**4 + 0 + 0*h**3 + 0*h + 2*h**2 + 0*h**7 + 1/150*h**6 - 1/840*h**8 + 0*h**5. Factor b(d).
-2*d*(d - 1)**2*(d + 1)**2/5
Suppose -d = -4*l + 17, 8*l - 3*l - 13 = 4*d. Solve 5 - 1 + 80*c**d - 12*c**2 + 45*c**5 - 14*c - 15*c**5 - 88*c**4 = 0 for c.
-2/5, 1/3, 1
Let a(v) be the first derivative of -v**4/14 - 2*v**3/21 + 4*v**2/7 + 8*v/7 + 15. Factor a(g).
-2*(g - 2)*(g + 1)*(g + 2)/7
Let z = -58 + 62. Let i(q) be the third derivative of 0*q - 1/60*q**5 + 1/6*q**z - 2*q**2 + 0 - 2/3*q**3. Find c such that i(c) = 0.
2
What is s in -28/11*s - 2/11*s**4 + 0 - 20/11*s**3 - 46/11*s**2 = 0?
-7, -2, -1, 0
Suppose 4*c + 55 = 7. Let q be (-136)/(-14) + c/(-42). Factor 7/2*p**4 + 23/2*p**3 + 0 + q*p**2 + 2*p.
p*(p + 1)*(p + 2)*(7*p + 2)/2
Let g(f) be the second derivative of f**9/30240 + f**8/8960 - f**6/2880 + f**4/2 + 3*f. Let r(m) be the third derivative of g(m). Suppose r(q) = 0. What is q?
-1, 0, 1/2
Let y(l) be the third derivative of l**7/30 + 2*l**6/15 - l**5/20 - 2*l**4/3 - 2*l**3/3 + 9*l**2. What is c in y(c) = 0?
-2, -1, -2/7, 1
Let h(u) be the second derivative of 1/10*u**6 + u + 0*u**3 + 0 + 0*u**2 + 1/6*u**4 - 1/4*u**5. Factor h(w).
w**2*(w - 1)*(3*w - 2)
Let z(j) = 2*j**2 + 2*j + 8. Let u(q) = q**2 + q + 3. Let c(n) = -8*u(n) + 3*z(n). Let g(s) = -s**2. Let w(b) = c(b) - 4*g(b). Factor w(i).
2*i*(i - 1)
Let l = -3 - -6. Let y(h) be the first derivative of -1/16*h**4 + 0*h**l + 0*h - 2 + 0*h**2 - 1/24*h**6 + 1/10*h**5. Solve y(w) = 0 for w.
0, 1
Let z be (2/(-28))/((-3)/(-7572)). Let f = -180 - z. Solve 2/7*m + 0 - f*m**3 + 2/7*m**2 - 2/7*m**4 = 0 for m.
-1, 0, 1
Suppose 0 = -r - 3*r + 4. Let j be (21/(-6)*r)/(-2). Solve -5/4*a**2 + 1/2*a - j*a**3 + 0 = 0 for a.
-1, 0, 2/7
Let h be ((-1)/(-2))/(1/(-18)). Let w(n) = -2*n - 13. Let f be w(h). Determine m so that 4/5 + 0*m - 11/5*m**2 - 3/5*m**3 + 7/5*m**4 + 3/5*m**f = 0.
-2, -1, 2/3, 1
Let l(y) be the first derivative of y**4/26 - 10*y**3/39 + 8*y**2/13 - 8*y/13 - 1. Suppose l(o) = 0. What is o?
1, 2
Factor 0*d + 6/7*d**2 + 0 - 6/7*d**3.
-6*d**2*(d - 1)/7
Let c be (0 - -1)/(3/6). Factor -7*v**3 + 0 + c*v - 38*v - 30*v**2 - 8.
-(v + 2)**2*(7*v + 2)
Let h(m) be the second derivative of m**5/300 + m**4/40 + m**3/15 + 7*m**2/2 - 2*m. Let b(p) be the first derivative of h(p). Find f such that b(f) = 0.
-2, -1
Let j(x) be the first derivative of 0*x + 2/9*x**3 - 1/12*x**4 - 1/6*x**2 + 2. Factor j(k).
-k*(k - 1)**2/3
Let x(p) be the third derivative of 0*p**4 + 0*p + 0 + 1/40*p**5 - 1/140*p**7 - 3/448*p**8 - 9*p**2 + 3/160*p**6 + 0*p**3. Solve x(c) = 0 for c.
-1, -2/3, 0, 1
Factor 3*p**2 - 3*p**2 + 6 + p - 3*p**2 - 4*p.
-3*(p - 1)*(p + 2)
Let k(n) be the second derivative of n**7/2520 - n**6/360 + n**5/120 - n**4/12 - 2*n. Let d(b) be the third derivative of k(b). Solve d(p) = 0 for p.
1
Let j(t) be the first derivative of 3*t**4/20 - t**3/15 - 6*t**2/5 + 4*t/5 + 54. Suppose j(m) = 0. Calculate m.
-2, 1/3, 2
Let o(a) be the third derivative of -2*a**7/105 + 2*a**6/15 + 12*a**2. Let o(u) = 0. What is u?
0, 4
Find j, given that 192/7*j**3 + 0 - 44/7*j**5 + 320/7*j**2 - 80/7*j**4 - 64/7*j = 0.
-2, 0, 2/11, 2
Let z = 92 - 458/5. Let j be (8 + -9)*4/(-10). Let j + 4/5*n**3 - z*n + 2/5*n**4 - 2/5*n**5 - 4/5*n**2 = 0. Calculate n.
-1, 1
Let w(f) = f + 9. Suppose 0 = 2*s - 4*d + 2, -2*s = d - 5 + 22. Let v be w(s). Find r such that 2*r - 1 - 5*r**2 + 4*r**2 + 0*r**v = 0.
1
Factor -8/5*f**3 + 6/5*f + 0*f**4 + 2/5*f**5 - 4/5 + 4/5*f**2.
2*(f - 1)**3*(f + 1)*(f + 2)/5
Factor 39/4*k**2 - 147/4 - 3/4*k**3 - 105/4*k.
-3*(k - 7)**2*(k + 1)/4
Solve 7*r - 75/4*r**3 - 5/2*r**2 + 2 = 0 for r.
-2/5, 2/3
Suppose -q + 5 = -3*m, 0*q + 2*q - 10 = -2*m. Suppose -q*u + 15 + 13 = 4*t, 3*u = 12. Suppose d**2 - 2*d**3 + 4*d**t - 3*d**2 = 0. What is d?
0, 1
Suppose -2*i**5 + 2*i**3 + 0 + 2/5*i**4 + 0*i - 2/5*i**2 = 0. Calculate i.
-1, 0, 1/5, 1
Let a(d) be the second derivative of -2*d + 1/24*d**4 - 1/12*d**3 - 1/2*d**2 + 0. Factor a(h).
(h - 2)*(h + 1)/2
Let u = -12 + 27. Find a, given that 14*a**2 - 12*a - u*a**3 - 6*a**2 - 44*a**2 = 0.
-2, -2/5, 0
Let y(r) = -3*r**3 - 2*r - 1. Let f be y(-1). Let n = -12/7 - -43/21. Let 1/3*p**2 - 1/3*p**5 + 0 - n*p**f + 0*p + 1/3*p**3 = 0. Calculate p.
-1, 0, 1
Let v(p) = p**3 - p. Let g(f) be the third derivative of f**6/60 + 7*f**5/60 + 5*f**4/24 - 4*f**2. Let t(a) = -g(a) - 3*v(a). Factor t(r).
-r*(r + 1)*(5*r + 2)
Let k(l) be the third derivative of 0*l**5 + 0*l + 0*l**3 - 5*l**2 + 0 + 1/1050*l**7 + 1/600*l**6 + 0*l**4. Factor k(i).
i**3*(i + 1)/5
Let h = 9 + -5. Suppose 2*l + 4*c + 10 = 30, -c + 5 = -h*l. Factor l*n + 0 - 2/7*n**2.
-2*n**2/7
Factor 2/17*k**2 + 2/17*k**3 - 2/17 - 2/17*k.
2*(k - 1)*(k + 1)**2/17
Let g(c) be the first derivative of 3*c**4/2 + 22*c**3/3 + 6*c**2 - 5. Solve g(f) = 0 for f.
-3, -2/3, 0
Suppose -5*q = -4*n + 5*n - 37, 0 = -5*q + 4*n + 52. Let b = q + -5. Suppose d + 9*d**b + 3*d**4 - 5*d**2 + 2*d**4 - 6*d**4 + 2*d**5 - 6*d**4 = 0. What is d?
0, 1/2, 1
Factor 4*k**3 - 4*k**3 + 2*k + 0*k - 2*k**3.
-2*k*(k - 1)*(k + 1)
Let i = -626/63 - -92/9. Find d, given that 2/7 - i*d**2 - 2/7*d**3 + 2/7*d = 0.
-1, 1
Let h be (3/3)/(3 - 2). Let f(x) be the first derivative of -1/3*x**6 + h + 0*x - 8/5*x**5 - 8/3*x**3 - 3*x**4 - x**2. Factor f(o).
-2*o*(o + 1)**4
Let y(z) be the first derivative of 5*z**4/4 - 5*z**3 + 9. Let y(m) = 0. What is m?
0, 3
Suppose -2*a + 4*q = -11 - 17, 0 = 2*a + 4*q + 12. What is v in 0*v**a + 0 + 2/3*v**3 + 0*v - 2/3*v**5 + 0*v**2 = 0?
-1, 0, 1
Let g(f) = -4*f**2 - 4*f + 4. Let o(k) = -k**3 - 4*k**2 - 4*k + 4. Let q(x) = -5*g(x) + 4*o(x). Factor q(a).
-4*(a - 1)**2*(a + 1)
Factor 3/2*t**4 + 0*t + 0 + 6*t**3 + 9/2*t**2.
3*t**2*(t + 1)*(t + 3)/2
Let f(m) = 3*m**5 - 12*m**4 + 18*m**3 - 12*m**2 + 4*m + 1. Let x(q) = q + 1. Let c(k) = f(k) - x(k). Suppose c(l) = 0. Calculate l.
0, 1
Let m(j) be the first derivative of -j**5/20 + j**4/8 + 3*j**2 - 3. Let p(k) be the second derivative of m(k). Factor p(g).
-3*g*(g - 1)
Let w(o) = o**2 - 6*o + 2. Let z be w(7). Suppose c + 2*c = z. Factor -q**2 + 0*q**3 - 2*q**c - 3*q**2 - 2*q.
-2*q*(q + 1)**2
Let h(r) be the third derivative of -r**5/80 - 9*r**4/32 - r**2 - 11. Suppose h(z) = 0. What is z?
-9, 0
Let l(y) be the first derivative of y**4 - 4*y**3 - 2*y**2 + 12*y - 3. Factor l(c).
4*(c - 3)*(c - 1)*(c + 1)
Let f be -5 + 1 + 21 + -14. Determine l, given that -2/3*l - 2/9*l**f - 8/9*l**2 + 0 = 0.
-3, -1, 0
Let i be -1 - (3 + (-75)/(-6)). Let q = -293/18 - i. Factor q*c**2 - 2/9*c + 0.
2*c*(c - 1)/9
Let a be (-3)/(2/(-4) - 1). Let i(p) be the second derivative of -4/5*p**5 + 2/3*p**3 - 1/3*p**6 + 0*p**a + 0 - 1/6*p**4 - 2*p. Factor i(c).
-2*c*(c + 1)**2*(5*c - 2)
Let v(q) be the second derivative of 5*q**4/12 - 25*q**3/6 - 7*q. Factor v(y).
5*y*(y - 5)
Let z(h) be the third derivative of h**9/25200 + h**8/4800 - h**7/4200 - h**5/10 - 6*h**2. Let u(r) be the third derivative of z(r). Solve u(a) = 0.
-2, 0, 1/4
Factor -2/3*a**2 - 4/3*a - 2/3.
-2*(a + 1)**2/3
Factor -3*f**5 - 5*f**2 - 3*f**2 + 14*f**2 - 9*f**4 + 3*f + 3*f**4.
-3*f*(f - 1)*(f + 1)**3
Let u(j) be the third derivative of 5*j**2 + 0*j + 1/120*j**5 + 0 - 1/24*j**4 + 1/12*j**3. Factor u(r).
(r - 1)**2/2
Let x be ((-28)/(-7))/(3 - 1). What is a in -2*a**3 - 3*a**3 + 3*a**3 + 4*a**3 - x*a**2 = 0?
0, 1
Let n be 6/(24/20) + 0. Factor 0*t**2 + 3*t**3 - t - 11*t**3 + 0*t + 4*t**4 + n*t**2.
t*(t - 1)*(2*t - 1)**2
Let h(i) = -5*i**2 - 4*i. Let f(o) = -o**2 + o + 1. Let l(p) = 10*p**2 - 4. Let s(v) = 4*f(v) + l(v). Let k(j) = 4*h(j) + 3*s(j). Factor k(w).
-2*w*(w + 2)
Let c(b) be the first derivative of -2*b**3/27 + b**2/3 + 1. Factor c(x).
-2*x*(x - 3)/9
Let f be (-21)/27*-3 + (0 - 2). Factor -1/3*b**4 - 1/3*b**3 + 1/3*b**2 + 0 + f*b.
-b*(b - 1)*(b + 1)**2/3
Factor 2*s + 14/5*s**3 + 2/5*s**4 + 0 + 22/5*s**2.
2*s*(s + 1)**2*(s + 5)/5
Factor 1/4*b**4 - b + 1/4 + 3/2*b**2 - b**3.
(b - 1)**4/4
Let n(q) = q**3 + 8*q**2 + q + 10. Let l be n(-8). Find c such that l*c**5 - c**5 - 4*c**5 + 6*c**3 - 3*c = 0.
-1, 0, 1
Let x(f) be the first derivative of f**5/60 - f**3/6 - f**2/3 + 4*f + 1. Let y(o) be the first derivative of x(o). Factor y(k).
(k - 2)*(k + 1)**2/3
Let i = 6122/35 + -175. Let v = i - -2/7. Factor 2/5*b + v + 1/5*b**2.
(b + 1)**2/5
Let y(w) be the third de