- 356. Let a = 277/3 - v. Let -a*r**2 + 2/3*r + 0 = 0. What is r?
0, 2
Let j(d) = -8*d**3 + 12*d**2 - 6*d + 6. Let i(h) = h**3 + h**2 - h + 1. Let l(w) = 6*i(w) - j(w). Factor l(m).
2*m**2*(7*m - 3)
Suppose -2*l + p + 11 = l, -4*p = 5*l - 24. Suppose 0 = h - s + 3, l + 16 = 5*h + 2*s. Factor 2 - z**h - 9*z**2 + 8*z**2.
-2*(z - 1)*(z + 1)
Factor -2/15*v**2 + 284/15*v - 10082/15.
-2*(v - 71)**2/15
Let x(o) be the third derivative of o**6/540 - o**5/90 - o**4/27 + 4*o**3/9 - 2*o**2 - 34. Find d, given that x(d) = 0.
-2, 2, 3
Let z(a) be the second derivative of 0 - 15*a + 1/25*a**5 - 2/15*a**3 - 4/5*a**2 + 2/15*a**4. Factor z(c).
4*(c - 1)*(c + 1)*(c + 2)/5
Let v(x) be the first derivative of x**5 + 245*x**4/4 + 1360*x**3 + 12160*x**2 + 20480*x + 235. Determine q, given that v(q) = 0.
-16, -1
Let y(q) = -220*q**3 - 760*q**2 - 868*q - 264. Let r(d) = -20*d**3 - 69*d**2 - 79*d - 24. Let l(h) = 32*r(h) - 3*y(h). Factor l(v).
4*(v + 1)*(v + 2)*(5*v + 3)
Let g(a) be the third derivative of -a**7/5880 - a**6/1260 - a**5/840 + 5*a**3/6 + 4*a**2. Let v(s) be the first derivative of g(s). Find f such that v(f) = 0.
-1, 0
Let p(v) be the first derivative of -2*v**3/15 + 7*v**2/5 - 12*v/5 - 74. Let p(n) = 0. What is n?
1, 6
Solve 1/5*c**4 + 0 + c**3 + 3/5*c**2 - 9/5*c = 0.
-3, 0, 1
Suppose -22*c + 172 = 64*c. What is r in 0 + 1/3*r - 3/2*r**c = 0?
0, 2/9
Suppose a - 2 = 3*p, 13*a = 9*a - 2*p + 8. Let o(g) be the second derivative of -5*g + 0 - 4/3*g**a - 5/9*g**3 - 1/18*g**4. Solve o(h) = 0 for h.
-4, -1
Let k(d) be the second derivative of -d**7/399 - d**6/57 - 7*d**5/190 - d**4/38 + 3*d + 4. Factor k(w).
-2*w**2*(w + 1)**2*(w + 3)/19
Let f be (0 + (-2 - 0))/(100/(-75)). Factor 0*h**3 + 3*h**2 - f*h**5 + 0 - 3*h**4 + 3/2*h.
-3*h*(h - 1)*(h + 1)**3/2
Let q be -1*(1074/180 - 6). Let w(u) be the second derivative of q*u**3 + 5*u - 1/100*u**5 - 1/10*u**2 + 1/60*u**4 + 0. Factor w(t).
-(t - 1)**2*(t + 1)/5
Suppose g - 74 = 3*k, k + 193 = 2*g + 4*k. Let y = 91 - g. Factor 0 + 1/5*v - 1/5*v**y.
-v*(v - 1)/5
Factor -3*f**3 + 0*f**2 - 1/2*f**4 + 0 + 16*f.
-f*(f - 2)*(f + 4)**2/2
What is z in 0*z + 4/15*z**2 + 2/5*z**3 + 0 + 2/15*z**4 = 0?
-2, -1, 0
Let v be (-30)/(-9) + 2/3. Solve -v*c + 9 + 29*c**2 + c - 35*c**2 = 0 for c.
-3/2, 1
Let p be 2/28*2*670/45. Let h = p + -14/9. What is m in -2/7*m**2 + h*m - 2/7 = 0?
1
Let u = -223/168 - -205/56. Let 5/3*a**3 - u*a**2 + 0 + 2/3*a = 0. Calculate a.
0, 2/5, 1
Suppose -392 = -10*y - 186*y. Find p such that 13/3*p + 2/3*p**3 - 8/3*p**4 + 7*p**y + 2/3 = 0.
-1, -1/2, -1/4, 2
Let g(u) be the second derivative of -u**7/14 + u**6/10 + 3*u**5/20 - u**4/4 - 108*u. Factor g(p).
-3*p**2*(p - 1)**2*(p + 1)
Let -a**4 - 13*a**3 - a**4 - 16*a**3 + 13*a**3 - 14*a**2 = 0. What is a?
-7, -1, 0
Let y(p) be the first derivative of -2450*p**6/3 - 85876*p**5 + 148664*p**4 - 303968*p**3/3 + 34144*p**2 - 5696*p + 637. Solve y(i) = 0.
-89, 2/7, 2/5
Suppose -2*n + 3 = -n. Let u = -81 + 85. Factor u - n*k + 2*k - 2*k**2 - k.
-2*(k - 1)*(k + 2)
Let d(z) = 193*z**2 - 1 + 4*z - 194*z**2 - 4*z + 2*z. Let i(c) = -c**3 + 3*c**2 - 3*c + 1. Let t(h) = 15*d(h) + 3*i(h). Factor t(r).
-3*(r - 1)**2*(r + 4)
Let q = -64 - -194/3. Let o = -888 + 1803/2. Solve 0 - q*f - 157/6*f**3 + 22/3*f**2 - o*f**5 + 33*f**4 = 0.
0, 2/9, 1
Solve 0 + 0*c + 2/9*c**4 - 34/9*c**3 - 4*c**2 = 0 for c.
-1, 0, 18
Let g = 10738/19 - 564. Solve -g*j + 8/19 - 6/19*j**2 = 0 for j.
-4, 1/3
Suppose 3*q - 2*u - 7 = 0, 4*q - 15 = 16*u - 19*u. Find r such that 2/3*r**q + 0*r**2 - 2/3*r + 0 = 0.
-1, 0, 1
Suppose -23*y = -54*y. Factor 0*v + 23/6*v**3 - v**2 + y - 7/6*v**4.
-v**2*(v - 3)*(7*v - 2)/6
Let t(v) be the first derivative of 2/7*v**2 + 15 + 3/7*v + 1/21*v**3. Solve t(i) = 0 for i.
-3, -1
Factor -54*z**3 - 183/2*z - 288*z**2 - 15/2.
-3*(z + 5)*(6*z + 1)**2/2
Let t(x) be the first derivative of -x**4/6 + x**3/3 + 7*x + 10. Let i(g) be the first derivative of t(g). Factor i(a).
-2*a*(a - 1)
Let r(h) be the third derivative of 0*h + 1/630*h**7 + 0 - 1/60*h**5 + 2*h**2 + 1/72*h**4 - 1/360*h**6 + 1/9*h**3. Factor r(f).
(f - 2)*(f - 1)*(f + 1)**2/3
Let s(i) be the second derivative of 17*i + 0*i**2 + 3/4*i**4 - 3/20*i**5 - 1/42*i**7 + 0*i**3 - 1/6*i**6 + 0. Factor s(m).
-m**2*(m - 1)*(m + 3)**2
Suppose -7*s + 6*s + 10 = 0. Suppose d - 5*k = 27, 2*d - k + 1 - s = 0. Find p, given that -p - p + 1 - p + d*p**2 = 0.
1/2, 1
Let v(n) = n + 1. Let g be v(-3). Let c be (g/3)/(2/(-6)). Factor c*a**2 - a**3 + 0*a**3 + a**5 - a**4 - a**2 + 0*a**2.
a**2*(a - 1)**2*(a + 1)
Suppose -2*n = 2*n + 64. Let m = n + 18. Let -20*j**m - 3 + 2 - 16*j + 5 = 0. Calculate j.
-1, 1/5
Let q = -70 - -74. Suppose q*p + 1 = 9. Factor 14/5*y**5 + 0*y + 22/5*y**3 + 0 + 4/5*y**p + 32/5*y**4.
2*y**2*(y + 1)**2*(7*y + 2)/5
Let i(q) = 11*q**2 - 23*q + 6. Let l(w) = -w**2 + w. Let x(r) = -i(r) - 2*l(r). Suppose x(m) = 0. Calculate m.
1/3, 2
Let q = 139450/7 + -19921. Solve -3/7*s**4 + 0 - 3/7*s**3 + q*s**5 + 3/7*s**2 + 0*s = 0 for s.
-1, 0, 1
Solve -9/7*g**4 + 3*g**2 + 9/7*g**3 + 0 - 18/7*g - 3/7*g**5 = 0 for g.
-3, -2, 0, 1
Factor 253/8*y**3 + 49/8*y + 9/2*y**5 + 39/2*y**4 + 0 + 91/4*y**2.
y*(y + 1)**2*(6*y + 7)**2/8
Let c(j) = -253*j - 4299. Let n be c(-17). Let 1/3*u + 2/3 - 1/3*u**n = 0. What is u?
-1, 2
Let y(m) be the third derivative of 7/120*m**4 - 1/75*m**5 + 0 - 33*m**2 + 0*m + 1/15*m**3. Factor y(r).
-(r - 2)*(4*r + 1)/5
Let n(b) be the second derivative of 2/9*b**3 - 20*b - 1/6*b**4 + 0 + 1/30*b**5 + 0*b**2. Factor n(w).
2*w*(w - 2)*(w - 1)/3
Let t = -26 - -29. Find q such that 6*q**2 - 3*q**2 - 5*q**3 - q - q**t + 4*q = 0.
-1/2, 0, 1
Let y = 86 - 83. Find b, given that -14*b**2 + 0*b**y + 2*b**2 + b**3 + 2*b**2 + 25*b = 0.
0, 5
Let q(f) = -35*f + 5819. Let y be q(166). Suppose -y*g - 3/4*g**2 + 39/4 = 0. What is g?
-13, 1
Let d be (-24)/18*(-12)/8. Suppose -53 + 6*u - 28*u - u**d - 68 = 0. Calculate u.
-11
Let g be (-394)/(-102) + 0 - 16/4. Let s = g - -311/408. Factor s*l**4 - 5/8*l**2 + 0 + 1/4*l**3 - 1/4*l.
l*(l - 1)*(l + 1)*(5*l + 2)/8
Let g(o) = -2*o**2 - 35*o - 8. Let p be g(-17). What is w in -20*w**2 + w - p*w - 36*w**2 + 4 + 44*w**2 = 0?
-1, 1/3
Let t = 10 + -8. Let x be (3 - 3 - -2) + t. Factor -3*b**4 + 2*b + 5*b**x + 5*b**4 + 10*b**2 - b**4 + 14*b**3.
2*b*(b + 1)**2*(3*b + 1)
Let l = -3/487 - -5877/5357. Factor 0 - 6/11*a**5 + 0*a**2 - 6/11*a + l*a**3 + 0*a**4.
-6*a*(a - 1)**2*(a + 1)**2/11
Suppose -g - 8 = -0. Let c be 6/4*g/(-20). Determine z so that 0*z**3 - c*z**2 - 2/5*z + 0 + 1/5*z**4 = 0.
-1, 0, 2
Suppose 0 = 11*k + 3*k - 14. Let w(y) = 15*y**2 + 42*y + 63. Let u(r) = -r**2 - r + 1. Let n(d) = k*w(d) + 12*u(d). Suppose n(h) = 0. Calculate h.
-5
Let v be 11793*4/(-36)*-3. Find d such that 52*d + 0*d**2 - v + 2*d**2 + 4269 = 0.
-13
Factor -8 + 2038*g**3 - 2036*g**3 + 9*g + 7*g - 10*g**2.
2*(g - 2)**2*(g - 1)
Factor 7/2*i**2 - 1/3*i**3 - 4 - 37/6*i.
-(i - 8)*(i - 3)*(2*i + 1)/6
Let z(s) be the first derivative of -s**5/15 - 5*s**4/12 - s**3/3 + 5*s**2/6 + 4*s/3 - 116. Factor z(a).
-(a - 1)*(a + 1)**2*(a + 4)/3
Let m(g) be the third derivative of -g**6/120 - g**5/10 - 3*g**4/8 + 2*g**3/3 + 10*g**2. Let p(q) be the first derivative of m(q). Factor p(u).
-3*(u + 1)*(u + 3)
Let y = -723 + 729. Let o(b) be the first derivative of -2 + 0*b**5 + 0*b**3 + 0*b - 2/3*b**2 - 2/9*b**y + 2/3*b**4. What is r in o(r) = 0?
-1, 0, 1
Factor -19/2*i - 6 - 4*i**2 - 1/2*i**3.
-(i + 1)*(i + 3)*(i + 4)/2
Let r(l) = l**3 + 18*l**2 - 18*l + 17. Let n be r(-19). Let h be 0 - 1 - 6/n. Find q, given that q - 102*q**h - 7*q + 98*q**2 - q**3 + 3*q = 0.
-3, -1, 0
Let q = -279 - -283. Let i(b) be the second derivative of 1/3*b**3 + 1/18*b**q + 0*b**2 + 6*b + 0. Factor i(n).
2*n*(n + 3)/3
Let y(l) be the second derivative of l**6/135 + l**5/45 - l**4/54 - 2*l**3/27 + 45*l + 2. Factor y(d).
2*d*(d - 1)*(d + 1)*(d + 2)/9
Let o(n) = 4*n**2 - 5*n - 5. Let y(c) = -2*c + 57*c**2 - 123*c**2 + 65*c**2 + 1 + 3*c. Let v(l) = -2*o(l) - 10*y(l). Let v(a) = 0. Calculate a.
0
Let n(r) be the third derivative of 1/60*r**5 + 11*r**2 + 0 + 1/12*r**4 + 0*r + 0*r**3. Determine i so that n(i) = 0.
-2, 0
Let n(i) = -2*i**3 + i**2 - i - 1. Let o(y) = -3*y**4 - 45*y**3 - 111*y**2 - 45*y + 6. Let v(s) = -6*n(s) - o(s). Factor v(u).
3*u*(u + 1)**2*(u + 