*3 + 16230*m**2 + 1670*m + 64. Let d(q) = -q**4 - q**2 - q. Let x(n) = c(n) + 6*d(n). Suppose x(v) = 0. Calculate v.
-2/13
Suppose 30 = 3*g + 5*k - 26, 0 = k - 4. Let z = g + -7. Factor -2 - z - 1 + 8*l - 2*l**2.
-2*(l - 2)**2
Let l(v) be the first derivative of 1/6*v**3 + 0*v - 1 - 1/4*v**2. Factor l(x).
x*(x - 1)/2
Let f be 24/(-9)*(15/12)/(-5). Let o = -9 - -28/3. Let 0 + 2/3*r**4 + 0*r**3 - f*r**2 + o*r**5 - 1/3*r = 0. What is r?
-1, 0, 1
Suppose 5*a - 5 = 5. Factor -1/4*p**3 - 1/4 - 3/4*p**a - 3/4*p.
-(p + 1)**3/4
Let p(w) be the second derivative of -4*w - 1/12*w**4 + 0 - 2/3*w**3 - 3/2*w**2. Suppose p(z) = 0. What is z?
-3, -1
Let a(r) be the second derivative of 2/231*r**7 - 1/110*r**5 + 0 + 1/55*r**6 - 1/33*r**3 - 1/22*r**4 + r + 0*r**2. Find h, given that a(h) = 0.
-1, -1/2, 0, 1
Let t = 11 + -8. Let j(m) = -7*m**2 + 3*m**2 + 4*m**t + 0*m**3. Let v(z) = -z**3 + z**2. Let u(r) = 2*j(r) + 9*v(r). Factor u(p).
-p**2*(p - 1)
Solve 0*c + 6 - 3/2*c**3 - 9/2*c**2 = 0 for c.
-2, 1
Let g(j) be the third derivative of -j**6/1080 + j**5/180 + j**3/6 - 3*j**2. Let f(v) be the first derivative of g(v). Factor f(p).
-p*(p - 2)/3
Suppose 3 + 5 = 4*t. Let f be 10 + (t + -1 - 3). Determine y, given that 9*y**3 + 3*y**2 - 4*y**2 - f*y**3 = 0.
0, 1
Factor -g**2 + 1 - 4*g + 3*g**2 + 1.
2*(g - 1)**2
Let p(i) be the first derivative of i**3/2 - 9*i**2/2 + 4. Factor p(q).
3*q*(q - 6)/2
Let 6/13 - 6/13*q**2 - 16/13*q = 0. What is q?
-3, 1/3
Let t(x) be the third derivative of x**6/540 - 2*x**5/135 + x**4/108 + 2*x**3/9 - x**2 + 15. Factor t(q).
2*(q - 3)*(q - 2)*(q + 1)/9
Let v = 0 - -3. Let i be (-1 + 5)*v/4. Suppose -2 - i*w - 2*w**4 + 4*w**2 + 3*w = 0. Calculate w.
-1, 1
Factor -9/4*y**2 - 3/4*y**3 + 0*y + 3.
-3*(y - 1)*(y + 2)**2/4
Let z = 143 - 143. Factor -3/4*w**3 - 1/4*w - 3/4*w**2 - 1/4*w**4 + z.
-w*(w + 1)**3/4
Let b = 33 + -24. Factor -8 - 17*h - 12*h**2 + b*h - 20*h.
-4*(h + 2)*(3*h + 1)
Let b(u) = u**2 + 5*u + 5. Let g be b(-3). Let z be 14/14*(1 - g). Find m such that 0 - 5/3*m**z + 5/3*m**4 + 7/3*m**5 + 2/3*m - 3*m**3 = 0.
-1, 0, 2/7, 1
Let f(g) be the third derivative of -g**8/168 + 2*g**7/21 - 3*g**6/5 + 9*g**5/5 - 9*g**4/4 + 2*g**2. What is t in f(t) = 0?
0, 1, 3
Let t = -62 - -120. Let r be (-3)/2 + t/12. Factor -r*g**2 - 2/3*g - 2*g**3 + 2/3.
-2*(g + 1)**2*(3*g - 1)/3
Let y(a) be the second derivative of -a**5/20 + a**4/12 + a**2/2 + a. Let d(s) = -s**4 - 3*s**2 - 3*s + 5*s**3 - 6 + 3*s. Let p(f) = d(f) + 5*y(f). Factor p(z).
-(z - 1)**2*(z + 1)**2
Let b = 32/155 + 6/31. Factor b + 1/5*y**2 + 3/5*y.
(y + 1)*(y + 2)/5
Let c(k) = k**5 - k**4 - 5*k**2 + 2*k + 3. Let j(a) = 2 + 2*a**5 + 2*a**4 - 10 - 5*a - 5*a**5 + 14*a**2. Let x(l) = 8*c(l) + 3*j(l). Factor x(h).
-h*(h - 1)*(h + 1)**3
Let x(f) = -8*f - 4. Let r(u) = -u**2 - 1. Let i(z) = 2*r(z) + x(z). Determine j, given that i(j) = 0.
-3, -1
Let w(h) be the second derivative of h**4/54 + 32*h**3/27 + 256*h**2/9 - 36*h. Factor w(g).
2*(g + 16)**2/9
Let k(i) be the second derivative of i**8/30240 - i**7/3780 + i**6/1620 - 5*i**4/12 + 4*i. Let v(f) be the third derivative of k(f). Factor v(c).
2*c*(c - 2)*(c - 1)/9
Let d(c) be the first derivative of 4*c**5/5 - c**4 - 4*c**3/3 + 2*c**2 + 9. Factor d(s).
4*s*(s - 1)**2*(s + 1)
Let w be 2 + -5 + 6 + -3. Factor -6/13*k**2 + 6/13*k**3 + w + 2/13*k - 2/13*k**4.
-2*k*(k - 1)**3/13
Suppose 0*a - 2*a - 6 = 5*r, -3*r - 12 = 4*a. Suppose 2*m + 3*o - 10 = 0, 0*m - m + o = r. Factor -4/7 - 10/7*b + m*b**2.
2*(b - 1)*(7*b + 2)/7
Suppose -z + 2 + 1 = 0. Factor -7*y + 6*y**4 + 19 + 2*y**5 + 2*y**z + 3*y - 6*y**2 - 19.
2*y*(y - 1)*(y + 1)**2*(y + 2)
Let p(n) be the first derivative of -1/90*n**5 - 1/135*n**6 + 2 + 1/54*n**4 + 0*n**2 + 1/27*n**3 + n. Let s(z) be the first derivative of p(z). Factor s(c).
-2*c*(c - 1)*(c + 1)**2/9
Let d(j) = -5*j + 135. Let x be d(27). Let i = 0 - 0. Factor 1/2*n**3 - 1/4*n + 0*n**2 + i - 1/4*n**5 + x*n**4.
-n*(n - 1)**2*(n + 1)**2/4
Let k(w) = w**3 - w + 1. Let r(n) = 5*n**5 - 30*n**4 + 74*n**3 - 80*n**2 + 41*n - 6. Let l(v) = 4*k(v) - r(v). Factor l(g).
-5*(g - 2)*(g - 1)**4
Let d(b) = -3*b**4 - 5*b**3 + b**2 + 4*b + 2. Let p = 26 + -22. Let s(z) = -z. Let f(m) = p*d(m) - 4*s(m). Determine r so that f(r) = 0.
-1, -2/3, 1
Let i = 3 - -1. Let q be 66/8 + (-1)/i. Factor q*t + 9*t**2 + 5*t**3 + t**4 + t - 1 - 2*t + 3.
(t + 1)**3*(t + 2)
Let j(o) be the first derivative of 3*o**5/10 + 3*o**4/4 - o**3/2 - 3*o**2/2 - 9. Factor j(x).
3*x*(x - 1)*(x + 1)*(x + 2)/2
Let q(y) be the second derivative of y**6/50 - 3*y**5/10 + 6*y**4/5 + y**3 - 15*y**2/2 - 27*y. Factor q(c).
3*(c - 5)**2*(c - 1)*(c + 1)/5
Determine u, given that 2*u - 10*u + 3*u**2 + u**2 = 0.
0, 2
Let x(s) be the first derivative of 3*s**5/40 - s**4/24 - s**3/6 - 3*s + 1. Let v(r) be the first derivative of x(r). Solve v(a) = 0 for a.
-2/3, 0, 1
Find t such that 35/3*t**4 + 4/3*t + 28/3*t**2 + 0 + 59/3*t**3 = 0.
-1, -2/5, -2/7, 0
Let j(l) be the first derivative of -l**5/20 + l**4/24 + l**3/3 + l**2/2 - 3. Let y(p) be the second derivative of j(p). Solve y(c) = 0 for c.
-2/3, 1
Let c be ((-7)/(-4))/(18/6). Let j(b) be the second derivative of 0*b**2 - 1/3*b**3 - 3/20*b**5 - c*b**4 + 2*b + 5/42*b**7 + 0 + 7/30*b**6. Factor j(s).
s*(s - 1)*(s + 1)**2*(5*s + 2)
Let x(f) be the second derivative of 1/2*f**2 + 0 - 1/4*f**3 - f + 1/40*f**5 + 0*f**4. Factor x(k).
(k - 1)**2*(k + 2)/2
Let y(r) = -2*r**2 - 4*r - 4. Let q(u) = 5*u**2 + 9*u + 9. Let v be 9/6*(-2)/(-3). Let d be 0 + 4*v/(-1). Let c(o) = d*q(o) - 9*y(o). Solve c(t) = 0 for t.
0
Let f(q) be the first derivative of q**4/60 + q**3/15 + q**2/10 - 4*q - 1. Let a(u) be the first derivative of f(u). Suppose a(w) = 0. What is w?
-1
Let h(z) be the first derivative of -3*z**5/5 + 2*z**3 - 3*z - 5. Determine q so that h(q) = 0.
-1, 1
Let f(g) = 4*g**2. Let x be f(1). Find h such that -10/9*h**x + 20/9*h**3 - 2/9 + 2/9*h**5 + 10/9*h - 20/9*h**2 = 0.
1
Let v(h) be the first derivative of h**4/48 - h**2/2 + 2*h + 2. Let d(c) be the first derivative of v(c). Factor d(a).
(a - 2)*(a + 2)/4
Let r(i) be the third derivative of -i**6/120 + i**5/36 - i**4/72 - i**3/18 + 7*i**2. Solve r(a) = 0 for a.
-1/3, 1
Suppose -22 = -2*a - 2*g, 60 = 4*a + 5*g + 11. Let i(r) = -7*r**5 - 6*r**4 - 4*r**3 - r. Let v(n) = -n**5 - n**4 - n**3. Let s(d) = a*v(d) - i(d). Factor s(w).
w*(w - 1)**2*(w + 1)**2
Let n(j) be the first derivative of -8*j**5/55 + 6*j**4/11 - 6*j**3/11 + 2*j**2/11 + 17. Factor n(m).
-2*m*(m - 2)*(2*m - 1)**2/11
Let s(d) be the third derivative of 0*d**3 + 0 - 1/18*d**4 + 1/30*d**5 + 0*d - 1/180*d**6 + 4*d**2. Let s(k) = 0. Calculate k.
0, 1, 2
Let t(n) be the third derivative of -1/72*n**4 + 0*n**3 + 1/315*n**7 + 0*n + 3*n**2 + 0*n**6 - 1/90*n**5 + 0 + 1/1008*n**8. Suppose t(o) = 0. What is o?
-1, 0, 1
Let j(h) be the second derivative of 0 - 1/70*h**5 + 1/21*h**3 - 3*h - 1/42*h**4 + 1/7*h**2. Determine c, given that j(c) = 0.
-1, 1
Let t(q) = 7*q**2 + 23*q - 137. Let l(a) = -3*a**2 - 12*a + 68. Let r(z) = -9*l(z) - 4*t(z). Let r(v) = 0. Calculate v.
8
Let o(d) be the second derivative of 5*d + 1/63*d**7 + 0*d**2 + 0 + 0*d**5 + 0*d**3 + 0*d**4 - 1/45*d**6. What is v in o(v) = 0?
0, 1
Let u(t) = -t**2 - 2. Let f(j) = -3. Let a(r) = 2*f(r) - 3*u(r). Factor a(n).
3*n**2
Let r be 47/198 + (-184)/44 + 4. Let s(p) be the second derivative of -r*p**4 + 3*p + 1/3*p**2 + 0*p**3 + 0. Factor s(b).
-2*(b - 1)*(b + 1)/3
Let t(q) = -6*q**5 + 2*q**4 + 7*q**3 - 7*q**2 - 7*q + 7. Let d(j) = -j**5 + j**3 - j**2 - j + 1. Let x(s) = -21*d(s) + 3*t(s). Factor x(a).
3*a**4*(a + 2)
Let 9*b**2 - 10*b + 18*b**2 + 15 + 0 - 32*b**2 = 0. Calculate b.
-3, 1
Let w be ((-234)/(-210) + -1)/((-2)/(-5)). Factor 0 - w*v - 1/7*v**2.
-v*(v + 2)/7
Let h be (-5)/3 + 3/(-9). Let l be (-1 - -2) + -1 - h. Let 0*s + 0*s**l + 0 + 0*s**4 + 1/3*s**5 - 1/3*s**3 = 0. What is s?
-1, 0, 1
Let z(h) be the third derivative of 3*h**5/10 + h**4/6 + 6*h**2. What is x in z(x) = 0?
-2/9, 0
Let l(c) = -c**2 + c. Suppose -s - s + 4 = 0. Let o(t) = -4*t**2 - 2. Let p(j) = s*o(j) - 6*l(j). Factor p(r).
-2*(r + 1)*(r + 2)
Let x be (-4)/(-8) + 33/6. Suppose -2*c = c - x. Suppose -15/4*i**3 - 3/2*i - 21/4*i**c + 0 = 0. What is i?
-1, -2/5, 0
Let b(m) be the first derivative of m**3/12 - m