- 1)*(q + 1)*(5*q + 2)/2
Let x = -41 + 62. Let y(k) = -7*k**2 + 13*k - 2. Let r(d) = -36*d**2 + 66*d - 9. Let s(i) = x*y(i) - 4*r(i). Factor s(z).
-3*(z - 2)*(z - 1)
Factor 107 + 4*z**2 + 19*z + 9*z - 30 - 29.
4*(z + 3)*(z + 4)
What is m in 1/5*m**4 + 0*m + 0 - 1/5*m**5 + 4/5*m**3 - 4/5*m**2 = 0?
-2, 0, 1, 2
Suppose -3*z - 2*y + 9 = 0, 3*z = 6*y - 10*y + 9. Determine l so that 3/4*l**z + 3/2 - 3/8*l**4 - 3*l + 9/8*l**2 = 0.
-2, 1, 2
Let v(a) be the second derivative of a**8/3780 + a**7/405 - 31*a**6/6480 + a**5/270 + 7*a**4/12 - 9*a. Let y(q) be the third derivative of v(q). Factor y(z).
(z + 4)*(4*z - 1)**2/9
Let a be 3 + 44 + -4 - -1. Let y = -41 + a. Factor 3/2*l + 3/2*l**2 + 0 - 3/2*l**y - 3/2*l**4.
-3*l*(l - 1)*(l + 1)**2/2
Suppose -43/6*k - 1/6*k**2 + 22/3 = 0. Calculate k.
-44, 1
Let n = -5129 + 5132. Suppose 16/7*g + 12/7*g**n + 0 - 24/7*g**2 - 2/7*g**4 = 0. What is g?
0, 2
Find c, given that -20/7*c + 24/7 - 4/7*c**2 = 0.
-6, 1
Let r be 1/(-3) - ((-1388)/(-12) - 5). Let q = -109 - r. Solve 0*k**3 - 1/6*k**4 + 0 + 1/3*k + 1/2*k**q = 0 for k.
-1, 0, 2
Let m(r) be the third derivative of 0 - 1/15*r**6 + 2/105*r**7 + 5*r**2 + 0*r + 0*r**4 + 1/15*r**5 + 0*r**3. Factor m(u).
4*u**2*(u - 1)**2
Let l(z) be the third derivative of z**8/10080 + z**7/630 + z**6/90 - 7*z**5/60 - 16*z**2. Let u(y) be the third derivative of l(y). Factor u(x).
2*(x + 2)**2
Let o(r) be the first derivative of -r**7/273 - 2*r**6/65 - r**5/10 - 2*r**4/13 - 4*r**3/39 - 23*r + 12. Let p(j) be the first derivative of o(j). Factor p(m).
-2*m*(m + 1)**2*(m + 2)**2/13
Let i(r) be the third derivative of 1/40*r**6 - r**3 + 2*r**2 + 0*r + 3/20*r**5 - 1/70*r**7 + 0 - 1/8*r**4. Factor i(q).
-3*(q - 2)*(q - 1)*(q + 1)**2
Let l(p) be the first derivative of -1331*p**4/8 - 242*p**3 - 132*p**2 - 32*p - 89. Solve l(z) = 0 for z.
-4/11
Let s be (-24)/(-9)*18/3. Let q = -12 + s. Solve 3*p**5 - 6*p**3 + 2*p**4 + 3 + 3*p + p**q + 0 - 6*p**2 + 0*p**4 = 0 for p.
-1, 1
Factor 32/3 - 8/3*r - 20/3*r**2 - 4/3*r**3.
-4*(r - 1)*(r + 2)*(r + 4)/3
Factor 54*j - 23*j**2 + 195 + 534 + 24*j**2.
(j + 27)**2
Let z(v) = 4*v**2 - 222*v - 14636. Let x(n) = -n**2 - 4*n - 1. Let f(a) = 10*x(a) + 2*z(a). Suppose f(l) = 0. What is l?
-121
Let b = -8882/5 + 1777. Let i(f) be the second derivative of -6*f**2 + 0 + 2*f + 3/4*f**4 + 2*f**3 - b*f**5 + 1/10*f**6. Determine h, given that i(h) = 0.
-1, 1, 2
Factor -36 - 61/4*y**2 + 159/2*y + 1/2*y**3.
(y - 24)*(y - 6)*(2*y - 1)/4
Let r(v) be the third derivative of v**6/12 - v**5/10 - v**4/6 + 2*v**2 - 63. Factor r(d).
2*d*(d - 1)*(5*d + 2)
Let i(p) be the second derivative of p**10/15120 + p**9/7560 - p**8/3360 - p**7/1260 + p**4/6 - 14*p. Let y(q) be the third derivative of i(q). Factor y(u).
2*u**2*(u - 1)*(u + 1)**2
Suppose 0 = 50*b - 134*b + 156 + 516. Factor -b*c - 4/3*c**2 + 28/3.
-4*(c - 1)*(c + 7)/3
Let o(l) = -3*l**2 + 102*l - 774. Let u(a) = -9*a**2 + 305*a - 2321. Let x(r) = -17*o(r) + 6*u(r). Let x(d) = 0. Calculate d.
16
Let v(j) be the first derivative of j**3/8 - 21*j**2/8 + 20. Determine k so that v(k) = 0.
0, 14
Let l(w) = -w**2 - 13*w + 3. Let v be l(-12). Factor 3 + 18*s**2 - v - 15*s - 21*s**2.
-3*(s + 1)*(s + 4)
Factor -17*a**3 + 8025*a**4 - 7*a**3 + 13*a**2 - 32*a - 8021*a**4 + 35*a**2.
4*a*(a - 2)**3
Let z(f) = f**4 - f**2 - f - 2. Let t(h) = 4*h**4 - 24*h**3 + 70*h + 36. Let s(i) = t(i) - 6*z(i). Factor s(d).
-2*(d - 2)*(d + 1)**2*(d + 12)
Factor 3/7*o**4 - 12/7*o + 0 + 0*o**2 + 9/7*o**3.
3*o*(o - 1)*(o + 2)**2/7
Let i(p) = -3*p**3 - 3*p**2 + 9*p + 18. Let u(z) = -6*z**3 - 7*z**2 + 20*z + 36. Let n(a) = -5*i(a) + 3*u(a). Factor n(w).
-3*(w - 2)*(w + 1)*(w + 3)
Let d(v) = 15*v**4 + 15*v**3 - 98*v**2 - 195*v - 97. Let q(o) = 5*o**4 + 5*o**3 - 33*o**2 - 65*o - 32. Let h(y) = -2*d(y) + 7*q(y). Factor h(c).
5*(c - 3)*(c + 1)**2*(c + 2)
Let u(p) be the first derivative of -4/21*p**3 + 0*p**5 + 1/2*p**4 + 0*p - 3/7*p**6 + 0*p**2 + 12. What is s in u(s) = 0?
-1, 0, 1/3, 2/3
Let 18/5*h**2 + 13/5*h**3 - 4/5*h - 4/5*h**4 - 3/5*h**5 - 8/5 = 0. Calculate h.
-2, -1, 2/3, 2
Let w = 61303 - 428034/7. Let h = -155 + w. Let h*q**3 + 0*q**2 - 2/7*q + 0 = 0. What is q?
-1, 0, 1
Let s be 3/((-3)/15 + (-13)/10). Let j be (-1)/s + (-6 - (-206)/36). Factor 4/9*g - j*g**2 - 2/9.
-2*(g - 1)**2/9
Let h(i) be the first derivative of i**6/42 - i**5/35 - 2*i**4/7 + 4*i**3/7 + 38. Factor h(c).
c**2*(c - 2)**2*(c + 3)/7
Find i, given that -6/5*i**2 - 2/5*i**3 + 2/5*i**4 + 4/5 + 2/5*i = 0.
-1, 1, 2
Let g = -1/633 - -427/3165. Let k(h) be the second derivative of 7*h + 0*h**3 - 1/3*h**4 + 0*h**2 + 0*h**5 + g*h**6 + 0. Solve k(m) = 0 for m.
-1, 0, 1
Let l(f) be the first derivative of -f**6/24 - 3*f**5/20 + f**3/3 + 28. Solve l(a) = 0 for a.
-2, 0, 1
Let r = 34 - 31. Solve 3*b - 3*b + 0*b**3 + b**2 + b**r = 0.
-1, 0
Find v, given that 0 + 56/3*v + 188/3*v**4 - 104/3*v**2 + 10*v**5 - 170/3*v**3 = 0.
-7, -2/3, 0, 2/5, 1
Suppose 0 = 3*q - c - 5, -39 + 29 = -3*q - 4*c. Suppose -16/7*s**q + 16/7*s + 0 + 4/7*s**3 = 0. What is s?
0, 2
Factor 37/3*v + 1/6*v**2 + 1369/6.
(v + 37)**2/6
Let -775*c**2 - 40*c + 386*c**2 - 100 + 385*c**2 = 0. Calculate c.
-5
Suppose -5*n = 2*z - 85, 4*z - 7*n + 2*n - 185 = 0. Let w = 47 - z. Factor -1/2*f**5 + w - 4*f + 1/2*f**2 - 1/2*f**4 + 5/2*f**3.
-(f - 1)**3*(f + 2)**2/2
Let t(a) = -2*a**2 + 27*a + 7. Let d(u) = -u**2 + u. Let l(m) = -5*d(m) + t(m). Suppose l(n) = 0. Calculate n.
-7, -1/3
Let p(t) be the second derivative of 7/2*t**3 + 33*t + 0 - 2/5*t**6 + 3*t**2 + 3/4*t**4 - 6/5*t**5. Suppose p(j) = 0. What is j?
-2, -1/2, 1
Let m = 184/27 + -812/135. Determine w, given that -32/5*w - 4/5*w**5 - m*w**4 + 16/5 + 4/5*w**2 + 4*w**3 = 0.
-2, 1
Let q(m) be the first derivative of 0*m**3 + 5 - 1/27*m**4 + 1/30*m**5 - 2*m - 1/135*m**6 + 0*m**2. Let b(g) be the first derivative of q(g). Factor b(t).
-2*t**2*(t - 2)*(t - 1)/9
Let n(x) be the first derivative of 2/3*x**3 - x**2 + 0*x - 8. Factor n(k).
2*k*(k - 1)
Suppose 20 = -5*d + 19*w - 14*w, -5*w + 44 = 3*d. Factor -9/4*o**5 - 3/2*o + 0 + 33/4*o**4 - 45/4*o**d + 27/4*o**2.
-3*o*(o - 1)**3*(3*o - 2)/4
Let n(q) be the second derivative of -q**6/10 - 9*q**5/20 + 5*q**4/4 + 3*q**3/2 - 6*q**2 + 12*q - 1. Suppose n(l) = 0. Calculate l.
-4, -1, 1
Suppose -4*p = -139 + 1199. Let b = p + 531/2. Factor -b*l + 0 + 1/2*l**2.
l*(l - 1)/2
Find d, given that 3*d**5 + 232*d**3 + 238*d**3 - 43 - 51*d**2 + 15*d**4 - 27*d - 461*d**3 + 7 - 57*d = 0.
-3, -2, -1, 2
Let -1/9*x**3 + 0 - 1/9*x**2 + 2/9*x = 0. Calculate x.
-2, 0, 1
Let v be (3 - (-1 + -1)) + 3. Let f be (v/6)/(9/54). Factor 5*z**2 + 5*z + f - 3*z**2 - 2*z + 5*z.
2*(z + 2)**2
Let g(o) be the third derivative of 2*o**7/315 + 2*o**6/45 - 2*o**5/45 - 2*o**4/3 + 2*o**3 - 2*o**2 + 10*o. Solve g(i) = 0.
-3, 1
Suppose 3*d = -6*h + 10*h + 4, 3*d = 5*h + 2. Let q(k) be the first derivative of 10 + 3/14*k**h - 2/7*k + 2/21*k**3. Find i such that q(i) = 0.
-2, 1/2
Let x(a) be the second derivative of -2/75*a**6 + 0*a**2 + 0 + 2/15*a**3 - 1/5*a**4 - 36*a + 3/25*a**5. Factor x(l).
-4*l*(l - 1)**3/5
Let a(v) = 3*v + 17. Let o be a(-5). Let 2*p**2 + p**2 - 5*p**o - 2*p + 2 + 2*p**3 = 0. Calculate p.
-1, 1
Let f = 719/42 + -221/14. Find g, given that 0*g - 4/3*g**5 + 0*g**4 + f*g**3 + 0*g**2 + 0 = 0.
-1, 0, 1
Let m(s) be the third derivative of -s**9/30240 + s**8/4480 - s**7/2520 - 11*s**4/24 + 9*s**2. Let i(n) be the second derivative of m(n). What is f in i(f) = 0?
0, 1, 2
Let i(y) be the first derivative of -10*y - 5/8*y**4 - 25/6*y**3 - 10*y**2 + 16. Factor i(k).
-5*(k + 1)*(k + 2)**2/2
Let g(l) be the third derivative of 1/315*l**7 + 0*l**3 - 1/60*l**6 + 0 - 1/18*l**4 + 1/504*l**8 + 0*l - 13*l**2 - 1/18*l**5. Find r such that g(r) = 0.
-1, 0, 2
Let i(d) be the third derivative of d**8/60480 - d**7/2520 + d**6/432 - 4*d**5/15 + 7*d**2. Let g(m) be the third derivative of i(m). Factor g(y).
(y - 5)*(y - 1)/3
Let j be -2*1*91/(-637). Let 4/7 + 2/7*t**3 - 2/7*t + j*t**4 - 6/7*t**2 = 0. What is t?
-2, -1, 1
Factor -36*u**2 + 505*u - 2*u**3 - 21 - 535*u + 89.
-2*(u - 1)*(u + 2)*(u + 17)
Let g(w) be the third derivative of -1/45*w**5 - 1/180*w**6 + 1/36*w**4 + 0 - 14*w**2 + 2/9*w**3 + 0*w. Let g(i) = 0. What is i?
-2, -1, 1
Let v(l) = -l**2 - 80*l - 576. Let b be v(-8). Factor 