2*a + 1)/5
Let c(z) be the second derivative of z**8/1008 - 5*z**2/2 + 8*z. Let v(y) be the first derivative of c(y). Determine i so that v(i) = 0.
0
Factor -8/7*n**4 + 2/7*n + 12/7*n**3 + 0 - 8/7*n**2 + 2/7*n**5.
2*n*(n - 1)**4/7
Let c(x) be the third derivative of -x**8/84 - 2*x**7/105 + x**6/10 + x**5/3 + x**4/3 - 6*x**2. What is f in c(f) = 0?
-1, 0, 2
Suppose 20*q - 24*q = -8. What is h in -3/4*h**q + 0*h**3 + 1/2*h + 0 + 1/4*h**4 = 0?
-2, 0, 1
Let y(r) = -r**2 - 20*r + 158. Let c be y(6). Determine o so that -4/3*o**c - 8/3 + 4*o = 0.
1, 2
Let m(o) be the second derivative of 2*o**4/3 - 2*o**3 + 2*o**2 + 6*o. Find g, given that m(g) = 0.
1/2, 1
Let r(x) be the third derivative of -5*x**2 + 0*x + 0 - 1/60*x**6 + 0*x**3 - 1/15*x**5 - 1/12*x**4. Suppose r(w) = 0. Calculate w.
-1, 0
Let q be 72/126*(-2)/(40/(-14)). Factor 4/5*l + 2/5*l**2 - q*l**3 + 0.
-2*l*(l - 2)*(l + 1)/5
Let t = 257/14 + -35/2. Let d = 3/26 + 31/182. Factor t*x**2 - d*x**3 - 6/7*x + 2/7.
-2*(x - 1)**3/7
Let a(g) be the first derivative of -4*g**5/25 + g**4/5 + 4*g**3/15 - 2*g**2/5 + 5. Factor a(d).
-4*d*(d - 1)**2*(d + 1)/5
Factor -1/9*r**2 + 1/9 + 1/9*r**3 - 1/9*r.
(r - 1)**2*(r + 1)/9
Let k be (10/(-5))/(-2*3). Let l(a) be the third derivative of 0 - 2*a**2 - k*a**3 + 0*a - 1/12*a**4 + 1/30*a**5 + 1/60*a**6. Factor l(z).
2*(z - 1)*(z + 1)**2
Determine q so that -4*q**4 + 25*q**3 + 43*q**3 - 52*q**3 - 16*q**2 = 0.
0, 2
Factor -3/5*o - 1/5 - 3/5*o**2 - 1/5*o**3.
-(o + 1)**3/5
Factor 3/8*r**4 - 3/2*r - 9/8*r**2 + 3/4*r**3 + 3/2.
3*(r - 1)**2*(r + 2)**2/8
Let p(g) = g**2 + 6*g + 7. Let r be p(-5). Let -31*f + 31*f + 3*f**3 - f**5 - r*f**2 = 0. What is f?
-2, 0, 1
Factor -17/3*g - 5*g**2 - 2/3.
-(g + 1)*(15*g + 2)/3
Let k(d) be the third derivative of -1/672*d**8 + 0*d**5 + 0*d**3 + 0*d**4 + 0 + 1/210*d**7 + 0*d - 1/240*d**6 - 2*d**2. Factor k(g).
-g**3*(g - 1)**2/2
Let a = 164/3 - 54. Determine i, given that i**2 - a*i - 1/3*i**3 + 0 = 0.
0, 1, 2
Let u(t) be the first derivative of t**5 - 5*t**4/4 - 20. Factor u(l).
5*l**3*(l - 1)
Suppose -10*h + 9*h + 2 = 0. Suppose 2*z + h*a - 10 = 0, 5*z + 4*a - 18 - 4 = 0. Find w such that 2/3 - 4/3*w + 2/3*w**z = 0.
1
Let s(x) be the first derivative of x**6/21 + 4*x**5/35 + x**4/14 - 8. Factor s(a).
2*a**3*(a + 1)**2/7
Suppose 2*s - 3 = 1. Let y(k) be the first derivative of 12/7*k**4 + 32/35*k**5 + 2/7*k - 6/7*k**s + 2/21*k**3 - 2. Factor y(d).
2*(d + 1)**2*(4*d - 1)**2/7
Let d(i) = i**5 + i**4 - 3*i**2 - 3. Let m(n) = 0*n**2 + n**4 - 4*n**2 + n**5 - 1 - n**2 - 4. Let o(b) = 5*d(b) - 3*m(b). What is y in o(y) = 0?
-1, 0
Suppose -r + 2*r = 0. Suppose r = n - 0*n. Find l such that n - 2/3*l - 2/3*l**2 = 0.
-1, 0
Let n(z) be the first derivative of 5*z**4/4 - 5*z**3/3 + 12. Find o such that n(o) = 0.
0, 1
Let r be (9 - (-16)/(-4))/(-1) - -8. Let 2/3*m + 4/3 - 2/3*m**r - 4/3*m**2 = 0. What is m?
-2, -1, 1
Let x = -11 - -13. Let p(i) be the first derivative of 2/21*i**3 - 3/7*i**4 + 18/35*i**5 + 2 + 0*i + 0*i**x. What is v in p(v) = 0?
0, 1/3
Let l = 15 - 9. Let n be 2*(-3)/l + 2. Suppose m - m**3 - 3 + m**2 + 2 - 1 + n = 0. Calculate m.
-1, 1
Let g(i) be the first derivative of -5*i**6/3 + i**5 + 5*i**4/2 - 5*i**3/3 + 12. Suppose g(q) = 0. What is q?
-1, 0, 1/2, 1
Let d(x) = -4*x + 23. Let o be d(5). Factor -2/3 - 8/3*w**o - w**2 + 4/3*w**4 + 7/3*w.
(w - 2)*(w + 1)*(2*w - 1)**2/3
Suppose 4*r + 19 - 59 = -4*y, y - 5 = 0. Factor 1/5 - 2/5*k**2 + 1/5*k**4 - 2/5*k**3 + 1/5*k + 1/5*k**r.
(k - 1)**2*(k + 1)**3/5
Suppose 3*h = 7 - 1. Factor -2*v + 2*v**h - 2*v**2 - v**2.
-v*(v + 2)
Let f(b) = b - 12. Let j be f(16). Factor 11*n**4 + 2*n**j - 2*n**4 - 9*n**3 + 3*n**2 - 3*n**5 - 2*n**4.
-3*n**2*(n - 1)**3
Let m(n) be the third derivative of -1/45*n**6 - 2*n**2 + 1/315*n**7 + 0*n**4 + 2/45*n**5 + 0*n**3 + 0*n + 0. Factor m(y).
2*y**2*(y - 2)**2/3
What is l in -1/4*l**3 - 5/4*l**2 - 3/4 - 7/4*l = 0?
-3, -1
Suppose -o = -5 + 3. Suppose o*i - 1 = 3. Factor u**3 - 1/2*u**i + 0 - 1/2*u**4 + 0*u.
-u**2*(u - 1)**2/2
Let s(w) be the third derivative of -w**7/2520 - w**6/540 - w**5/360 + w**3/3 - 2*w**2. Let a(z) be the first derivative of s(z). Factor a(d).
-d*(d + 1)**2/3
Let v(u) = -u**3 + 4*u**2 + 4*u + 5. Let h be v(5). Let k = 8 + -6. Factor h*c**k + 2/7*c**3 + 0*c + 0 - 2/7*c**4.
-2*c**3*(c - 1)/7
Let p(b) = -3*b**3 - 15*b**2 + 11*b. Let h(g) = -2*g**3 - 14*g**2 + 10*g. Let u(j) = -7*h(j) + 6*p(j). Find n such that u(n) = 0.
0, 1
Suppose 3*b - 24 = -4*r - 9, 7 = 2*r + b. Let v(w) be the second derivative of -1/8*w**2 + 1/12*w**r - 1/48*w**4 + 0 - 3*w. Factor v(t).
-(t - 1)**2/4
Let w(i) = -i**4 - 6*i**3 - 30*i**2 - 11*i. Let k(c) = -2*c**3 - 10*c**2 - 4*c. Let d(q) = -14*k(q) + 4*w(q). Let d(g) = 0. Calculate g.
-1, 0, 3
Let s(f) be the first derivative of 3*f**4/16 - f**3/2 + 3*f**2/8 + 1. Factor s(m).
3*m*(m - 1)**2/4
Let s(c) = -c**3 - 6*c**2 + 4*c - 10. Let w be s(-7). Let g = -11 + w. Factor g*f**2 - 2/5 + 3/5*f - 1/5*f**3.
-(f - 1)**2*(f + 2)/5
Suppose 3*f = 7*f - 8. Let i = 17/117 - -1/13. Solve -2/3*h + i*h**f + 4/9 = 0 for h.
1, 2
Let t(x) be the first derivative of -7*x**3/5 - 24*x**2/5 - 12*x/5 - 2. Suppose t(h) = 0. Calculate h.
-2, -2/7
Let f be (4/6 - 0) + -26 + 26. Let u(g) be the first derivative of -3 + 4*g**2 - f*g**3 - 8*g. Factor u(a).
-2*(a - 2)**2
Let u(n) = -8*n + 8. Let r(q) = q**2 - 8*q + 7. Let l(y) = 4*r(y) - 5*u(y). Factor l(o).
4*(o - 1)*(o + 3)
Solve 3*s + 4*s + 3*s**3 - 4*s + 6*s**2 = 0 for s.
-1, 0
Let u be (-10)/(-20) + 3/2. Solve -67*g**u - 40*g + 34*g**3 + 48*g + 4 + 21*g**3 = 0.
-2/11, 2/5, 1
Let j(p) be the second derivative of 0*p**2 - p + 0 - 1/3*p**3 + 5/12*p**4. Factor j(f).
f*(5*f - 2)
Let r(k) be the first derivative of -3 + 1/6*k**6 - 1/4*k**4 + 0*k + 1/3*k**3 + 0*k**2 - 1/5*k**5. Determine o so that r(o) = 0.
-1, 0, 1
Let o(n) be the third derivative of n**5/20 + 3*n**4/2 + 18*n**3 - n**2. Solve o(x) = 0 for x.
-6
Let c(a) be the third derivative of -a**8/672 - a**7/420 + a**6/240 + a**5/120 - 7*a**2. Find w such that c(w) = 0.
-1, 0, 1
Suppose -4*r + 7 = -s, -5*r = -2*s - 0*r - 5. Determine i so that -4*i + 94*i**4 + i**2 - 4 - 35*i**s - 87*i**3 + 4 + 31*i**2 = 0.
0, 2/7, 2/5, 1
Let o(z) be the first derivative of -1 + 1/6*z**3 + 2*z + z**2. Suppose o(s) = 0. Calculate s.
-2
Let m = 1819/60 - 121/4. Let c(d) be the third derivative of -1/12*d**4 - 3/50*d**5 - m*d**3 - 7/300*d**6 + d**2 + 0*d - 2/525*d**7 + 0. Factor c(u).
-2*(u + 1)**3*(2*u + 1)/5
Let g = 2/101 - -299/202. Let f(d) be the first derivative of 1 + 1/2*d**3 - g*d**2 + 0*d. What is c in f(c) = 0?
0, 2
Let n be (-30)/(-10)*4/(-6) + 5. Let 0 + 1/5*u + 1/5*u**2 - 1/5*u**n - 1/5*u**4 = 0. Calculate u.
-1, 0, 1
Let w(f) be the second derivative of -5*f**4/36 - 5*f**3/18 + 5*f**2/3 - 10*f. Factor w(q).
-5*(q - 1)*(q + 2)/3
Solve 3/4*r**2 + 0 - 1/2*r - 1/4*r**3 = 0.
0, 1, 2
Suppose 2*r + 0 - 2 = 2*n, -3*r + 27 = 5*n. Let o(x) be the first derivative of 0*x + 0*x**n + 1/6*x**6 + 2/5*x**5 + 1/4*x**4 + 0*x**2 - 2. Factor o(l).
l**3*(l + 1)**2
Let f(n) = -n - 10. Let m be f(10). Let k be 2/m*55/(-22). What is h in -4*h**5 - 1/4*h**3 - k*h + 3/2*h**2 + 0 - 6*h**4 = 0?
-1, 0, 1/4
Let a be 4/9 + (-2)/(-9). Let f(z) be the third derivative of -z**2 - 7/12*z**4 + 0 + a*z**3 + 7/60*z**6 + 0*z - 1/15*z**5. Factor f(j).
2*(j - 1)*(j + 1)*(7*j - 2)
Let t(h) = h**3 - h**2. Let x(o) = 14*o**4 + 6*o**3 - 14*o**2 - 10*o + 4. Suppose -24 = -3*j + j. Suppose -n - 11 = -j. Let y(p) = n*x(p) + 4*t(p). Factor y(v).
2*(v - 1)*(v + 1)**2*(7*v - 2)
Factor 0*r**3 - 2*r + r + 5*r**3 - 4*r**3.
r*(r - 1)*(r + 1)
Suppose v = -v + 6. Suppose m**2 - 3*m**2 - v*m + m = 0. What is m?
-1, 0
Let p = 84 - 36. What is w in 3*w**3 - 64 + p + w**3 + 12*w**2 = 0?
-2, 1
Let i(g) be the third derivative of -g**8/80640 - g**7/20160 + g**6/1440 + g**5/30 - 4*g**2. Let y(z) be the third derivative of i(z). Factor y(m).
-(m - 1)*(m + 2)/4
Let d = -50 + 53. Suppose 0*a - 2/7*a**5 + 0*a**2 + 0*a**4 + 0 + 0*a**d = 0. Calculate a.
0
Let c(x) be the second derivative of -5/18*x**4 + 7/30*x**5 + 3*x - 2/9*x**3 + 0*x**2 + 0. Factor c(s).
2*s*(s - 1)*(7*s + 2)/3
Let o = 594 - 2968/5. Factor -o + 2/5*s**2 + 2/5*s**3 - 2/5*s.
2*(s - 1)*(s + 1)**2/5
Let m(r) be the first derivative of -2*r**3/45 + r