9/7*p - 1/7*p**3.
-p*(p - 3)**2/7
Suppose -5*x = 2*w - 20, -w + 15 = 2*w. Let p(g) be the first derivative of 14/15*g**3 + 0*g - 3 - 2/5*g**x. Factor p(s).
2*s*(7*s - 2)/5
Let 25*n**4 - 6*n - 5*n**5 + 0*n + 35*n**2 - 45*n**3 - 4*n = 0. What is n?
0, 1, 2
Let y(j) = -9*j**2 - 29*j + 3. Let m(q) = -8*q**2 - 30*q + 2. Let c(f) = 5*m(f) - 6*y(f). Determine k so that c(k) = 0.
-2, 2/7
Let i(a) = 11*a**3 - 3*a**2 - 3*a + 11. Let j(x) = 4*x**3 - x**2 - x + 4. Let n = 13 - 21. Let k(h) = n*j(h) + 3*i(h). Factor k(q).
(q - 1)**2*(q + 1)
Suppose 12*d - 13*d + 2 = 0. Let y = -11/3 + 4. Determine w so that -1/6*w**d + y*w + 0 = 0.
0, 2
Find z, given that -2*z**2 - 3*z**2 - 19*z**2 - 3*z**2 - 12 + 36*z = 0.
2/3
Let a(h) be the first derivative of -27*h**6/8 - 9*h**5/4 + 2*h**4 - h**3/3 + 29. Factor a(g).
-g**2*(g + 1)*(9*g - 2)**2/4
Suppose 2/3*m**2 - 8/3 + 20/3*m - 5/3*m**3 = 0. Calculate m.
-2, 2/5, 2
Let s(j) be the second derivative of 0*j**2 + 1/6*j**4 + 1/3*j**3 - 1/10*j**5 + 2*j - 1/15*j**6 + 0. Factor s(f).
-2*f*(f - 1)*(f + 1)**2
Let q be -25*-1*(-2)/(-8). Let x = -23/4 + q. Find l such that x*l**5 + 1/2 - l**3 - l**2 + 1/2*l + 1/2*l**4 = 0.
-1, 1
Let y(q) = -q**2 + 5*q - 4. Let h be y(2). Factor -3*f + 5*f**h - 2*f**2 - f**2 - f.
2*f*(f - 2)
Let p = 5 + -3. Let q(k) be the first derivative of -3 + 1/3*k**3 + k + k**p. Factor q(o).
(o + 1)**2
Let a(v) be the second derivative of -v**6/40 - 3*v**5/80 + 7*v**4/16 + 13*v**3/8 + 9*v**2/4 + 19*v. Solve a(z) = 0 for z.
-2, -1, 3
Suppose 0 = 2*k + 4*t + 10, 0 = 7*t - 11*t - 16. Factor -2/15*b + 0 + 2/15*b**k + 0*b**2.
2*b*(b - 1)*(b + 1)/15
Let d(x) be the third derivative of -x**8/504 - 2*x**7/315 + x**5/45 + x**4/36 + 40*x**2. Suppose d(g) = 0. What is g?
-1, 0, 1
Let w(k) = k**3 + 4*k**2 + 2*k - 1. Let h be w(-3). Let i be (2*(-1)/(-10))/((-6)/(-5)). Factor -i + 1/6*s**h + 0*s.
(s - 1)*(s + 1)/6
Let o(a) = -3*a**2 - 2*a + 3. Let b(q) be the first derivative of -4*q**3/3 - 3*q**2/2 + 4*q + 1. Let g(m) = -2*b(m) + 3*o(m). Factor g(s).
-(s - 1)*(s + 1)
Let x(i) be the third derivative of i**5/30 - 5*i**4/36 - 2*i**3/9 + 6*i**2. Determine m so that x(m) = 0.
-1/3, 2
Suppose 31 - 70 = -13*u. Factor 0 + 0*r**2 - 2/3*r**u + 0*r.
-2*r**3/3
Factor -23*d**3 + 33*d**3 + 12*d**2 - 18*d**3 - 3*d**4 - d**4.
-4*d**2*(d - 1)*(d + 3)
Find m, given that m**2 - 9 + 15*m**2 + 12*m**3 - 12*m - 8*m**4 + 1 = 0.
-1, -1/2, 1, 2
Let y(g) be the second derivative of -g**5/25 + 8*g**3/15 + 39*g. Factor y(w).
-4*w*(w - 2)*(w + 2)/5
Suppose -5*p = -u + 43, -3*u + 33 = -p - 2*p. Let d be (-3)/p - (-63)/24. Factor 2/11*y**d + 4/11*y**2 - 4/11 - 2/11*y.
2*(y - 1)*(y + 1)*(y + 2)/11
Suppose 0 = 2*i - 6*i + 8. Let h = 12 + -8. Suppose h*l**3 - i*l**2 + 3*l**2 + 2*l + 16*l**4 - 11*l**2 = 0. Calculate l.
-1, 0, 1/4, 1/2
Let u be 1/4 - (-14)/8. Let r(b) be the first derivative of u*b - 7/4*b**4 - 3 - 11/2*b**2 + 16/3*b**3. Factor r(k).
-(k - 1)**2*(7*k - 2)
Let j(l) = -7*l + 196. Let x be j(28). Find n, given that 2/5*n**4 - 2/5*n**3 + x + 2/5*n - 2/5*n**2 = 0.
-1, 0, 1
Let f(s) be the first derivative of 3*s**4/4 - 2*s**3 + 3*s**2/2 + 8. Solve f(d) = 0.
0, 1
Let c(m) be the third derivative of m**9/1512 + m**8/1120 - m**7/630 - m**4/6 + m**2. Let y(u) be the second derivative of c(u). Factor y(d).
2*d**2*(d + 1)*(5*d - 2)
Let n(u) be the second derivative of 1/42*u**7 - 1/24*u**4 + 3/40*u**5 + 0 - 1/12*u**3 + 0*u**2 + 7*u + 1/12*u**6. Determine i, given that n(i) = 0.
-1, 0, 1/2
Let y(i) be the first derivative of 0*i**4 - 1/210*i**7 - i**2 + 1/120*i**6 + 0*i**5 - 2 + 0*i + 0*i**3. Let p(c) be the second derivative of y(c). Factor p(n).
-n**3*(n - 1)
Let i(s) = -5*s**5 + 7*s**4 + s**3 + s**2 - 4*s - 4. Let r(u) = u**5 - u**4 - u**3 + u + 1. Let f(c) = -i(c) - 4*r(c). Determine m so that f(m) = 0.
0, 1
Let j be 12/3 + 1 + 1. Let h be (-2 - -1)/(j/(-3)). Factor -i**2 + 1 + 1/2*i - h*i**3.
-(i - 1)*(i + 1)*(i + 2)/2
Let t(c) be the first derivative of c**5/100 - c**4/30 - 2*c**3/15 + 4*c**2/5 + 3*c - 8. Let x(l) be the first derivative of t(l). Factor x(i).
(i - 2)**2*(i + 2)/5
Let c be 3 + (-5 - -3) + 3. Determine u so that 109*u**5 + 2*u**2 - 5*u**3 - 104*u**5 - u**4 - u**c = 0.
-1, 0, 2/5, 1
Suppose -8 = -4*q - q - 2*l, 0 = -4*l - 4. Let w(z) be the first derivative of 1/2*z**q + 1/2*z - 1 + 1/6*z**3. Find h such that w(h) = 0.
-1
Solve -7*a**2 - 2 - 9*a**2 - 6*a + 18*a**2 + 6 = 0 for a.
1, 2
Let b(j) be the first derivative of -4*j**3/3 - 5. Let b(i) = 0. Calculate i.
0
Let x(v) = 5*v**2 + v + 4. Let d(t) = 9*t**2 + t + 7. Let f(m) = -4*d(m) + 7*x(m). Factor f(p).
-p*(p - 3)
Suppose 14/5*r**3 - 8/5*r**5 - 8/5*r**2 + 34/15*r**4 - 8/15*r + 0 = 0. What is r?
-1, -1/4, 0, 2/3, 2
Let g = 8/89 + 227/445. Factor 1/5 + g*y + 1/5*y**3 + 3/5*y**2.
(y + 1)**3/5
Let j = -1 + 1. Find v such that 1/3*v**2 + j - 1/3*v = 0.
0, 1
Let j(o) = -4*o + 2. Let b be j(-3). Factor -2*p**2 + 6*p**3 + b - 10 - 6*p + 0*p - 2*p**4.
-2*(p - 2)*(p - 1)**2*(p + 1)
Let s be (2 - 0)/(2/4). Let y(n) be the third derivative of 0*n**s + 0 + 0*n**5 - n**2 - 2/525*n**7 + 0*n + 0*n**3 + 1/300*n**6 + 1/840*n**8. Factor y(z).
2*z**3*(z - 1)**2/5
Let f be -1 + (1/2)/(150/1140). Solve -f*a - 2*a**2 - 4/5 = 0.
-1, -2/5
Let o(c) be the first derivative of -6/95*c**5 + 2/19*c**3 - 1 + 1/38*c**4 - 2/19*c**2 + 1/57*c**6 + 0*c. Suppose o(t) = 0. What is t?
-1, 0, 1, 2
Let h(z) be the third derivative of -1/2016*z**8 - 1/120*z**6 - z**2 - 1/90*z**5 + 0*z**3 + 0 - 1/315*z**7 - 1/144*z**4 + 0*z. Factor h(a).
-a*(a + 1)**4/6
Let o(b) be the first derivative of -b**3 - 18*b**2 - 108*b + 4. Determine m, given that o(m) = 0.
-6
Suppose -1 = -4*o + 3*b, 9*o + 3*b = 4*o - 19. Let c be ((-5)/o)/(0 + 2). Factor c*w**3 - 1/2 + 1/4*w + 2*w**2.
(w + 1)**2*(5*w - 2)/4
Suppose 0 - h**3 + 1/3*h**5 + 2/3*h + 1/3*h**2 - 1/3*h**4 = 0. Calculate h.
-1, 0, 1, 2
Factor -4*y**3 - 4*y**5 - 12*y**5 + 20*y**5.
4*y**3*(y - 1)*(y + 1)
Let h(m) be the third derivative of 0 + 1/480*m**6 + 1/6*m**3 + m**2 - 1/80*m**5 + 0*m**4 + 0*m. Find z such that h(z) = 0.
-1, 2
Let d(t) be the second derivative of -t**4/60 + 2*t**3/15 - 2*t**2/5 - 28*t. Factor d(v).
-(v - 2)**2/5
Let y = 1 - 0. Suppose 2*l + b - 6 = 0, -l - b + 2 = -y. Factor i**3 + 2*i**5 - l*i**5 - i**2 + i**4 + 0*i**3.
-i**2*(i - 1)**2*(i + 1)
Let v be (-51)/12 - (-1)/4. Let b = -2 - v. Factor -2*d - b*d + 5*d - 4*d**2.
-d*(4*d - 1)
Let v(c) be the second derivative of c**5/5 + c**4 - 2*c**3/3 - 6*c**2 + 31*c. Factor v(y).
4*(y - 1)*(y + 1)*(y + 3)
Suppose -5 = n - 8. Let f be 0 + -4*n/(-36). Factor 1/3*s**3 - 1/3 - f*s + 1/3*s**2.
(s - 1)*(s + 1)**2/3
Let v(n) = 27*n**2 - 30*n + 12. Let l(c) = -11*c**2 + 12*c - 5. Let i(j) = -12*l(j) - 5*v(j). Factor i(h).
-3*h*(h - 2)
Let y = -1 - -3. Determine s, given that -4*s + 2*s - s**3 - 2*s**y + s = 0.
-1, 0
Suppose -60*g**4 - 927/4*g**2 - 6 + 129/2*g + 294*g**3 = 0. Calculate g.
1/4, 2/5, 4
Let a(i) be the third derivative of -1/3*i**4 + 0*i**5 - 2/3*i**3 + 2/105*i**7 + 7*i**2 + 1/15*i**6 + 0 + 0*i. Factor a(r).
4*(r - 1)*(r + 1)**3
Suppose 5*c + u - 12 = 0, 0 = -5*c + 3*u + 2*u. Find n such that 4/3*n**c + 0 + 2/3*n**3 + 0*n = 0.
-2, 0
Let w(s) be the first derivative of -s**5/50 - s**4/40 + 3*s**2 - 8. Let z(q) be the second derivative of w(q). Factor z(b).
-3*b*(2*b + 1)/5
Factor -41 - 5*v + 75 - 34 - 5*v**2.
-5*v*(v + 1)
Let c(y) be the first derivative of 0*y**3 + 3/10*y**2 - 4 - 1/20*y**4 + 2/5*y. Factor c(r).
-(r - 2)*(r + 1)**2/5
Suppose -2*t + 15 - 11 = 0. Factor r**t + 1/2 + 9/4*r.
(r + 2)*(4*r + 1)/4
Let b(m) = 6*m - 9. Let a(s) = s**2 - 7*s + 8. Let z(c) = -3*a(c) - 2*b(c). Factor z(r).
-3*(r - 2)*(r - 1)
Let r(j) be the third derivative of j**7/245 - 11*j**6/420 + 2*j**5/35 - j**4/21 + 2*j**2. Find c such that r(c) = 0.
0, 2/3, 1, 2
Let q be (-1 - -38)*9/7. Let h = -47 + q. Factor -18/7*v + h + 8/7*v**2.
2*(v - 2)*(4*v - 1)/7
Let d(m) be the third derivative of -m**7/560 - m**6/120 - m**5/80 + m**3 + 3*m**2. Let o(w) be the first derivative of d(w). Let o(i) = 0. What is i?
-1, 0
Let l(j) be the third derivative of 1/135*j**5 + 0*j**3 + 0 + 1/540*j**6 + 0*j + 0*j**4 + 4*j**2. Let l(a) = 0. Calculate a.
-2, 0
Suppose -5*u = -o + 1, 5*u - 2*u + 5 = 5*o. Let i(h) be the second derivative of -3*h + 1/6