q(l) = l**2 + 6*l + 8. Let t be q(-5). Let w(m) be the first derivative of -1/2*m**4 + 0*m + 2/3*m**t + 2/15*m**5 - 1/3*m**2 - 1. Factor w(p).
2*p*(p - 1)**3/3
Let h(a) be the first derivative of 1/7*a**3 + 2/7*a**2 + 2*a + 1/42*a**4 - 3. Let n(k) be the first derivative of h(k). Factor n(d).
2*(d + 1)*(d + 2)/7
Let w(d) be the third derivative of d**6/135 - d**5/36 + d**4/36 - d**3/2 + 4*d**2. Let k(r) be the first derivative of w(r). Factor k(j).
2*(j - 1)*(4*j - 1)/3
Let p(t) be the third derivative of t**8/1176 - t**7/245 + t**6/420 + t**5/70 - t**4/42 + 12*t**2. What is f in p(f) = 0?
-1, 0, 1, 2
Let o be ((-5)/15)/(1/(-5)). Let v = 13/6 - o. Determine h, given that 0*h - 1/2*h**5 + v*h**3 + 0 + 1/2*h**2 - 1/2*h**4 = 0.
-1, 0, 1
Let r(v) = v**3 + 6*v**2 + v + 4. Let z(f) = -3*f**3 - 12*f**2 - 3*f - 9. Suppose 24 = 5*y - 21. Let a(w) = y*r(w) + 4*z(w). Find g, given that a(g) = 0.
0, 1
Let q(w) = -5*w**2 + 4*w - 4. Let v(y) be the third derivative of y**5/60 - y**4/24 + y**3/6 - y**2. Let u(a) = -q(a) - 4*v(a). Solve u(i) = 0 for i.
0
Let p(h) be the first derivative of h**5/120 - h**4/48 - h**3/6 - 3*h**2/2 - 5. Let x(g) be the second derivative of p(g). Factor x(t).
(t - 2)*(t + 1)/2
Suppose 0 = 4*n + 41 - 1. Let y = n - -12. Factor 1/6*h + 0 + 1/6*h**3 - 1/3*h**y.
h*(h - 1)**2/6
Let k(u) = 2*u**4 + 4*u**3 - 2*u**2. Let y(n) = -n**3 - n. Let t(z) = 2*k(z) + 4*y(z). Suppose t(v) = 0. Calculate v.
-1, 0, 1
Solve 2/3 - 4/3*w + 2/3*w**2 = 0 for w.
1
Let m(h) be the third derivative of h**9/5040 - h**8/1120 + h**7/840 + h**4/8 - 5*h**2. Let g(k) be the second derivative of m(k). Factor g(j).
3*j**2*(j - 1)**2
Find f such that -11*f**3 + 9*f**2 + f + 13*f**3 + 5*f - f**2 = 0.
-3, -1, 0
Let t(n) be the first derivative of n**6/45 + 4*n**5/75 - 4*n**3/45 - n**2/15 - 6. Factor t(d).
2*d*(d - 1)*(d + 1)**3/15
Let o(p) be the first derivative of 2*p**3/21 + p**2/7 + 35. Factor o(i).
2*i*(i + 1)/7
Suppose 24*i + 22 = 142. Determine m so that 2/5*m**i + 0 + 2/5*m + 0*m**4 + 0*m**2 - 4/5*m**3 = 0.
-1, 0, 1
Factor 113 - 113 + r**2.
r**2
Suppose 6*g - 27*g + 42 = 0. Factor -1/2*a**g + a - 1/2.
-(a - 1)**2/2
Let r(z) = z**2 - 4*z - 7. Let x be r(6). Find v such that 4/5*v**4 - 4/5*v**2 + 0 + 0*v**3 - 2/5*v**x + 2/5*v = 0.
-1, 0, 1
Let g(w) = 10*w. Let c be g(3). Let q be (-2)/(-10)*100/c. Factor -q*i**2 + 2*i - 4/3.
-2*(i - 2)*(i - 1)/3
Let b(v) be the first derivative of 0*v - 10 + 4/3*v**3 + 4*v**2 - v**4. Factor b(j).
-4*j*(j - 2)*(j + 1)
Let t be (-6)/16 + 265/600. Let b(z) be the second derivative of -1/5*z**5 + 1/21*z**7 + 1/3*z**4 + 1/3*z**3 - z**2 - t*z**6 + 0 + z. Solve b(q) = 0.
-1, 1
Suppose 4 - 10 = -2*d. Factor 0*r + 17 - 11 - 6*r**2 + 3*r**3 - d*r + 0.
3*(r - 2)*(r - 1)*(r + 1)
Let g be 1*-2*22/(-4). Factor -3*q**4 - q**2 + 8*q**2 - 11*q**4 + g*q**3 - 2*q**2 - 2*q.
-q*(q - 1)*(2*q + 1)*(7*q - 2)
Let x be ((-9)/15)/(14/(-70)). Determine s, given that 49*s**x - 8/5 + 126/5*s**2 - 343/5*s**4 - 4*s = 0.
-2/7, 2/7, 1
Factor 25*x - 7*x + 25*x - 40*x**2 - 8*x - 5 - 80*x**3.
-5*(x + 1)*(4*x - 1)**2
Let t be (0 - -1) + 18/4. Let i = -245 + 252. Suppose t*a - i*a**2 - 1 - 2*a**3 - 7/2*a**5 + 8*a**4 = 0. Calculate a.
-1, 2/7, 1
Find p, given that -2/7*p**2 + 2/7*p**4 + 0 - 2/7*p**3 + 2/7*p = 0.
-1, 0, 1
Let a(h) be the second derivative of h**10/15120 + h**9/3780 + h**8/3360 - h**4/4 - 5*h. Let d(n) be the third derivative of a(n). Factor d(v).
2*v**3*(v + 1)**2
Let d(n) be the second derivative of n**8/16800 + n**7/2100 + n**6/600 + n**5/300 + n**4/4 - 2*n. Let q(r) be the third derivative of d(r). Factor q(m).
2*(m + 1)**3/5
Factor 0 + 3/7*j**3 - 1/7*j**4 + 0*j**2 + 0*j.
-j**3*(j - 3)/7
Let o(t) be the third derivative of 0 + 1/120*t**5 - 1/420*t**7 + 1/240*t**6 + 0*t**3 - 2*t**2 - 1/48*t**4 + 0*t. Find k, given that o(k) = 0.
-1, 0, 1
Let u be (34/(-136))/((-2)/24). Suppose -3/4*d**4 - 3/4*d + 1/4 + 1/4*d**5 + 1/2*d**u + 1/2*d**2 = 0. What is d?
-1, 1
Let b(k) be the third derivative of k**6/180 + k**5/30 + k**4/12 + k**3/9 - 8*k**2. Factor b(l).
2*(l + 1)**3/3
Suppose -42 = 2*j + 2*k - 0*k, 2*j + 22 = 3*k. Let h = j + 17. Suppose -2/7 + h*y + 2/7*y**2 = 0. What is y?
-1, 1
Let w(g) = 6*g**4 - 6*g**3 - 19*g**2 - 7*g + 13. Let q(b) = 3*b**4 - 3*b**3 - 9*b**2 - 3*b + 6. Let c(a) = -13*q(a) + 6*w(a). Determine n, given that c(n) = 0.
-1, 0, 1
Let g(t) be the third derivative of 1/336*t**8 + 0 - 2*t**2 + 0*t + 0*t**4 + 0*t**3 - 1/60*t**5 - 1/120*t**6 + 1/210*t**7. Find k such that g(k) = 0.
-1, 0, 1
Let s(a) be the first derivative of -a**4/20 - 4*a**3/15 - a**2/10 + 6*a/5 - 17. Factor s(g).
-(g - 1)*(g + 2)*(g + 3)/5
Let x(a) be the second derivative of -1/8*a**2 + 0 - 1/8*a**3 - 7*a - 1/24*a**4. Factor x(l).
-(l + 1)*(2*l + 1)/4
Suppose 8*r - 3*r - 15 = 0. Factor 0*i**r - 3*i**4 + 6*i**2 + 5*i**4 - 2*i + 0*i**3 - 6*i**3.
2*i*(i - 1)**3
Suppose 2*g + 4*t - 22 = 0, -3*g + 0*t = -5*t. Let v(f) be the first derivative of -1 + 1/15*f**g + 0*f + 1/12*f**4 + 0*f**3 + 0*f**2. Factor v(p).
p**3*(p + 1)/3
Let l(p) = 2*p**5 - 5*p**4 + 11*p**3. Let m(g) = -2*g**3 - 3*g**4 + 4*g**5 + 25*g**3 - 6*g**4. Let w(s) = 7*l(s) - 3*m(s). Solve w(i) = 0 for i.
0, 2
Let f(c) be the third derivative of -c**7/280 + c**6/30 - c**5/8 + c**4/4 - c**3/2 + c**2. Let j(m) be the first derivative of f(m). Find i such that j(i) = 0.
1, 2
Let k(f) be the second derivative of f**6/15 + f**5/10 - f**4/2 - f**3/3 + 2*f**2 - 3*f. Solve k(b) = 0 for b.
-2, -1, 1
Let c(q) be the second derivative of 2*q**7/315 + 2*q**6/45 + 4*q**5/45 - 5*q**2/2 + 8*q. Let l(r) be the first derivative of c(r). Suppose l(o) = 0. What is o?
-2, 0
Let p(v) be the first derivative of -v**4/24 + 5*v**3/9 - 25*v**2/12 - 9. Suppose p(h) = 0. What is h?
0, 5
Let n(c) = -c**2 - 8*c - 7. Let u be n(-6). Let b be -1 + 0 + 1*5. Factor -2*v**4 + 2*v + 0 - b*v**3 + 3*v**5 + 4*v**2 - v**u - 2.
2*(v - 1)**3*(v + 1)**2
Let c = 35 - 34. Let d be ((-9)/(-12))/(c/4). Factor -2/3*u + 4/9*u**d + 2/9 + 4/9*u**2 - 2/3*u**4 + 2/9*u**5.
2*(u - 1)**4*(u + 1)/9
Let m be ((-3)/4)/((-3)/(-12)). Let r(l) = -5*l**2 + 4*l - 2. Let t(p) = 4*p**2 - 4*p + 2. Let d(c) = m*t(c) - 2*r(c). Factor d(k).
-2*(k - 1)**2
Suppose 0 = -z + 5 - 1. Let -z*s - 49*s**2 + 35*s**2 - 15*s**3 + 2 + 7*s**3 = 0. Calculate s.
-1, 1/4
Suppose 399 = -j + 401. Factor 4/3*k + j + 2/9*k**2.
2*(k + 3)**2/9
Let t(r) be the second derivative of -r**4/78 + 5*r**3/39 - 32*r. Factor t(x).
-2*x*(x - 5)/13
Let y be ((-4)/2)/1 + 4 + 0. Let v(b) be the second derivative of -4*b + 0 + 0*b**y - 1/5*b**3 + 1/20*b**4. Solve v(o) = 0.
0, 2
Let m(k) be the third derivative of k**6/90 + 7*k**5/45 + 8*k**4/9 + 8*k**3/3 + 11*k**2. Find o, given that m(o) = 0.
-3, -2
Suppose 0 = -4*y + 9*y + 15. Let i = 4 + y. Let d - i - 1/4*d**2 = 0. What is d?
2
Suppose 2*m = m + 2. Suppose -m*v = v - 15. Solve 2 + i - 3*i - 2*i**v - 3*i**4 - 4*i**2 + 4*i**3 + 5*i**4 = 0.
-1, 1
Let u(v) be the second derivative of 32*v**7/21 - 16*v**6/5 - 5*v**5 + 35*v**4/6 + v**3 - 2*v**2 - 17*v. Suppose u(p) = 0. Calculate p.
-1, -1/4, 1/4, 1/2, 2
Let s(l) be the first derivative of 2*l**6/3 + 12*l**5/5 + 3*l**4 + 4*l**3/3 - 1. Factor s(g).
4*g**2*(g + 1)**3
Suppose -4*n + 4 = 3*g - 7, 0 = -3*n + 3*g + 3. Let c be (-1 + -1)/(-3 + 2). Solve c + 2*k + 1/2*k**n = 0 for k.
-2
Let c(n) = 5*n**2 - n - 1. Let y be c(-1). Let b(i) = i**2 + 3*i - 2. Let t be b(-4). Factor -6*a**3 + 8*a - 8*a**t - y*a**3 - 19*a**3.
-2*a*(3*a + 2)*(5*a - 2)
Let j(t) be the second derivative of -t**6/75 + t**5/50 + t**4/30 - t**3/15 + 24*t. Find q such that j(q) = 0.
-1, 0, 1
Factor -460/7*s**2 + 1728/7*s**5 + 68/7*s - 2592/7*s**4 - 4/7 + 1548/7*s**3.
4*(3*s - 1)**3*(4*s - 1)**2/7
Let h = 17 - 82/5. Factor 3/5*x**2 + h - 6/5*x.
3*(x - 1)**2/5
Factor 8/3*d**3 - 4/3*d - 4/3*d**5 + 0*d**2 + 0 + 0*d**4.
-4*d*(d - 1)**2*(d + 1)**2/3
Let r(q) = 9*q**3 - 26*q**2 + 28*q - 12. Let n(h) = h**3 - h**2 - 1. Let g(i) = 4*n(i) - r(i). Factor g(y).
-(y - 2)**2*(5*y - 2)
Let y(o) = -o**3 + 7*o**2 + 9*o - 3. Let f be y(8). Factor 2*j**3 - 7*j**5 + 2*j**5 + 0*j**f - j**4 - 2*j**4.
-j**3*(j + 1)*(5*j - 2)
Let a be (-3 + (-12)/(-4))/(-1). Let q(d) be the first derivative of a*d + 1/25*d**5 + 2 + 0*d**4 + 0*d**2 + 0*d**3. Factor q(f).
f**4/5
Suppose -6*n - 3 = -