*2/9
Suppose 0 = -2*b + 4. Let m(w) be the first derivative of -2/7*w + 4/21*w**3 - 2/35*w**5 + 1 + 0*w**b + 0*w**4. Suppose m(s) = 0. What is s?
-1, 1
Suppose -3*u - a = -14, 2*a - 20 = -2*a. Factor f - f**2 + f**u + 0*f**3 - f.
f**2*(f - 1)
Suppose 0 = -2*c + 2*w - 0*w - 4, -5*w + 13 = -4*c. Let f(m) be the first derivative of -3 - 2/33*m**c + 0*m**2 + 0*m. Determine i so that f(i) = 0.
0
Factor -12/5*d**2 - 27/5*d - 6/5.
-3*(d + 2)*(4*d + 1)/5
Suppose f = 4*f + 3. Let i(l) = -l**3 - 1. Let o be i(f). Solve 0*t**3 + 0 - 1/3*t**4 + 1/3*t**2 + o*t = 0 for t.
-1, 0, 1
Let g(q) be the first derivative of -2*q**5/5 - 11*q**4/4 - 7*q**3 - 8*q**2 - 4*q - 7. Factor g(l).
-(l + 1)*(l + 2)**2*(2*l + 1)
Let p(w) be the first derivative of -w**4/20 - w**3/5 - w**2/5 + 19. Factor p(c).
-c*(c + 1)*(c + 2)/5
Factor 5*b**3 - 15*b**2 - 390*b + 390*b.
5*b**2*(b - 3)
Let y(n) = -n - 4. Let k be y(-6). Suppose -3*x = k*i - 18, x - 16 = -3*x. Factor -4*d**4 - 5*d**2 + 3*d**4 + 2*d**2 - 3*d**i - d.
-d*(d + 1)**3
Let a(b) be the first derivative of 2/3*b**3 + b**2 - 2*b - 1/2*b**4 - 1. Let a(c) = 0. Calculate c.
-1, 1
Let t(l) be the first derivative of 0*l + 0*l**2 + 3*l**4 + 8 + 4/3*l**3. Factor t(a).
4*a**2*(3*a + 1)
Let h be ((-1 - 1) + (1 - -2))*0. Factor h*o + 0 - 3/2*o**3 - 3/4*o**2 - 3/4*o**4.
-3*o**2*(o + 1)**2/4
Let v be (0/3)/(18 + -19). Let v + 0*i - 2/13*i**2 = 0. Calculate i.
0
Let s(l) be the third derivative of l**5/360 - 4*l**2. Solve s(c) = 0.
0
Let s = 414 + -414. Factor 1/2*t**3 + 0 + 1/4*t**4 + 1/4*t**2 + s*t.
t**2*(t + 1)**2/4
Let y(m) be the first derivative of -27*m**5/140 - 3*m**4/14 - 2*m**3/21 + m**2 - 5. Let c(q) be the second derivative of y(q). Factor c(o).
-(9*o + 2)**2/7
Let n(h) be the first derivative of 0*h - 4/21*h**3 - 7 + 1/14*h**4 + 1/7*h**2. Factor n(j).
2*j*(j - 1)**2/7
Let i = -43 - -43. Factor i + 1/2*p**4 - 1/2*p**2 + 0*p + 0*p**3.
p**2*(p - 1)*(p + 1)/2
Let p(w) = 2*w**5 - 6*w**4 + 6*w**3 - 4*w**2 - 2*w. Let h(k) = -k**2 - k. Let s be (-6)/(-10) - 26/10. Let m(t) = s*h(t) + p(t). Find a such that m(a) = 0.
0, 1
Let a be 1*-2*(-6 - -5). Let c be -1 - (-4)/18 - -1. Factor 0 + c*t - 4/9*t**3 + 2/9*t**5 + 0*t**4 + 0*t**a.
2*t*(t - 1)**2*(t + 1)**2/9
Let x(p) be the first derivative of 3 - 1/3*p**2 + 1/6*p**4 + 0*p**3 + 0*p. Factor x(j).
2*j*(j - 1)*(j + 1)/3
Let r(q) = -q**4 + 4*q**3 - q**2 - 2*q + 2. Let l(w) = w**4 - 7*w**3 + w**2 + 5*w - 5. Let k(a) = -2*l(a) - 5*r(a). What is p in k(p) = 0?
0, 1
Let x(b) be the third derivative of b**8/168 + b**7/35 + b**6/20 + b**5/30 + 28*b**2. Suppose x(i) = 0. What is i?
-1, 0
Let a be 13/65 + (-9)/(-5). Let u(l) be the first derivative of l + a - 3/2*l**2 + l**3 - 1/4*l**4. Factor u(t).
-(t - 1)**3
Let w be ((-248)/(-186))/(3 + 0). Factor 4/9*h**2 + 0 + 2/9*h**5 - 2/9*h - w*h**4 + 0*h**3.
2*h*(h - 1)**3*(h + 1)/9
Let c(w) be the third derivative of w**6/1620 - w**3/3 - w**2. Let a(z) be the first derivative of c(z). Factor a(x).
2*x**2/9
Let w(o) = -o**3 - 3*o**2 - o + 1. Let q be w(-3). Let v(y) be the first derivative of 4/3*y**3 + 1 + 0*y + 1/2*y**q + y**2. Let v(h) = 0. Calculate h.
-1, 0
Determine h so that 0*h**4 + 0*h - 2/5*h**5 + 0*h**3 + 0*h**2 + 0 = 0.
0
Let l(j) = -120*j**2 + 220*j - 135. Let q(i) = 7*i**2 - 13*i + 8. Let f(h) = -2*l(h) - 35*q(h). Factor f(w).
-5*(w - 2)*(w - 1)
Let q(y) be the first derivative of -3/8*y**6 - 9/8*y**2 + 3 - 1/2*y**3 + 3/4*y + 3/20*y**5 + 9/8*y**4. Determine x so that q(x) = 0.
-1, 1/3, 1
Let u(x) be the second derivative of -5*x**7/126 + 5*x**6/18 - 2*x**5/3 + 5*x**4/9 - 8*x. Let u(m) = 0. Calculate m.
0, 1, 2
Factor 1/3*z**3 + 2/3 + 4/3*z**2 + 5/3*z.
(z + 1)**2*(z + 2)/3
Suppose 0 = -a + 8*a. Let x(d) be the third derivative of 3*d**2 + a*d**4 + 0 + 1/480*d**6 + 0*d**3 + 0*d - 1/240*d**5. Factor x(y).
y**2*(y - 1)/4
What is m in -3*m - 4 + 2*m + 3 - 1 + m**2 = 0?
-1, 2
Let a = -45 + 33. Let b be (18/60)/(a/(-10)). Factor -3*x + 2 + 3/2*x**2 - b*x**3.
-(x - 2)**3/4
Let b(h) = -h**2. Suppose -14 = -4*p + 10. Let u(z) be the second derivative of 2*z**4/3 + 4*z**3/3 + 4*z**2 + 9*z. Let f(n) = p*b(n) + u(n). Factor f(j).
2*(j + 2)**2
Let b(p) be the second derivative of -p**8/280 + p**7/105 + p**6/180 - p**5/30 - p**3/6 + p. Let i(o) be the second derivative of b(o). Factor i(q).
-2*q*(q - 1)**2*(3*q + 2)
Suppose 106 = 5*b + h, 40 = 2*b + 3*h - 5*h. Determine o so that 15*o**2 + 3*o**4 - 12*o**3 + 3 + 0*o + 6*o**5 - b*o**2 + 4*o + 2*o = 0.
-1, -1/2, 1
Let s(n) be the first derivative of -14/3*n**3 + 8*n + 0*n**2 + 1 + 3/2*n**4. Factor s(g).
2*(g - 2)*(g - 1)*(3*g + 2)
Suppose 2*y = -5*u + 28, -5*y + 4 = 4*u - 15. Factor -3*a**4 + 29*a - u + 2*a**3 + 13*a**3 - 27*a**2 - 8*a.
-3*(a - 2)*(a - 1)**3
Let w(j) be the second derivative of j**4/30 - 2*j**3/15 - 3*j**2/5 + 3*j. Find r such that w(r) = 0.
-1, 3
Suppose 12*c = 14*c. Let s = 361/5 + -72. Determine z so that c*z - 2/5*z**3 - 3/5*z**2 + s = 0.
-1, 1/2
Suppose 0*i - 25 = -5*i. Let j(v) be the third derivative of 0*v**3 + 0*v**i - 1/12*v**4 - 2*v**2 + 0 + 1/60*v**6 + 0*v. Suppose j(m) = 0. Calculate m.
-1, 0, 1
Let h(x) be the first derivative of x**3/3 - 6*x**2 + 36*x + 20. Factor h(o).
(o - 6)**2
Let o = 129 - 127. Find p such that -1/2*p**o - 3/2*p - 1 = 0.
-2, -1
Suppose -s + 3*y + 13 = 0, -4*s + 0 + 1 = 5*y. Suppose 3*c - 16 = -s. Factor 0*f**5 - 2*f**3 - 1 + 0*f - f**c + f + 2*f**2 + f**5.
(f - 1)**3*(f + 1)**2
Let t = -27 + 200/7. Let o = 69/35 - t. Factor -2/5 - 2/5*w**3 + o*w**2 + 2/5*w.
-2*(w - 1)**2*(w + 1)/5
Let y(o) be the second derivative of -2*o**7/21 - 2*o**6/5 - 3*o**5/5 - o**4/3 + 2*o. Factor y(h).
-4*h**2*(h + 1)**3
Let f be (-5 - (-9 + 10)) + (-56)/(-9). Let u be (-1 - 6/(-10))*-10. Factor -2/3*p**2 + 2/9*p + 0 + 2/3*p**3 - f*p**u.
-2*p*(p - 1)**3/9
Let s(k) be the second derivative of k**3 + 0*k**2 - 1/4*k**4 + 0 - 4*k. Solve s(o) = 0.
0, 2
Let w(l) be the first derivative of -12*l**5/35 - 2*l**4/7 + 16*l**3/21 + 4*l**2/7 - 4*l/7 + 1. Determine t so that w(t) = 0.
-1, 1/3, 1
Let j be (-5 - -5)/((-1)/1). Let n(i) be the second derivative of 1/60*i**4 + 0*i**3 + 3/100*i**5 - i + j*i**2 + 0. Factor n(s).
s**2*(3*s + 1)/5
Let f = 1 + 0. Let s = 1 + f. Find l, given that 2*l**2 - 2 + s = 0.
0
Let j(m) be the first derivative of 2/9*m + 0*m**2 - 2/27*m**3 + 7. Factor j(r).
-2*(r - 1)*(r + 1)/9
Let k = 41/3 + -286/21. Let y(p) be the second derivative of p + 1/35*p**5 - 1/147*p**7 + 0*p**4 + 0 + 0*p**2 + 0*p**6 - k*p**3. Find u, given that y(u) = 0.
-1, 0, 1
Let i(k) be the third derivative of -3/40*k**6 + 0*k**3 - 3*k**2 + 1/112*k**8 + 0 + 1/4*k**4 + 0*k + 1/70*k**7 - 1/20*k**5. Factor i(q).
3*q*(q - 1)**2*(q + 1)*(q + 2)
Let g(o) = 7*o**5 + o**4 - o**3 - o**2 - 6*o. Let s be 34/6 + 1/3. Let t(c) = 6*c**5 + c**4 - c**3 - c**2 - 5*c. Let i(x) = s*t(x) - 5*g(x). Factor i(v).
v**2*(v - 1)*(v + 1)**2
Suppose -21*q + 12*q = -18. Let s(z) be the second derivative of 1/24*z**4 - 1/2*z**2 + 0 + q*z + 1/12*z**3. Find c such that s(c) = 0.
-2, 1
Factor 21*r**4 - 54*r**2 - 24*r**4 - 8*r**3 - 16*r**3 + 81.
-3*(r - 1)*(r + 3)**3
Factor 4/3*j**2 - 8 - 20/3*j.
4*(j - 6)*(j + 1)/3
Let n be 77/63 - 1/3. Determine r, given that n*r**2 + 2/9*r**3 + 10/9*r + 4/9 = 0.
-2, -1
Let v(b) be the first derivative of -b**3/6 - b**2/2 - 1. Suppose v(y) = 0. Calculate y.
-2, 0
Let v = -90 + 814/9. Determine j, given that 2/9 + v*j + 2/9*j**2 = 0.
-1
Let q(z) be the second derivative of 115*z**4/12 - 35*z**3/2 - 5*z**2 - 24*z. Factor q(i).
5*(i - 1)*(23*i + 2)
Let n(a) = a**3 - a**2 - 2*a + 3. Suppose 4 = -0*o + 2*o. Let u be n(o). Solve 1/4*q**u + 1/4*q**4 - 1/4*q + 0 - 1/4*q**2 = 0 for q.
-1, 0, 1
Let p(h) be the first derivative of 3/5*h**5 + 3/2*h**2 + 4 + 0*h - 3/4*h**4 - h**3. Determine b so that p(b) = 0.
-1, 0, 1
Let n(i) be the first derivative of -3/11*i**2 + 4 + 2/33*i**3 + 4/11*i. Solve n(y) = 0 for y.
1, 2
Let n(u) = -u**3 - u**2 - 1. Let i be n(-1). Let c be 2 - 0*i/(-2). Factor -3*z + c*z**2 - z**2 + 5*z.
z*(z + 2)
Solve -10/3*c + 4*c**2 + 0 - 2/3*c**3 = 0.
0, 1, 5
Let -16*b**2 - 42 - 28*b - 56 + 14*b**2 = 0. Calculate b.
-7
Let j = 1 - 3. Let m be 2*(j/(-4) - 0). Solve 0*n + m - 1 + n**3 - n = 0.
-1, 0, 1
Let w be (5/25*0)/(1 + 0). Factor -1/2*s**2 + 1/2*s**4 - 1/2*s + w + 1/2*s**3.
s