1, 1
Let o(b) be the first derivative of -b**7/168 - b**6/120 + 2*b - 1. Let t(d) be the first derivative of o(d). Factor t(m).
-m**4*(m + 1)/4
Let i(a) be the first derivative of a**3/6 + a**2/2 - 3*a/2 + 8. Factor i(j).
(j - 1)*(j + 3)/2
Let h(c) = -3*c**3 + 14*c**2 + 35*c + 16. Let p(k) = 3*k**3 - 15*k**2 - 36*k - 15. Let g(a) = -3*h(a) - 2*p(a). Let g(z) = 0. What is z?
-1, 6
Let q be (-3)/(-4) + (-18666)/(-2184). Let p = 132/13 - q. Factor -6/7*v - 2/7*v**3 + 2/7 + p*v**2.
-2*(v - 1)**3/7
Let k(w) be the third derivative of -1/30*w**6 + 0*w**3 + 3*w**2 - 1/12*w**4 + 0*w - 1/10*w**5 + 0. Factor k(g).
-2*g*(g + 1)*(2*g + 1)
Let m = -30959/60 + 516. Let t(k) be the third derivative of -m*k**5 + 0*k + 0 + 0*k**3 + 1/90*k**6 + 2*k**2 - 1/72*k**4. Determine b, given that t(b) = 0.
-1/4, 0, 1
Determine b so that 0 - 16/3*b + 16/3*b**2 - 4/3*b**3 = 0.
0, 2
Let x(m) be the second derivative of 0*m**4 - 1/4*m**2 - 1/8*m**3 + 0 - 3*m + 1/80*m**5. Suppose x(t) = 0. What is t?
-1, 2
Factor 2/3*y - 1/2*y**2 - 1/3*y**3 + 1/6*y**4 + 2/3.
(y - 2)**2*(y + 1)**2/6
Determine o so that -13/4*o**3 + 0*o + 0 - 1/2*o**4 - 3/2*o**2 = 0.
-6, -1/2, 0
Let n(f) be the third derivative of f**5/15 - f**4/6 + 6*f**2 + 5. Find q such that n(q) = 0.
0, 1
Let m(h) be the second derivative of -h**5/5 + 2*h**3/3 + 3*h. Factor m(z).
-4*z*(z - 1)*(z + 1)
Let t(c) = -6*c**2 - c - 4. Suppose 6 = u + 21. Let v(h) = h**2 - h - 1. Let m(s) = u*v(s) - 3*t(s). Factor m(q).
3*(q + 3)**2
Let h be (-4)/3 - (-3)/(441/574). Let f(p) = -p**2 + p + 2. Let v be f(2). Determine c so that -4/7*c**3 + h*c**4 - 8/7*c**5 + 0*c**2 + 0*c + v = 0.
0, 1/4, 2
Let v(i) be the second derivative of -i**6/60 + i**5/105 + 2*i**2 - 4*i. Let a(z) be the first derivative of v(z). Determine l so that a(l) = 0.
0, 2/7
Let o(n) be the second derivative of 3*n**5/100 + 3*n**4/20 - 2*n**3/5 - 18*n**2/5 - 15*n. Solve o(p) = 0 for p.
-3, -2, 2
Let t(r) be the second derivative of r**4/8 - r**3/4 - 3*r**2/2 - 6*r. Factor t(y).
3*(y - 2)*(y + 1)/2
Let n(o) = -2*o**4 - 8*o**3 + 4*o**2 + 6*o - 6. Let v(y) = y**5 + 9*y**4 + 32*y**3 - 16*y**2 - 24*y + 25. Let c(t) = -18*n(t) - 4*v(t). Factor c(w).
-4*(w - 1)**3*(w + 1)*(w + 2)
Let o be (-60)/(-16) - (-1)/4. Let y(u) be the third derivative of 1/6*u**3 - u**2 + 0 - 1/24*u**o + 1/120*u**6 + 0*u - 1/60*u**5. Factor y(b).
(b - 1)**2*(b + 1)
Let u be 2/20 - 4/(-10). Suppose 4*b = -3*b. Factor 0 + b*g**2 + 0*g + u*g**3.
g**3/2
Let g(p) be the second derivative of p**5/170 + p**4/34 - 4*p**2/17 - p - 34. Factor g(k).
2*(k - 1)*(k + 2)**2/17
Suppose -x - 12 = -5*x. Factor -4 + 4*a + x - 2*a**2 + a**2 - 2*a.
-(a - 1)**2
Let l(r) be the third derivative of 0*r + 1/240*r**5 + 0 + 1/24*r**3 + 5*r**2 + 1/48*r**4. Suppose l(w) = 0. What is w?
-1
Let v(k) be the second derivative of -k**4/3 - 4*k**3/3 + 6*k**2 + 9*k. Factor v(f).
-4*(f - 1)*(f + 3)
Let f(u) be the third derivative of u**8/336 - u**7/35 + 13*u**6/120 - u**5/5 + u**4/6 + 5*u**2. Solve f(x) = 0.
0, 1, 2
Let q(m) = m + 8. Let y be q(-6). Let w(k) = k**3 - 2*k**2 + 2*k - 1. Let f be w(y). Factor 2/9*r**f + 4/9*r**2 + 0*r + 0.
2*r**2*(r + 2)/9
Let w(o) = o**5 + 11*o**4 + 3*o**2 - 5. Let s(f) = -5*f**4 - f**2 + 2. Let p(c) = -15*s(c) - 6*w(c). Factor p(r).
-3*r**2*(r - 1)**2*(2*r + 1)
Let c(f) = -4*f - 40. Let x be c(-10). Let n be -1 + -2*11/(-18). Determine j, given that -2/9*j**3 - 4/9*j**2 - n*j + x = 0.
-1, 0
Let o be 2 + ((-52)/12 - -5). Solve o*p**3 + 4/3*p**2 + 4/3 - 8/3*p**4 + 2/3*p**5 - 10/3*p = 0.
-1, 1, 2
Let z(u) be the second derivative of -7*u**4/48 - 5*u**3/24 + u**2/4 + 5*u. Factor z(h).
-(h + 1)*(7*h - 2)/4
Let k(r) be the third derivative of -r**7/2520 - r**6/720 + r**4/12 + 2*r**2. Let m(w) be the second derivative of k(w). Suppose m(o) = 0. What is o?
-1, 0
Let j be (-220)/770 - (-2)/7. Factor 2/11*q**3 + j + 0*q**2 - 2/11*q.
2*q*(q - 1)*(q + 1)/11
Let v(q) be the second derivative of -q**6/30 - q**5/5 - q**4/3 + 5*q**2/2 - 4*q. Let x(t) be the first derivative of v(t). Determine j, given that x(j) = 0.
-2, -1, 0
Let w(y) = -2*y - 2. Let f(p) be the first derivative of -1 + 1/3*p**3 + 3*p + 3/2*p**2. Let o(j) = 2*f(j) + 3*w(j). Factor o(u).
2*u**2
Suppose 2*q**5 - 13*q**3 + 11*q**3 + 0*q**5 = 0. What is q?
-1, 0, 1
Let f(p) be the first derivative of 0*p**3 - 6 - 1/20*p**4 + 0*p + 1/10*p**2. Solve f(j) = 0 for j.
-1, 0, 1
Let y(x) be the second derivative of 2/45*x**6 - 1/9*x**4 + 1/63*x**7 - 1/9*x**3 + 0*x**2 + 0 - 7*x + 0*x**5. Factor y(m).
2*m*(m - 1)*(m + 1)**3/3
Let m be -4 + (-44)/(-12) - 4/(-10). Let s(f) be the first derivative of 2 + m*f**3 + 2/5*f + 3/10*f**2. Factor s(t).
(t + 1)*(t + 2)/5
Let 5*o**3 + 5/4*o**4 - 5*o - 15/4 + 5/2*o**2 = 0. What is o?
-3, -1, 1
Factor 4/5*w**2 - 2/5*w**3 + 0 + 0*w.
-2*w**2*(w - 2)/5
Let k(u) = -2*u**5 - 4*u**4 + 3*u**3 + 5*u**2 - 5*u. Let t(a) = -3*a**5 - 6*a**4 + 5*a**3 + 8*a**2 - 8*a. Let c(p) = -8*k(p) + 5*t(p). Factor c(l).
l**3*(l + 1)**2
Let m(r) = r + 9. Suppose -7 = -6*d + 7*d. Let a be m(d). Factor 2/9*x**a + 0 + 2/9*x.
2*x*(x + 1)/9
Let m(u) be the second derivative of -u**4/4 - 5*u**3/2 + 9*u**2 - 26*u. Let m(t) = 0. Calculate t.
-6, 1
Let t be -3 + (-3)/(126/(-122)). Let q = 13/84 - t. Suppose q*d**3 + 1/2 + 0*d**2 - 3/4*d = 0. Calculate d.
-2, 1
Find x such that 15*x**2 + 21*x**2 + 0 - 14*x**3 - 30*x + 8 = 0.
4/7, 1
Let k(f) be the third derivative of -f**6/120 + f**5/60 + f**4/24 - 2*f**2. Let t(n) = 2*n**3 + 5*n**2 + n. Let m(o) = 6*k(o) - 3*t(o). Factor m(w).
-3*w*(w + 1)*(4*w - 1)
Let k be -5*2/(-44)*28/35. Let -2/11*q**2 + k*q + 0 = 0. What is q?
0, 1
Let u(i) be the second derivative of 0*i**2 - 3/2*i**3 + 2*i + 1/4*i**4 + 0. Solve u(l) = 0 for l.
0, 3
Let -180 + 30*o - 5/4*o**2 = 0. Calculate o.
12
Let k(o) be the third derivative of o**5/270 - o**4/54 - o**3/9 + 6*o**2. Suppose k(s) = 0. What is s?
-1, 3
Let b be (-12)/(-20) - 54/(-10). Suppose v = -2*r + 2*v + b, 0 = 4*r + v - 12. Factor 0*d + 1/4*d**4 + 0 + 0*d**r - 1/4*d**2.
d**2*(d - 1)*(d + 1)/4
Let r = -1454 - -2749/2. Let p = r + 81. Factor p*y**2 + 3/4*y - 3/4*y**3 - 3/2.
-3*(y - 2)*(y - 1)*(y + 1)/4
Let o(s) be the first derivative of -s**7/3780 + s**6/1620 - 4*s**3/3 - 1. Let j(q) be the third derivative of o(q). Solve j(u) = 0 for u.
0, 1
Let i(w) be the third derivative of 0*w**3 + 0*w**6 - 5*w**2 + 1/840*w**8 + 0*w - 1/175*w**7 + 2/75*w**5 + 0 + 0*w**4. What is h in i(h) = 0?
-1, 0, 2
Suppose -3*z + 2*z = -n, z - 5*n + 12 = 0. Factor -z*c**3 - 21/5*c**2 + 0 - 6/5*c.
-3*c*(c + 1)*(5*c + 2)/5
Let j(h) = -h**2 + 9*h - 6. Let f be j(8). Find g, given that 2*g**2 + 0*g**2 + g**3 + g**4 - 3*g**f - g = 0.
-1, 0, 1
Let u be ((4 + -9)/(-5))/180. Let k(j) be the third derivative of 0 + 0*j**3 - 1/36*j**4 + 3*j**2 - u*j**6 - 1/45*j**5 + 0*j. Find s such that k(s) = 0.
-1, 0
Let v be (-13)/(-9) - (2 - 1). Let -v*l + 0 - 2/9*l**4 + 4/9*l**3 + 2/9*l**2 = 0. Calculate l.
-1, 0, 1, 2
Suppose 2 = y - 1. Let i(b) = b**2 + b + 3. Let o(t) = -t**2 - t - 5. Let j(f) = y*o(f) + 5*i(f). Factor j(m).
2*m*(m + 1)
Suppose -3*i - 4*n = -15 - 3, -n = -2*i + 1. Let k = i + 1. What is a in 0*a - 2*a**3 + 4*a**2 - 5*a + k*a = 0?
0, 1
Let g be (-3 - (-7 - 0)) + -1. Let j(v) be the first derivative of 1/22*v**4 + g + 2/33*v**3 - 5/11*v**2 + 6/11*v. Suppose j(x) = 0. What is x?
-3, 1
Let c be (-3 + (-14)/(-4))*0. Let z(d) be the second derivative of 0*d**4 + 0*d**2 - 1/50*d**5 + c*d**3 + 0 + d + 1/75*d**6. Determine r so that z(r) = 0.
0, 1
Suppose 2*a + 29 = 5*s, -3*s + 25 = -0*a - 5*a. Let d be 6/(-12)*a/3. Suppose -p - d - 1/3*p**3 - p**2 = 0. What is p?
-1
Let s(w) = -2*w**3 - w**2 + 2*w + 1. Let x be s(-2). Factor -x*k - 5*k**3 + k + 12*k**3 - 5*k**3.
2*k*(k - 2)*(k + 2)
Let k = 46/5 + -77/10. Let r(u) be the second derivative of 0*u**3 + 1/4*u**4 + u + 0 - k*u**2. Determine m so that r(m) = 0.
-1, 1
Suppose 0 = -2*h + 5*u + 33, -4*h - 4*u = -5*h + 24. Solve 4/7*z + 18/7*z**h - 18/7*z**2 - 4/7*z**3 + 0 = 0 for z.
-1, 0, 2/9, 1
Suppose 5*g**3 + g**4 - g**5 + 4 - 22*g - 5*g**2 + 5*g + 13*g = 0. Calculate g.
-2, -1, 1, 2
Let p(g) be the first derivative of g**7/420 + g**6/180 - g**5/60 - g**4/12 - 2*g**3/3 - 3. Let t(f) be the third derivative of p(f). Factor t(j).
2*(j - 1)*(j + 1)**2
Let b(d) be the seco