**2*(p + 2)/2
Let d(i) be the second derivative of -1/3*i**3 - 1/14*i**5 - 1/105*i**6 + i + 0 - 2/7*i**2 - 3/14*i**4. Factor d(r).
-2*(r + 1)**3*(r + 2)/7
Suppose 2*d - 4*d = 0. Suppose -2*j + 5*j - 3 = d. Factor 3*r**2 - 4*r + j + r - r**3 + 0*r.
-(r - 1)**3
Let s(m) be the second derivative of -m**6/6 + m**5/4 + 5*m**4/4 - 25*m**3/6 + 5*m**2 + 49*m. Factor s(p).
-5*(p - 1)**3*(p + 2)
Suppose -2*l + 6 = 6*w - 4*w, -12 = -4*l - 3*w. Find t such that 4/11*t**l + 2/11*t**4 + 0*t + 0 + 2/11*t**2 = 0.
-1, 0
Let o(l) = 10*l**3 + 2*l**2 - 8*l - 3. Suppose 0 = q - 2 - 0. Let n(t) = -2 + 3 - t**3 - 2 + t**q. Let z(u) = -n(u) - o(u). Factor z(x).
-(x - 1)*(3*x + 2)**2
Let s(h) be the first derivative of -h**6/24 - 3*h**5/20 + h**4/4 - 1. Determine t, given that s(t) = 0.
-4, 0, 1
Let q = 11 + -2. Suppose 5*v + 3*j = -q, 0*j = j + 3. Factor -2*b**3 + 0*b - 14/9*b**4 + v - 4/9*b**2.
-2*b**2*(b + 1)*(7*b + 2)/9
Let t(y) be the third derivative of -9*y**2 - 1/45*y**4 + 4/45*y**3 + 0 + 1/450*y**5 + 0*y. Find x, given that t(x) = 0.
2
Let o(r) be the second derivative of -2*r**7/21 + 2*r**5/5 - 2*r**3/3 - 16*r. Factor o(w).
-4*w*(w - 1)**2*(w + 1)**2
Let r(b) be the third derivative of 0*b**3 + 0 + 13/210*b**7 + 7/60*b**5 + 1/8*b**6 - 2*b**2 + 1/24*b**4 + 1/84*b**8 + 0*b. Determine n so that r(n) = 0.
-1, -1/4, 0
Suppose 0*a + 4*b - 4 = -3*a, 3*b - 3 = -2*a. Determine w so that 0*w + a - 1/3*w**2 = 0.
0
Let f(k) be the first derivative of -k**5/15 - k**4/3 - 4*k**3/9 - 3. Find y such that f(y) = 0.
-2, 0
Let j(o) be the third derivative of o**6/24 - o**5/6 + 5*o**4/24 + 2*o**2 - 7*o. Factor j(u).
5*u*(u - 1)**2
Let f(a) be the third derivative of 0*a**3 + 1/210*a**7 - 1/60*a**5 + 0 + 0*a**4 + 0*a - 10*a**2 + 0*a**6. Let f(l) = 0. Calculate l.
-1, 0, 1
Let p(b) = -3*b**2 - 3*b + 48. Let h(g) = -g**2 - g + 24. Let j(y) = 5*h(y) - 3*p(y). Solve j(a) = 0.
-3, 2
Let f(m) be the third derivative of -m**11/997920 + m**10/151200 - m**9/90720 - m**5/30 - 4*m**2. Let d(n) be the third derivative of f(n). Factor d(y).
-y**3*(y - 2)*(y - 1)/3
Factor 2/7*j**2 - 4/7*j + 2/7.
2*(j - 1)**2/7
Let k(c) = -c**2 + 6*c - 3. Let d be (-10)/65 - (-67)/13. Let p be k(d). Suppose 2/7*i + 2/7*i**p + 0 = 0. What is i?
-1, 0
Suppose -47*p**4 + 5*p - 27*p**3 + 8*p**4 - 15*p**5 + 3*p**2 + p = 0. Calculate p.
-1, 0, 2/5
Let y(f) be the third derivative of 2/135*f**5 - 1/27*f**4 + 0 - 1/540*f**6 + 5*f**2 + 0*f**3 + 0*f. Factor y(g).
-2*g*(g - 2)**2/9
Let v(z) = 7*z**3 - 28*z**2 + 57*z - 39. Let s(t) = 36*t**3 - 140*t**2 + 284*t - 196. Let k(q) = 3*s(q) - 16*v(q). Factor k(f).
-4*(f - 3)**2*(f - 1)
Let q be -7 - -4 - 3 - (-4 - 4). Factor 2/9*r**5 + 0 + 8/3*r**q + 4/3*r**4 + 26/9*r**3 + 8/9*r.
2*r*(r + 1)**2*(r + 2)**2/9
Let v(l) = -21*l**2 - 61*l - 9. Let u(f) be the first derivative of 22*f**3/3 + 31*f**2 + 8*f + 4. Let k(y) = 3*u(y) + 4*v(y). Determine g, given that k(g) = 0.
-3, -2/9
Let o(f) be the third derivative of 0 - 1/420*f**5 + 1/168*f**4 + 3*f**2 + 0*f + 1/21*f**3. Factor o(z).
-(z - 2)*(z + 1)/7
What is r in 5*r**2 + 2*r**2 - 5*r**3 + 0*r**2 - 2*r**2 = 0?
0, 1
Let i = -21 + 127/6. Let v(u) be the first derivative of -1/2*u**2 - 1/2*u - i*u**3 + 1. Factor v(z).
-(z + 1)**2/2
Let z(f) be the first derivative of f**6/5 - 2*f**5/5 - 5*f**4/6 + 2*f**3/3 + f + 1. Let b(d) be the first derivative of z(d). Factor b(p).
2*p*(p - 2)*(p + 1)*(3*p - 1)
Let z(a) = -a. Let p be z(-4). Factor 0 + 2/9*s**p - 2/9*s + 2/9*s**3 - 2/9*s**2.
2*s*(s - 1)*(s + 1)**2/9
Let r(p) be the second derivative of 1/15*p**6 + 0*p**3 + 0 + 0*p**2 - 1/21*p**7 + p - 1/6*p**4 + 1/10*p**5. What is t in r(t) = 0?
-1, 0, 1
What is l in 2/13*l + 4/13*l**4 - 2/13*l**5 + 0 + 0*l**3 - 4/13*l**2 = 0?
-1, 0, 1
Let m(y) be the first derivative of -y**4/66 + 2*y**3/33 - y**2/11 - 2*y - 8. Let j(n) be the first derivative of m(n). Factor j(q).
-2*(q - 1)**2/11
Let p(u) be the first derivative of -u**4 + u**3 + u**2/2 + 10. Solve p(s) = 0 for s.
-1/4, 0, 1
Let b be (-4)/(-12)*0 + 5. Let p(o) be the first derivative of -1/5*o**b - 1/4*o**4 + 5/2*o**2 + 2*o + o**3 - 3. Find i, given that p(i) = 0.
-1, 2
Let n(d) = 7*d**4 - 7*d**3 - 9*d**2 - 5. Let b(v) = 6*v**4 - 6*v**3 - 8*v**2 - 4. Let l(m) = 5*b(m) - 4*n(m). Let l(t) = 0. What is t?
-1, 0, 2
Let x(d) be the second derivative of -2*d + 0*d**2 + 0 - 1/12*d**4 - 1/3*d**3. Factor x(m).
-m*(m + 2)
Let i = -4 - -13. Find y such that -i*y**3 + 8 - 8 - y**3 - 4*y + 14*y**2 = 0.
0, 2/5, 1
Suppose 8*b = 7*b - 1. Let n(g) = -g - 1. Let t be n(b). Suppose 0*y**2 + t + 0*y + 4/5*y**3 - 14/5*y**4 = 0. Calculate y.
0, 2/7
What is a in 108 - a**3 - 4*a**4 - a**5 + 2*a**2 + 5*a - 3*a**3 - 49 - 57 = 0?
-2, -1, 1
Let a(w) be the third derivative of -w**2 + 0*w + 1/90*w**5 + 0*w**3 + 0 + 1/36*w**4. Factor a(l).
2*l*(l + 1)/3
Let k(c) be the second derivative of 2/13*c**2 + 1/13*c**3 - 1/130*c**5 - 6*c + 0 + 0*c**4. Determine h so that k(h) = 0.
-1, 2
Factor 0 - 9/2*g**3 + 0*g - g**2 - 7/2*g**4.
-g**2*(g + 1)*(7*g + 2)/2
Let d(v) = 4*v**5 + 3*v**4 + 3*v**3 - 2*v**2 - 3*v + 3. Let g(q) = q**5 - q**2 - q + 1. Let i(o) = 5*d(o) - 15*g(o). Factor i(t).
5*t**2*(t + 1)**3
Let t(z) be the third derivative of -z**5/90 + z**4/18 + 2*z**2. Find a, given that t(a) = 0.
0, 2
Let q(d) be the third derivative of -4*d**7/147 - d**6/420 + d**5/210 - 15*d**2. Solve q(o) = 0 for o.
-1/4, 0, 1/5
Let p(u) be the first derivative of -u**5/40 + u**4/24 + 2*u - 5. Let o(r) be the first derivative of p(r). Determine w, given that o(w) = 0.
0, 1
Let i(z) be the second derivative of -z - 1/18*z**3 + 0*z**2 + 1/18*z**4 + 0. Factor i(c).
c*(2*c - 1)/3
Let k(r) be the second derivative of -r**4/3 - 16*r. Factor k(v).
-4*v**2
Let d be 1 - 2/18*1. Let g(x) be the second derivative of d*x**4 + x + x**3 + 2/15*x**6 + 2/3*x**2 + 7/15*x**5 + 0 + 1/63*x**7. Find k such that g(k) = 0.
-2, -1
Let n(h) = 2*h**2 + 1. Let u be n(1). Factor 5*b**3 - 3*b**3 - 3*b**u.
-b**3
Let x(l) be the second derivative of -l**5/60 + l**4/18 + l**3/6 + 7*l. Solve x(g) = 0.
-1, 0, 3
Let g(l) = -3*l**2 + 12*l + 6. Suppose 5*j = 5*s + 80, -2*s = -s - 4*j + 19. Let c(v) = -v. Let i(w) = s*c(w) - g(w). Factor i(z).
3*(z - 1)*(z + 2)
Let v(d) = -2*d**3 + d**2 + d - 2. Let x(f) = f**3 + f**2. Let y(p) = v(p) + x(p). Let y(k) = 0. Calculate k.
-1, 1, 2
Let m(u) be the second derivative of -u**6/360 + u**5/120 + 2*u**3/3 - 3*u. Let q(h) be the second derivative of m(h). Factor q(d).
-d*(d - 1)
Let k be 16/20 - -2*(-16)/(-10). Let w(v) be the first derivative of 0*v - 1/2*v**k - 2/3*v**3 - 3 + 0*v**2. Determine n, given that w(n) = 0.
-1, 0
Let b(h) = -12*h**3 + 12*h**2 + 4*h. Let a(y) = -y**2. Suppose 0*r = -2*r - 2. Let d(w) = r*b(w) - 4*a(w). Factor d(u).
4*u*(u - 1)*(3*u + 1)
Factor 0*s + 2/5*s**4 + 2/5*s**3 - 2/5*s**5 - 2/5*s**2 + 0.
-2*s**2*(s - 1)**2*(s + 1)/5
Let k(b) be the first derivative of 5*b**3/3 - 13*b**2/2 - 6*b + 40. Factor k(u).
(u - 3)*(5*u + 2)
Let k(u) be the first derivative of 0*u**3 - u + 1 - 1/50*u**5 + 0*u**2 + 1/30*u**4. Let s(y) be the first derivative of k(y). Factor s(a).
-2*a**2*(a - 1)/5
Let o(b) be the first derivative of -2/27*b**3 - 2/9*b**5 - 2/9*b**2 + 0*b - 1 + 4/9*b**4. Solve o(q) = 0 for q.
-2/5, 0, 1
Find l, given that -8 - 3*l - 16*l**4 + 7*l - 5*l - 16*l**3 + 12*l**5 + 5*l + 24*l**2 = 0.
-1, -2/3, 1
Let x(b) be the second derivative of 0*b**4 - 1/900*b**6 - 1/150*b**5 - b + 0*b**2 + 0 - 1/6*b**3. Let h(q) be the second derivative of x(q). Solve h(o) = 0.
-2, 0
Let r be -1 + -2 + (3 - 2). Let s be 2*(1 - (r - -1)). Solve 2*l**3 - s*l - l**5 + 3*l + 2*l**4 - 2*l**4 = 0.
-1, 0, 1
Suppose -2 = -k + 2*a + 2, 5*a = -k - 10. Let o(w) be the second derivative of k + 0*w**4 - w + 1/60*w**5 + 0*w**2 - 1/90*w**6 + 0*w**3. Factor o(m).
-m**3*(m - 1)/3
Let g(u) = -4*u**2 + 6*u - 8. Let i(j) = -5*j**2 - j - 5. Let x(a) = 6*a**2 + a + 6. Let f(t) = 7*i(t) + 6*x(t). Let h(p) = 6*f(p) + g(p). Factor h(l).
2*(l - 1)*(l + 1)
Let a = -5171/7 + 740. Factor 3/7*g**3 - 3/7 - a*g**2 + 9/7*g.
3*(g - 1)**3/7
Let u(a) be the first derivative of -a**7/280 - a**6/60 + a**5/40 + a**4/4 - a**3/3 + 1. Let x(q) be the third derivative of u(q). Factor x(d).
-3*(d - 1)*(d + 1)*(d + 2)
Factor -3*n**4 + 0 + 0*n - 9/2*n**3 + 0*n**2 + 3/2*n**5.
3*n**3*