
-1, 1, 2
Let g(j) = j**3 + 7*j**2 + j. Let s(q) = -q**3 - 6*q**2 - 2*q. Let z(f) = -2*g(f) - 3*s(f). Factor z(k).
k*(k + 2)**2
Let w be -1 + 5/(-4)*-5. Let p = -59/12 + w. Determine o so that 0*o + p*o**3 + 0*o**2 + 0 - 2/3*o**4 = 0.
0, 1/2
Let o(w) = 7*w**2 + 5*w - 6. Let u(p) = -p**2 - p + 1. Let s(t) = -o(t) - 6*u(t). Factor s(m).
-m*(m - 1)
Let d(o) be the third derivative of -o**8/672 - o**7/70 - 11*o**6/240 - o**5/60 + o**4/4 + 2*o**3/3 + 11*o**2. Determine b, given that d(b) = 0.
-2, -1, 1
Let t = 15 + -3. Let g be t/(-42) - 102/(-14). Let -6*z + g*z + z + 2*z**2 = 0. Calculate z.
-1, 0
Let a(u) be the first derivative of -u**4/2 + 8*u**3/3 - 3*u**2 + 3. Let a(m) = 0. What is m?
0, 1, 3
Suppose 0 = 2*w - 7*w - 5*w. Suppose -1/5*l**5 + 0*l**2 + 0 + 0*l**3 + 1/5*l**4 + w*l = 0. Calculate l.
0, 1
Let o be (-2)/(112/132) - -2. Let t = o - -71/42. Factor -t*r**2 + 4/3*r**3 + 2/3*r**5 + 2*r**4 - 2/3 - 2*r.
2*(r - 1)*(r + 1)**4/3
Let u(q) = -14*q**2 + 14*q**3 - 2*q**3 + 2*q + 6*q. Let w(b) = 23*b**3 - 27*b**2 + 15*b. Let l(d) = -11*u(d) + 6*w(d). Factor l(a).
2*a*(a - 1)*(3*a - 1)
Suppose 5*d + 3*g = 30, -d - 5*g + 10 = -6*d. Suppose 9 + d = 4*o. Factor 0*j - 2/5*j**2 + 0 - 1/5*j**o.
-j**2*(j + 2)/5
Let g = 15 - 15. Suppose g = 2*u - 6*u. Factor 4/5*t**2 + u - 2/5*t - 2/5*t**3.
-2*t*(t - 1)**2/5
Let f(s) = s**5 - 5*s**4 + 4*s**3 - 3*s**2 + 3*s - 3. Let k(o) = 3*o**5 - 10*o**4 + 7*o**3 - 5*o**2 + 5*o - 5. Let d(u) = -5*f(u) + 3*k(u). Factor d(b).
b**3*(b - 1)*(4*b - 1)
Let u be (4 - (-909)/(-240)) + 5/(-25). Let o(k) be the second derivative of 0*k**2 - 3*k + 0*k**4 + 0*k**3 - u*k**5 + 0. Let o(m) = 0. What is m?
0
Let d(x) be the first derivative of -x**4/42 + x**3/21 - 3*x + 3. Let y(i) be the first derivative of d(i). Solve y(o) = 0 for o.
0, 1
Let w(x) be the second derivative of x**6/40 - 3*x**4/8 - x**3 + x**2 - x. Let a(o) be the first derivative of w(o). Factor a(c).
3*(c - 2)*(c + 1)**2
Let z(u) be the third derivative of -u**7/105 + u**5/30 + 8*u**2. Factor z(m).
-2*m**2*(m - 1)*(m + 1)
Let u(w) be the first derivative of -1 + 1/3*w**3 - 1/2*w**2 - 1/16*w**4 + 0*w. Let u(m) = 0. Calculate m.
0, 2
Let o(s) = s + s**2 - 2 + 5*s + 2*s - 5*s. Let h(r) be the third derivative of -r**5/20 - 5*r**4/12 + 7*r**3/6 + r**2. Let z(f) = 4*h(f) + 14*o(f). Factor z(t).
2*t*(t + 1)
Suppose 171*h - 173*h + 4 = 0. Let 70/3*f**3 - 4/3 + f**h - 49/3*f**4 - 20/3*f = 0. Calculate f.
-2/7, 1
Let -10/7*r**2 - 4/7*r + 0 = 0. Calculate r.
-2/5, 0
Let x(d) = d**2 + 4*d - 3. Let t be x(-5). Let j(c) be the first derivative of 0*c - 2/5*c**5 - 1 + 0*c**t + 1/3*c**4 - 2/27*c**3. Factor j(q).
-2*q**2*(3*q - 1)**2/9
Find w, given that 0*w**2 + 0 - 1/5*w**3 + 1/5*w = 0.
-1, 0, 1
Let y be 21/2 + (-2)/4. Let p be -5 + 8 - 26/y. Factor 6/5*a + 4/5 - p*a**3 + 0*a**2.
-2*(a - 2)*(a + 1)**2/5
Let c(s) be the second derivative of -2/3*s**4 - s + s**2 + 0 + s**3. Determine r, given that c(r) = 0.
-1/4, 1
Let c(g) be the first derivative of -g**5/30 + g**4/4 - 2*g**3/3 + 3*g**2/2 + 6. Let p(b) be the second derivative of c(b). Factor p(f).
-2*(f - 2)*(f - 1)
Let l(r) be the third derivative of -2*r**7/105 + r**5/15 + 5*r**2. Solve l(t) = 0 for t.
-1, 0, 1
Let h(k) = k**3 + 3*k**2 - 5*k - 4. Suppose -8*o + 3*o = 20. Let j be h(o). Factor -2*p**3 - 2*p**4 + j*p**4 - p**4 + 0*p**2 + p**2.
-p**2*(p + 1)*(3*p - 1)
Let c(w) be the second derivative of -8/5*w**5 - 1/3*w**3 + 0 - 4/3*w**4 + 0*w**2 - 2*w. Factor c(f).
-2*f*(4*f + 1)**2
Suppose v = -3*v + 8. Let -3*a**2 + 2*a**v + 4*a**2 + 6*a = 0. What is a?
-2, 0
Let i(x) be the first derivative of x**6/21 - 2*x**5/35 + 14. Factor i(u).
2*u**4*(u - 1)/7
Let q be (-2472)/21 - -3 - -2. Let k = q - -113. Solve -k*h**2 + 0*h + 2/7*h**4 + 0 + 0*h**3 = 0.
-1, 0, 1
Let n(h) = -h**2 + 32*h + 64. Let g(s) = 2*s**2 - 32*s - 64. Let k(d) = -5*g(d) - 6*n(d). Determine z, given that k(z) = 0.
-4
Let v(j) be the first derivative of j**6/40 + 4*j + 1. Let r(u) be the first derivative of v(u). Suppose r(z) = 0. What is z?
0
Let g(t) = 50*t**5 + 6*t**4 - 50*t**3 - 14*t**2 + 8*t - 4. Let b(l) = -l**4 + l**3 - l**2 + l - 1. Let j(x) = -4*b(x) + g(x). Solve j(u) = 0 for u.
-1, -2/5, 0, 1/5, 1
Let n(h) be the first derivative of -2/3*h**3 - h**2 + 1 + 1/2*h**4 + 2*h. Factor n(l).
2*(l - 1)**2*(l + 1)
Let p be (-1 + 2)/((-2)/(-4)). Let t be 2/(-8) - 12/(-24). Determine x, given that -3/4*x + t*x**p + 1/2 = 0.
1, 2
Let m = 157/5 + -31. Factor m*o**2 - 4/5*o + 0.
2*o*(o - 2)/5
Let u(t) be the third derivative of -1/735*t**7 - 1/420*t**6 + 1/1176*t**8 + 0*t**4 + 1/210*t**5 + 0*t + t**2 + 0 + 0*t**3. Factor u(s).
2*s**2*(s - 1)**2*(s + 1)/7
Let s(u) be the third derivative of u**6/120 + 7*u**5/60 + u**4/4 + u**3/2 + 2*u**2. Let d be s(-6). Factor -q**3 - 2*q**3 - 3*q**2 + d*q - 1 + 4*q**3.
(q - 1)**3
Let x be -7 + 5 - (-3 - (3 - 1)). Let w(p) be the first derivative of 0*p + 2 - p**2 + 1/3*p**x + 1/4*p**4. Factor w(t).
t*(t - 1)*(t + 2)
Let z(i) be the third derivative of 1/35*i**7 + i**3 - i**2 + 19/40*i**5 + 0 - 5/32*i**6 + 0*i - 1/448*i**8 - 7/8*i**4. Determine y so that z(y) = 0.
1, 2
Let f(x) = -x**2 + 4*x - 4. Let i(s) = -3*s**2 + 15*s - 15. Let y(r) = 15*f(r) - 4*i(r). Factor y(h).
-3*h**2
Factor 2 - 2*f**3 - 2 + 3*f**3 + 3*f**2 + 2*f.
f*(f + 1)*(f + 2)
Let l(s) be the first derivative of 5*s**3/3 + 5*s**2/2 - 10*s + 11. Find n, given that l(n) = 0.
-2, 1
Let o(x) = x**2 + x + 2. Let n be o(0). Factor 0*j**3 + 6*j**2 - 3*j**3 + j**3 - 6*j + n*j.
-2*j*(j - 2)*(j - 1)
Let v(j) be the second derivative of 3*j**5/20 - 5*j**4/2 + 23*j**3/2 - 21*j**2 - 41*j. What is p in v(p) = 0?
1, 2, 7
Let y(b) be the first derivative of -3*b**4/4 + 5*b**3 - 12*b**2 + 12*b - 1. Factor y(x).
-3*(x - 2)**2*(x - 1)
Suppose -21 = f - 2*f + 4*o, 0 = -3*f - 5*o - 5. Let r = -15/4 + f. Let -1/2*d + 0 + r*d**3 - 3/4*d**2 = 0. Calculate d.
-2/5, 0, 1
Let l(n) = -n**2 - n - 3. Let b be l(0). Let q be (4/2*b)/(-4). Find y, given that 3/2*y - q*y**3 + 0 + 0*y**2 = 0.
-1, 0, 1
Let p be 3 - (-10)/(-9) - 1/(-9). Solve -1/3*z**p - 2/3*z - 1/3 = 0.
-1
Let m(c) be the first derivative of -c**6/360 - c**3/3 - 4. Let q(o) be the third derivative of m(o). Factor q(p).
-p**2
Let c = -2 + -4. Let n be (-2)/40 + c/(-24). Solve n*j**2 + 0*j + 0 = 0.
0
Let m(q) be the second derivative of 4*q**2 + 0 + q - 10*q**3 + 19/3*q**4 + 36/5*q**5. Factor m(w).
4*(w + 1)*(4*w - 1)*(9*w - 2)
Let n(j) = j**4 - j. Let p(m) be the first derivative of 4*m**5/5 + m**4/2 + m**3/3 - 7*m**2/2 + 5. Let h(v) = 5*n(v) - p(v). Factor h(x).
x*(x - 2)*(x - 1)*(x + 1)
Let x(n) be the third derivative of -n**5/180 - n**4/72 + n**3/9 + 43*n**2. Factor x(s).
-(s - 1)*(s + 2)/3
Let x(g) = -2*g + 13. Let d be x(5). Factor -2*p**3 + 7*p**3 + 0*p**d - 7*p**3 + 1 - p**4 + 2*p.
-(p - 1)*(p + 1)**3
Let a(n) be the first derivative of n**4/10 - 6*n**3/5 + 27*n**2/5 - 54*n/5 + 3. Determine x so that a(x) = 0.
3
Let b(u) = -u**3 + u**2 - u - 1. Let i(p) = -3 + 6 + 8*p**3 + 5*p - 3*p - 4*p**2 + 3. Let r(