Let i(l) be the second derivative of -l - 1/12*l**4 - 1/20*l**5 + 0 + 1/2*l**2 + 1/6*l**r. Factor i(f).
-(f - 1)*(f + 1)**2
Suppose 6 = 5*j + 1. Let g(d) be the first derivative of 1/6*d**2 - 1/9*d**3 + 0*d + j. Solve g(s) = 0.
0, 1
Let b(q) be the second derivative of 0 + 3*q + 0*q**2 + 1/60*q**6 - 1/8*q**4 - 1/6*q**3 + 0*q**5. Determine j, given that b(j) = 0.
-1, 0, 2
Solve 36/7*w + 108/7 + 3/7*w**2 = 0.
-6
Let y(r) be the first derivative of 0*r**3 - 1/8*r**6 + 0*r**5 + 0*r + 3/16*r**4 + 9 + 0*r**2. Solve y(h) = 0 for h.
-1, 0, 1
Let a be (2/(-14))/((-2)/6). Suppose -62 + 11 = -17*c. Determine l so that -3/7*l**2 + 1/7*l**c - 1/7 + a*l = 0.
1
Let l(u) = 5*u**4 + 9*u**3 - 5*u**2 - 9*u + 7. Let g(s) = s**4 + s**3 - s**2 - s + 1. Let k(z) = -14*g(z) + 2*l(z). Solve k(n) = 0 for n.
-1, 0, 1
Let f(y) be the second derivative of -y**7/630 + y**6/360 + y**5/180 - y**4/72 - y**2 + 2*y. Let a(m) be the first derivative of f(m). What is i in a(i) = 0?
-1, 0, 1
Let n(w) be the first derivative of 2*w**3/15 - 6*w**2/5 + 2*w + 9. Find u, given that n(u) = 0.
1, 5
Suppose 4*x - 5*x = 5. Let j be ((-96)/(-150))/((-2)/x). Factor -j*o - 1/5*o**3 + 4/5 + o**2.
-(o - 2)**2*(o - 1)/5
Let r(p) = p**2 + 4*p - 5. Let z be r(5). Let b = -36 + z. Factor -1/5*g**5 + 0*g**3 + 0 - 3/5*g**b + 4/5*g**2 + 0*g.
-g**2*(g - 1)*(g + 2)**2/5
Suppose -3*x + 5*q = -31, -28*x - 16 = -31*x + 2*q. Factor -77/4*s**x - 8*s - 1 - 49/4*s**3.
-(s + 1)*(7*s + 2)**2/4
Suppose 8/9*k + 2/9*k**2 + 8/9 = 0. What is k?
-2
Suppose 7*p = 2*p + 5. Let j be (2/(-3))/(2/(-6)). Factor p - j + y**2 + 1.
y**2
Let n(p) be the third derivative of 0 + 4*p**2 - 1/24*p**4 + 1/1050*p**7 - 1/15*p**3 + 0*p - 1/100*p**5 + 1/600*p**6. Let n(t) = 0. Calculate t.
-1, 2
Suppose s - 30 = 2*s. Let n be ((-4)/10)/(24/s). Factor -1/4 - 1/4*t**2 - n*t.
-(t + 1)**2/4
Solve s + 7*s - 3*s**3 - s**3 - 4*s = 0.
-1, 0, 1
Let z be (-290)/(-495) - (-1 - (-55)/45). Factor 0*f + z*f**2 + 6/11*f**3 + 0 + 2/11*f**4.
2*f**2*(f + 1)*(f + 2)/11
Factor 1/2 - 1/4*w - 1/4*w**2.
-(w - 1)*(w + 2)/4
Let n(t) be the third derivative of 5*t**5/12 - 85*t**4/24 + 5*t**3 - 20*t**2. Factor n(s).
5*(s - 3)*(5*s - 2)
Let y(s) = -s**2 - 3*s + 4. Let c be ((-2)/(-4))/((-1)/(-4)). Suppose 0 + 4 = 4*z. Let b(m) = m**2 - 1. Let l(t) = c*b(t) + z*y(t). Factor l(o).
(o - 2)*(o - 1)
Let a(o) be the first derivative of -o**8/144 + o**7/315 - o**2 + 3. Let g(s) be the second derivative of a(s). Factor g(p).
-p**4*(7*p - 2)/3
Let i(h) be the first derivative of 1 + h + 7/4*h**2 + 5/6*h**3. Solve i(p) = 0 for p.
-1, -2/5
Let o(r) be the first derivative of -r**4/6 - 2*r**3/3 - r**2 - 2*r/3 + 3. Suppose o(s) = 0. What is s?
-1
Suppose 3*q + 25 = 7*q - p, 4*p - 14 = -3*q. Factor -6*c - 29*c**2 - 9*c**3 - q*c + 5*c**2.
-3*c*(c + 2)*(3*c + 2)
Let q(h) be the third derivative of 5*h**2 - 1/20*h**5 + 0 + 0*h**3 - 1/8*h**4 - 1/160*h**6 + 0*h. Factor q(o).
-3*o*(o + 2)**2/4
Let g = -26 - -28. Let x(n) be the second derivative of -1/20*n**5 + 0*n**g - 3*n + 1/9*n**4 + 0 - 1/18*n**3 + 2/63*n**7 - 2/45*n**6. What is f in x(f) = 0?
-1, 0, 1/2, 1
Let t be 6/8 + (-5 - 267/(-60)). Let r(a) be the second derivative of -1/60*a**4 + 1/10*a**3 + 0 - t*a**2 - 2*a. Factor r(d).
-(d - 2)*(d - 1)/5
Let s = 1 + 1. Solve -3*m - s - 2*m**2 + 3*m**2 + 2*m = 0.
-1, 2
Let y be ((-294)/(-35))/(1/(-5)). Let x be (24/y)/(6/(-7)). Determine t, given that -1/3*t + x - 1/3*t**2 = 0.
-2, 1
Let x(t) be the first derivative of -t**4 + 8*t**3/3 + 2*t**2 - 8*t + 10. Solve x(k) = 0 for k.
-1, 1, 2
Let j(r) = -2*r**2 - 4*r + 4. Let s(x) = -x**2 + x - 1. Let b(c) = 5*c**2 - 4*c + 4. Let y(f) = 2*b(f) + 9*s(f). Let a(g) = -j(g) - 4*y(g). Factor a(q).
-2*q**2
Suppose 1/2*c + 1/2*c**4 - 3/2*c**2 + 1 - 1/2*c**3 = 0. What is c?
-1, 1, 2
Let i be -1 + (-2)/(2/(-3)). Suppose -2*l**3 - l**2 + i*l**3 - 4*l**3 = 0. Calculate l.
-1/4, 0
Let r be 0 + (-7)/(-189)*6. Suppose 4/9*z**2 + 2/9*z**3 - 4/9 - r*z = 0. Calculate z.
-2, -1, 1
Determine h, given that 0 + 0*h**2 + 2/11*h - 2/11*h**3 = 0.
-1, 0, 1
Let r(n) be the third derivative of 9*n**6/40 + 4*n**5/5 + 5*n**4/8 - n**3 - 33*n**2. Factor r(h).
3*(h + 1)**2*(9*h - 2)
Suppose f - 7 = 3*j, 4*f - j - 22 = -5. Let x(v) be the second derivative of 0*v**3 + 1/2*v**2 + 0 + 3*v - 1/12*v**f. Solve x(g) = 0 for g.
-1, 1
Let b(x) be the second derivative of -x**4/60 + 2*x**3/15 - 2*x**2/5 - 6*x. Factor b(f).
-(f - 2)**2/5
Let t(x) = -12*x**2 - 2*x**2 + 9*x + 5*x**2 - 8 - x**3. Let d be t(-10). Find j, given that -1/5*j**d + 1/5 + 0*j = 0.
-1, 1
Let k(q) be the first derivative of -q**5/10 - 7*q**4/24 - 5*q**3/18 - q**2/12 + 12. Let k(p) = 0. What is p?
-1, -1/3, 0
Let h(g) be the second derivative of -25*g**4/12 - 10*g**3/3 - 2*g**2 - 9*g. Factor h(j).
-(5*j + 2)**2
Let k(l) be the third derivative of 3*l**2 + 1/105*l**5 + 0*l + 0*l**3 + 1/84*l**4 + 1/420*l**6 + 0. Factor k(h).
2*h*(h + 1)**2/7
Let z(h) be the second derivative of -h**6/15 + 3*h**5/5 - 5*h**4/6 - 24*h. Determine w so that z(w) = 0.
0, 1, 5
Let x be (-28)/(-6)*2/7. Solve 2/3*t**4 - x*t**2 - 7/3*t**5 - 7/3*t + 14/3*t**3 + 2/3 = 0 for t.
-1, 2/7, 1
Suppose -9 = -0*z - 3*z. Let d = 14 + -10. What is r in 2*r - r**d - r**z + r**2 + 0*r**4 - r = 0?
-1, 0, 1
Let b be 1 + 5/((-20)/(-44)). Suppose 0 = 3*w + 4*v - b, -5*w + 6*w - 4 = 2*v. Determine r so that -3 + 3*r - 3/2*r**3 + 9/4*r**2 - 3/4*r**w = 0.
-2, 1
Let a be 6/21 - (-44)/(-7). Let b(q) = q**2 - q + 1. Let n(j) = 7*j**2 - 5*j + 6. Let i(g) = a*b(g) + n(g). Suppose i(h) = 0. What is h?
-1, 0
Factor 10/9*n**3 + 2/9*n + 0 + 4/3*n**2.
2*n*(n + 1)*(5*n + 1)/9
Suppose 4*o - 7 - 1 = 0. Let s(w) be the first derivative of -3 - 1/2*w - 1/4*w**3 - 7/8*w**o. Factor s(z).
-(z + 2)*(3*z + 1)/4
Factor 9*h**3 - 10*h**3 + h + 0*h**3.
-h*(h - 1)*(h + 1)
Let k(y) = -y**4 - y**2. Let z(a) = -6*a**4 + 3*a**3 - 7*a**2. Let p(c) = 5*k(c) - z(c). Factor p(w).
w**2*(w - 2)*(w - 1)
Suppose -3*w + 5 = -2*p - 0, 2*w + 4 = 5*p. Let a be (-4)/6 - 42/(-9). Solve -4 - d - 2*d**3 + 0*d**4 + 5*d - d**a + 3*d**p = 0 for d.
-2, 1
Let l(k) be the second derivative of k**4/6 - 4*k**3/3 + 4*k**2 - 2*k. Factor l(d).
2*(d - 2)**2
Let -1/4*h**2 - 25/4 - 5/2*h = 0. Calculate h.
-5
Factor 1 - 100*a**2 - 17 - 64*a - 5*a**5 - 28*a**4 - 76*a**3 + a**5.
-4*(a + 1)**3*(a + 2)**2
Let p(g) be the third derivative of g**10/680400 - g**8/90720 + g**5/12 + g**2. Let a(i) be the third derivative of p(i). Factor a(v).
2*v**2*(v - 1)*(v + 1)/9
Let d(b) be the first derivative of -b**6/27 - 2*b**5/45 + b**4/6 + 10*b**3/27 + 2*b**2/9 + 13. Let d(m) = 0. What is m?
-1, 0, 2
Let r(w) be the third derivative of -3*w**6/40 - w**5/5 + 5*w**4/8 + w**3 - 14*w**2. Factor r(q).
-3*(q - 1)*(q + 2)*(3*q + 1)
Let w be (-2)/7 - (-80)/35. Determine m so that 2*m**w + 3 + 0*m + 8*m - m = 0.
-3, -1/2
Factor -1/3*f**3 + 4/3 + 5/3*f**2 - 8/3*f.
-(f - 2)**2*(f - 1)/3
Let k(o) = 19*o**3 + o. Let g be k(1). Let r = 22 - g. Factor 0 + 0*i - 1/5*i**3 - 1/5*i**5 + 0*i**r + 2/5*i**4.
-i**3*(i - 1)**2/5
Let s = 847/4 + -211. Factor 0 + 3/4*i**2 + 9/4*i**4 + s*i**5 + 9/4*i**3 + 0*i.
3*i**2*(i + 1)**3/4
Let m(c) be the first derivative of c**4 - 4*c**3/3 - 4*c**2 + 10. Factor m(d).
4*d*(d - 2)*(d + 1)
Suppose -17*n - 2*n = 2*n. Factor n*i + 0 + 3/2*i**2.
3*i**2/2
Let q(z) be the second derivative of 15*z**7/56 - z**6/5 - 21*z**5/40 + z**4/2 - z**3/8 + 17*z. Let q(f) = 0. What is f?
-1, 0, 1/5, 1/3, 1
Let i(v) = v**3 + 2*v**2 - v. Let p be i(-2). Factor f + 0*f**p - 2*f**3 + 2*f**3 + f**2 - f**3 - f**4.
-f*(f - 1)*(f + 1)**2
Let p(h) be the third derivative of 1/180*h**6 + 0 + 1/1512*h**8 + 1/315*h**7 + 0*h**4 + 0*h**3 - h**2 + 1/270*h**5 + 0*h. Factor p(k).
2*k**2*(k + 1)**3/9
Solve -6/5 - 3/5*t**3 - 12/5*t**2 - 3*t = 0.
-2, -1
Let m = -8 + 10. Let d(v) be the first derivative of 1/10*v**2 - m + 0*v + 1/15*v**3. Let d(f) = 0. What is f?
-1, 0
Let f(b) be the first derivative of -b**4/27 - 5*b**3/27 - 2*b**2/9 + 7*b - 3. Let w(u) be the first derivative of f(u). Suppose w(t) = 0. What is t?
-2, -1/2
Let m(t) be the first derivative of -t**6/10 + 3*t**5/10 + 3*t**4/4 - 2*t**3 - 6*t**2 - 3*t - 5. Let o(n) be the first derivative of m(n). Factor o(d).
-3*(d - 2)**2*(d + 1)**2
Let t(b) be the first derivative of 0*b + 0*b**2 + 4 + 3/16*