r 6*p**3 - 23*p**3 + 11*p**3 - l*p + 10*p**3.
4*p*(p - 1)*(p + 1)
Let j(c) be the third derivative of -c**7/840 - c**6/480 + c**5/240 + c**4/96 + 66*c**2. Solve j(x) = 0.
-1, 0, 1
Let i(d) = 3*d**5 + 2*d**4 + 4*d**3 - 2*d**2 - 3*d. Let w(c) = 8*c**5 + 5*c**4 + 9*c**3 - 5*c**2 - 7*c. Let n(a) = 5*i(a) - 2*w(a). Solve n(h) = 0 for h.
-1, 0, 1
Let q(c) = -3*c**3 + c**2 - 9*c. Let y(r) = r**3 + 3*r. Let o(w) = -3*q(w) - 8*y(w). Let b be o(2). Let -2/7*j**b + 2/7*j + 0 = 0. What is j?
0, 1
Let l(b) be the first derivative of b**6/200 - b**5/50 + b**4/40 + 23*b**2/2 + 20. Let s(x) be the second derivative of l(x). Factor s(m).
3*m*(m - 1)**2/5
Let t be (-1)/((-110)/20 - (-7 - -2)). Let g(h) be the second derivative of 1/18*h**4 + 0 - 1/27*h**3 + 0*h**2 + t*h - 1/45*h**5. Factor g(w).
-2*w*(w - 1)*(2*w - 1)/9
Let r(a) be the first derivative of 9*a**5/100 - a**4/20 - 3*a**3/10 + 3*a**2/10 + 3*a - 7. Let m(z) be the first derivative of r(z). Factor m(g).
3*(g - 1)*(g + 1)*(3*g - 1)/5
Suppose l = -3*c - 193, 4*c + c + 935 = -5*l. Let j be 2/(-6) - l/12. Find z such that -5*z**2 - 35*z + 65*z**3 + 7*z**4 - 30*z + 6*z**4 + 7*z**4 - j = 0.
-3, -1, -1/4, 1
Let x be (-15)/3 + 1 - 161/(-40). Let g(i) be the second derivative of 0*i**2 + 0*i**3 + 0 + 0*i**4 + 0*i**5 - x*i**6 - 8*i. Factor g(l).
-3*l**4/4
Let u(x) be the third derivative of -x**7/105 - 13*x**6/30 - 56*x**5/15 - 25*x**4/2 - 21*x**3 - 967*x**2. Factor u(i).
-2*(i + 1)**2*(i + 3)*(i + 21)
Suppose -25 = -4*t - t. Factor -20*o**3 - o**2 - t*o**4 - 24*o**2 + 5*o**2.
-5*o**2*(o + 2)**2
Let d(q) = -q**2 - 6*q + 2. Let m be d(-6). Factor -17 + 7 - 5 + 10*g + 5*g**m + 0*g.
5*(g - 1)*(g + 3)
Let g = -178 + 174. Let p be (g/(-9))/(1/9*2). Factor -4/5*h + 0 + 2/5*h**p.
2*h*(h - 2)/5
Let m(l) = -26*l**2 - 54*l + 158. Let g(z) = -2*z**2 - z - 3. Let f(c) = 28*g(c) - 2*m(c). Factor f(d).
-4*(d - 10)**2
Let w = -26 - -26. Suppose 5*v + v - 12 = w. Factor 4 - 3 + 5 + v*s - 4 - 2*s**3 - 2*s**2.
-2*(s - 1)*(s + 1)**2
What is k in -116/7*k**2 - 162/7*k**4 + 120/7*k - 414/7*k**3 - 16/7 = 0?
-2, -1, 2/9
Let t(w) = w**3 - 3*w**2 - w + 3. Let v(f) = -f**3 + 3*f**2 - 2. Let z(q) = 2*t(q) + 3*v(q). Find g such that z(g) = 0.
0, 1, 2
Suppose -15*d + 4*d = 34*d - 135. Let 20*f - 24 + 64/3*f**2 + 4*f**d = 0. What is f?
-3, 2/3
Suppose -3*w - 14 = 5*h, -5*w + 14 = h - 2*h. Let b be 2/w - (-10)/10. Let 2/11*c - 32/11*c**3 + 0*c**b + 0 = 0. Calculate c.
-1/4, 0, 1/4
Let q(l) be the first derivative of -l**7/1680 + l**6/360 + 13*l**5/240 + 5*l**4/24 - 6*l**3 - 2. Let y(f) be the third derivative of q(f). Factor y(n).
-(n - 5)*(n + 1)*(n + 2)/2
Let t(s) be the first derivative of s**6/72 + s**5/90 - 2*s**2 + 31. Let j(i) be the second derivative of t(i). Factor j(k).
k**2*(5*k + 2)/3
Let w(l) = 4*l**4 + 50*l**3 + 384*l**2 + 622*l + 286. Let c(m) = m**4 - m**3 - m**2 - m - 1. Let d(j) = 4*c(j) - 2*w(j). Factor d(s).
-4*(s + 1)**2*(s + 12)**2
Let r = -8 + 9. Let b = 3 - r. Suppose 0*a**5 - 3*a**3 + 2*a**b + 3*a**5 + 3*a**4 - 5*a**2 = 0. What is a?
-1, 0, 1
Factor -196/3 - 28/3*x - 1/3*x**2.
-(x + 14)**2/3
Let v = 23 + -15. Factor -v*z**4 + 22*z**3 - 24*z**2 + 10*z + z**5 - 4*z + 3*z.
z*(z - 3)**2*(z - 1)**2
Let g(q) be the first derivative of 3*q**5/5 - 213*q**4/4 + 1656*q**3 - 18144*q**2 - 41472*q - 200. Factor g(s).
3*(s - 24)**3*(s + 1)
What is y in -8 - 14*y**2 - 32 - y**2 + 16*y + 8*y**2 + 9*y**2 = 0?
-10, 2
Let m(z) be the first derivative of z**5/10 - z**4/8 - z**3/6 + z**2/4 + 128. Factor m(f).
f*(f - 1)**2*(f + 1)/2
Let w be 55/66 - (-2)/(-6). Let j be 1 - 0 - (-5 + 88/16). Factor -j + 0*p + w*p**2.
(p - 1)*(p + 1)/2
Let m(p) = 2*p**5 + 8*p**4 - 18*p**3 - 2*p**2 - 5*p + 5. Let g(a) = a**5 - a**4 - a**3 - a**2 - a + 1. Let w(n) = -15*g(n) + 3*m(n). Let w(x) = 0. Calculate x.
0, 1/3, 1, 3
Let d(q) be the third derivative of -q**4/8 - 2*q**3/3 + q**2. Let f be d(-2). Factor 24/5*n - f*n**2 - 8/5.
-2*(n - 2)*(5*n - 2)/5
Let a(u) be the first derivative of -u**6/5 + 18*u**5/25 - 3*u**4/5 - 4*u**3/5 + 9*u**2/5 - 6*u/5 - 77. Factor a(q).
-6*(q - 1)**4*(q + 1)/5
Factor 53*o - 100*o + 11*o - 88 + 4*o**2.
4*(o - 11)*(o + 2)
Let t(v) = -2*v**2. Let o(p) = -12*p**2 - 24*p + 160. Let z(g) = -o(g) + 4*t(g). Suppose z(n) = 0. Calculate n.
-10, 4
Let m(b) be the first derivative of b**3/4 + 3*b**2 - 27*b/4 + 75. Factor m(n).
3*(n - 1)*(n + 9)/4
Let x be 610/(-549)*(-5)/25. Factor x*m**2 - 8/9 + 0*m.
2*(m - 2)*(m + 2)/9
Let q = 15877 + -15877. Determine l, given that 0 + 2/7*l**2 + q*l = 0.
0
Factor 6*w - w**2 - w**2 - 2*w**2 - 22*w + 84.
-4*(w - 3)*(w + 7)
Let l(p) be the third derivative of -p**6/360 - 41*p**5/270 + 19*p**4/72 + 14*p**3/27 + 300*p**2. Factor l(v).
-(v - 1)*(v + 28)*(3*v + 1)/9
Let 21/4*o**3 - 1/4*o**4 + 50 + 15*o - 59/2*o**2 = 0. Calculate o.
-1, 2, 10
Let a(h) be the first derivative of h**7/84 + h**6/24 - 5*h**4/48 - h**3/12 + 3*h - 12. Let i(f) be the first derivative of a(f). Suppose i(t) = 0. Calculate t.
-2, -1, -1/2, 0, 1
Suppose -3*d = -3*v + 3, -v - 8 = -7*d + 3*d. Suppose -v = 4*l, -q - 5*l + 31 - 6 = 0. Solve 4*r - 20*r**2 + 9*r**5 - q*r**4 + 6 - 6 + 37*r**3 = 0 for r.
0, 2/3, 1
Let s(q) be the first derivative of 3*q**4/16 + 5*q**3/4 + 9*q**2/4 + 511. Factor s(f).
3*f*(f + 2)*(f + 3)/4
Find k such that -2/19*k**2 + 2/19*k**3 + 2/19 - 2/19*k = 0.
-1, 1
Let m be 1*(-8)/16*0. Find g, given that 3/2*g**4 - 1/2*g**5 + 0*g - g**3 + m*g**2 + 0 = 0.
0, 1, 2
Let o(f) = -f**2 + 9*f - 18. Suppose 3*m = 5*z - 24, -2*z + m + 22 = 2*z. Let u be o(z). Suppose 0*x + 2/3*x**2 + 2/3*x**3 + u = 0. Calculate x.
-1, 0
Factor 25*g**2 + 5*g**3 + 28*g + 16*g + 15 - 9*g.
5*(g + 1)**2*(g + 3)
Let f(v) = v**3 - 5*v**2 - v + 6. Let t be f(5). Let j be 6/(t/(3/6)). Factor 8 + j*d**2 + 15*d - 3*d + 1 + 0*d**2.
3*(d + 1)*(d + 3)
Let n be 49/(-21)*(-6)/28. Let v(u) be the first derivative of n*u**2 - 2*u - 6 + 1/3*u**3. Factor v(l).
(l - 1)*(l + 2)
Factor 33*n - 3/2*n**2 - 108.
-3*(n - 18)*(n - 4)/2
Determine b so that 2*b**5 - 52/7*b**2 - 64/7 - 256/7*b + 242/7*b**3 + 116/7*b**4 = 0.
-4, -1, -2/7, 1
Solve 4*t**2 + 7 + 5 - 3*t**2 + 7*t - 15*t = 0 for t.
2, 6
Suppose -5*m - v + 27 = 7, -4*m = 3*v - 27. Determine u so that u**2 + 4*u**2 + 6*u + m - 2*u**2 = 0.
-1
Suppose 24 = -42*a + 39*a. Let o(y) = -y**2 - 8*y + 10. Let u be o(a). Solve -19/4*v + 25/4*v**3 - 1/2 - u*v**2 = 0.
-1/5, 2
Suppose a = -3 + 6. Determine d so that 0*d + 3/7*d**4 + 0 - 3/7*d**2 + 0*d**a = 0.
-1, 0, 1
Let a(t) be the third derivative of t**6/1020 - t**5/85 - t**4/204 + 2*t**3/17 - 2*t**2 - 16. Let a(c) = 0. Calculate c.
-1, 1, 6
Find s, given that -12*s**4 + 7 - 8*s**3 - 358*s**2 + 8*s + 11*s**4 + 352*s**2 = 0.
-7, -1, 1
Suppose -3*i + o = -8, 0*o + 4*o = 4*i - 16. Let u be (6/(-75))/(2/(-10)). Let 0*b - 1/5*b**5 + u*b**4 + 0 - 1/5*b**3 + 0*b**i = 0. What is b?
0, 1
Find q such that -2/5 + 1/5*q - 2/5*q**4 + 2*q**3 + 12/5*q**2 - 3/5*q**5 = 0.
-1, 1/3, 2
Let u = 7 - 5. Factor -u*k**2 - 4*k**3 - 2*k - 41*k**4 + 43*k**4 + 6*k**3.
2*k*(k - 1)*(k + 1)**2
Let f be ((1 - 0) + 1418)*128/(-480). Let z = f - -380. Determine n, given that -4/5*n**2 - 2/5 + 6/5*n**4 - 8/5*n**3 + z*n = 0.
-1, 1/3, 1
Let k(n) = -n**2 + n + 3. Let c be k(0). Suppose c*d = 2*m - 2, -4*d - m = 2*m - 20. Factor 383 + d*h**3 - 2*h**2 - 383.
2*h**2*(h - 1)
Let o(h) = h + 26. Let q be o(0). Let b = 28 - q. Let -3*g**3 + 8*g**b - g**2 - 4*g**2 = 0. Calculate g.
0, 1
Suppose -4 = -5*d + 2*d + p, 5*p - 10 = 0. Determine b, given that 49 - 2*b**3 - 49 - 4*b**d + 2*b**4 = 0.
-1, 0, 2
Let b = -241 + 473. Let d = -1621/7 + b. Suppose -3/7*v**4 + 0*v + 3/7*v**2 + 3/7*v**3 - d*v**5 + 0 = 0. Calculate v.
-1, 0, 1
Let l(u) be the second derivative of u**6/5 - 3*u**5/20 - u**4/2 + u**3/2 + 49*u. Factor l(p).
3*p*(p - 1)*(p + 1)*(2*p - 1)
Factor -291*t**3 + 9*t + 144*t**3 + 2*t**2 + 146*t**3 + 11*t + 24.
-(t - 6)*(t + 2)**2
Let m be (-7)/(280/(-64))*5/2. Let n(p) be the second derivative of 0 - 9/80*p**5 + 1/120*p**6 + 0*p**2 + 6*p - 9/8*p**3 + 9/16*p**m. Let n(d) = 0. Calculate d.
0, 3
Let q be 12/14 + (-420)/735. Factor -q*c**5 - 2/7*c**2 + 2/7*c**3 + 0*c + 0 + 2/7*c**4.
-2*c**2*(c - 1)**2*(c + 1)/7
Let f(q) be the first derivative of -3*q**5/20 - 3*q**4/16 + q**3/4 + 3*q**2/8 + 23. Find h, given that f(h) =