. What is i?
0, 2
Let a be (8*(-6)/(-192))/1 + 5/10. Solve -9/4*d**3 - 3/2*d**4 - a*d**2 + 0*d + 0 = 0 for d.
-1, -1/2, 0
Let w(m) = -13*m**3 - 112*m**2 - 241*m - 46. Let z(l) = -38*l**3 - 331*l**2 - 724*l - 139. Let r(c) = 11*w(c) - 4*z(c). Solve r(f) = 0.
-5, -2/9
Let d = 46197 - 509558/11. Let u = d - -127. Factor u*b - 2/11*b**3 + 0*b**2 + 4/11.
-2*(b - 2)*(b + 1)**2/11
Let k be 608/114 - (-1 + 1). Let 20/3*h**5 + 8/3 + 20/3*h + 8/3*h**4 - 40/3*h**3 - k*h**2 = 0. Calculate h.
-1, -2/5, 1
Let j(w) be the third derivative of -w**6/24 + 3*w**5/2 - 175*w**4/8 + 490*w**3/3 - 377*w**2. Factor j(r).
-5*(r - 7)**2*(r - 4)
Let i be (-52)/(-21) + (-976)/(-1464). Suppose i*l**3 + 0 - 4/7*l**2 + 0*l - 4*l**4 = 0. Calculate l.
0, 2/7, 1/2
Determine w, given that 4*w**3 - 10*w**5 - 31*w**5 + 81*w**5 - 8*w**2 - 16*w**5 + 76*w**4 - 16*w**2 = 0.
-3, -2/3, 0, 1/2
Let q(b) = 4*b**3 - b**2 + 19*b. Let g be q(0). Factor -1/4*s + g - 1/4*s**3 - 1/2*s**2.
-s*(s + 1)**2/4
Let w be (-9)/15 - (-18)/10. Find h such that -4/5 + w*h + 2/5*h**2 - 6/5*h**3 + 2/5*h**4 = 0.
-1, 1, 2
Let o be (3 + 282/3)/1. Let r = o - 97. Factor 0 - 8/7*l**3 + 0*l + r*l**2 - 4/7*l**4.
-4*l**3*(l + 2)/7
Let x(s) be the third derivative of -s**5/240 + 11*s**4/48 + 2*s**3 - 3*s**2 - s. Let x(i) = 0. Calculate i.
-2, 24
Let k(c) be the third derivative of -c**5/15 + 31*c**4/3 + 42*c**3 + 2*c**2 - 54*c. Let k(f) = 0. Calculate f.
-1, 63
Suppose -4*d - 28 = 4*p, -3*d - 15 = -5*p + 2*d. Let c be (p - -10) + -2 + -1. Let -29*y**5 + 26*y**c + 5*y**3 - 2*y**3 = 0. Calculate y.
-1, 0, 1
Suppose k - 6*k - 5 = 0. Let i = -4 - k. Let y(r) = -2*r**2 + 6*r - 1. Let u(a) = -3*a**2 + 11*a - 1. Let h(d) = i*u(d) + 5*y(d). Factor h(o).
-(o + 1)*(o + 2)
Factor 10/9*h**2 + 0*h + 2/3*h**4 + 0 + 2*h**3 - 2/9*h**5.
-2*h**2*(h - 5)*(h + 1)**2/9
Let m be (6/(-5))/(42/(-140)). Let f be ((-270)/4)/(-9)*m/25. Solve -12/5*q**3 - 12/5*q**4 + f*q**2 + 6/5 + 3*q - 3/5*q**5 = 0 for q.
-2, -1, 1
Suppose 174*k - 172 = 131*k. Factor 1/3*r**5 + 0*r + 1/3*r**k + 0*r**3 + 0*r**2 + 0.
r**4*(r + 1)/3
Let x(g) be the third derivative of g**5/240 - 5*g**4/16 - 31*g**3/24 - 12*g**2 - 2. Suppose x(v) = 0. Calculate v.
-1, 31
Let a(w) be the first derivative of 2/3*w**3 - 14 + 0*w - w**2. Factor a(t).
2*t*(t - 1)
Let t(v) be the second derivative of -1/90*v**5 + v + 0*v**2 + 0 + 2/9*v**3 - 1/54*v**4. Find h such that t(h) = 0.
-3, 0, 2
Let y(x) = -5*x**2 + 15*x + 91. Let j be y(-3). Factor -j - 11/5*t - 7/5*t**2 - 1/5*t**3.
-(t + 1)**2*(t + 5)/5
Suppose 81 = 40*x + 1. What is q in -2*q + 3*q**2 + 1/2 + 1/2*q**4 - x*q**3 = 0?
1
Let v = -8473 + 8475. Factor 5/2 + 35/4*u - 5*u**v.
-5*(u - 2)*(4*u + 1)/4
Let v(r) = -4*r - 9. Let m(l) = 3*l + 10. Let w(p) = 3*m(p) + 2*v(p). Let t be w(6). Factor 3*s**2 - 21 + t*s + 12 + 36.
3*(s + 3)**2
Let h(w) = 5*w**3 - 60*w**2 + 8*w. Let o(p) = 8*p**3 - 120*p**2 + 14*p. Let x(z) = -7*h(z) + 4*o(z). Factor x(a).
-3*a**2*(a + 20)
Find u, given that 7*u**3 - 107 - 55*u + 11 - 550*u**2 - 30*u + 235*u**3 - 411*u = 0.
-4/11, 3
Let q = -578 + 60692/105. Let d(o) be the third derivative of 0*o**4 - 8*o**2 + 0 + 0*o**5 + 0*o**3 - 1/30*o**6 - q*o**7 + 0*o. Find m such that d(m) = 0.
-1, 0
Let v be 81/(-18)*((-4)/(-6))/(-1). Let c(k) be the second derivative of -1/30*k**5 + 2/9*k**4 - 5/9*k**v + 0 - k + 2/3*k**2. Factor c(j).
-2*(j - 2)*(j - 1)**2/3
Solve -20/7 + 18/7*c**2 - 2*c**3 + 2/7*c**4 + 2*c = 0.
-1, 1, 2, 5
Suppose 122*n - 4 = -4. Let u(z) be the second derivative of 1/6*z**3 + n + 0*z**2 + 3*z + 1/12*z**4. Factor u(f).
f*(f + 1)
Factor -98/3 + 7*o + 4*o**2 + 1/3*o**3.
(o - 2)*(o + 7)**2/3
Let j(u) be the first derivative of -u**4/4 + 2*u**3/3 + 7*u**2/2 + 4*u + 113. Solve j(z) = 0 for z.
-1, 4
Let s be 80/16 - -6*2/(-4). Factor 0*a**s - 1/3*a**4 + 0*a + 2/3*a**3 + 0.
-a**3*(a - 2)/3
Let s(y) be the third derivative of y**7/420 + 5*y**6/192 + 7*y**5/80 + 3*y**4/64 + y**2 + 6*y. Factor s(o).
o*(o + 3)**2*(4*o + 1)/8
Let h(y) be the first derivative of 2*y**3/21 + 124*y**2/7 + 246*y/7 + 1038. Suppose h(d) = 0. Calculate d.
-123, -1
Let s(w) be the third derivative of 0*w + 1/1512*w**8 + 1/945*w**7 + 2/27*w**4 - 4/27*w**3 - 6*w**2 + 0 - 1/270*w**5 - 1/108*w**6. Solve s(f) = 0.
-2, 1
Let j(s) be the third derivative of -s**8/10080 + s**6/360 + s**5/12 - 2*s**2. Let y(t) be the third derivative of j(t). Suppose y(u) = 0. What is u?
-1, 1
Factor 512/7 + 98*n**4 - 560*n**3 - 2816/7*n + 768*n**2.
2*(n - 4)*(7*n - 4)**3/7
Let a(u) be the third derivative of u**5/180 + 37*u**4/72 + 2*u**3 - 149*u**2. Find h such that a(h) = 0.
-36, -1
Let d(z) = 5*z**3 + 7*z**2 - 5*z - 15. Let r(u) = -4*u**3 - 7*u**2 + 4*u + 14. Let c(g) = 5*d(g) + 6*r(g). Let v be c(7). Factor 0*o + o - o**v + 2 - 2.
-o*(o - 1)
Let o(x) be the third derivative of 0*x + 0*x**3 + 0 - 1/280*x**6 + 0*x**4 - 11*x**2 + 1/140*x**5. Factor o(w).
-3*w**2*(w - 1)/7
Let n(b) be the third derivative of b**6/24 - 7*b**5/12 - 5*b**4/24 + 35*b**3/6 + 135*b**2. Determine l so that n(l) = 0.
-1, 1, 7
Let o be 2682/745 - 12/20. Find z such that 57/5*z + 38/5*z**o + 68/5*z**2 + 1/5*z**5 + 2*z**4 + 18/5 = 0.
-3, -2, -1
Let -540*x + 36*x**2 - 3/5*x**3 + 0 = 0. What is x?
0, 30
Let h be 4/14 - 1168/(-28). Let o(a) = h*a**2 - 3 - 45*a**2 + 3. Let m(u) = -u**2. Let i(c) = 6*m(c) - o(c). What is s in i(s) = 0?
0
Suppose 2*j + 69 = -279. Let v = j - -177. Determine o, given that -4/9*o**v - 2/9*o**4 + 4/9*o + 2/9 + 0*o**2 = 0.
-1, 1
Suppose 5*l - 6 = -r - 1, -2*l - 3*r - 11 = 0. Solve -5*c**l - 24*c + 53*c - 24*c = 0 for c.
0, 1
Let c = -1769 + 1772. Find o, given that 0*o**2 + 1/4*o**c - 1/4*o + 0 = 0.
-1, 0, 1
Let m(c) be the first derivative of 3*c**4/4 + 14*c**3 + 147*c**2/2 - 84. Solve m(v) = 0.
-7, 0
Let r(n) be the third derivative of -n**7/945 + n**6/135 + n**5/270 - n**4/27 - 35*n**2. Suppose r(u) = 0. Calculate u.
-1, 0, 1, 4
Let x(w) = -2*w - 10. Let f be x(-9). Suppose -5*l + l = -f. Solve 13*a**3 + 17*a - 19*a**3 + 20*a**l + 4 + 10*a**3 = 0 for a.
-4, -1/2
Suppose 4 - 93 = -k. Let a = 91 - k. Find y, given that 0 - 1/4*y**a + 3/4*y = 0.
0, 3
Let h(u) be the third derivative of u**5/300 - 7*u**4/30 - 29*u**3/30 - 2*u**2 - 3*u. Find l, given that h(l) = 0.
-1, 29
Let s be (24/42)/(((-24)/126)/(-2)). Let x(k) be the first derivative of 1/24*k**s + 0*k**2 + 5/16*k**4 + 1/6*k**3 - 13 + 1/5*k**5 + 0*k. Factor x(o).
o**2*(o + 1)**2*(o + 2)/4
Let b(d) = 5*d**4 + 10*d**3 + 11*d**2 - 3*d. Let f(t) = 21*t**4 + 39*t**3 + 46*t**2 - 11*t. Let q(s) = -26*b(s) + 6*f(s). Suppose q(n) = 0. What is n?
-6, -1, 0, 1/2
Let c(y) be the first derivative of y**4/16 + 11*y**3/12 + 4*y**2 + 7*y - 14. Factor c(d).
(d + 2)**2*(d + 7)/4
Let o = 405 - 400. Let x(n) be the second derivative of 0 - 1/27*n**3 + 0*n**4 + 0*n**2 + 1/90*n**o - 2*n. Factor x(w).
2*w*(w - 1)*(w + 1)/9
Suppose 9*k = 15 + 12. Factor 10*y**k - 5*y**5 + 0*y + 71*y**4 - 76*y**4 + 0*y.
-5*y**3*(y - 1)*(y + 2)
Let t(r) = 10*r**3 - 16*r - r**3 + 2 + 0*r**3 - 15*r**2. Let p(s) = s**2 + s + 1. Let i(h) = -6*p(h) - t(h). Determine n so that i(n) = 0.
-1, 2/3, 4/3
Let f(l) be the first derivative of -l**4/108 - l**3/18 - l**2/9 + 54*l + 35. Let m(d) be the first derivative of f(d). Solve m(y) = 0 for y.
-2, -1
Factor -24 - 138*s - 47*s**2 - 10*s**2 + 16*s**2 - 22*s**2.
-3*(s + 2)*(21*s + 4)
Let a(y) = -2 - 3*y**3 - 8*y - 8*y + 19*y. Let w(k) = 16*k**3 - 15*k + 10. Let r(b) = -11*a(b) - 2*w(b). Factor r(c).
(c - 1)**2*(c + 2)
Let v(r) = 4*r + 4*r + 1 + 2*r**2 + 4. Let h(p) = 16*p - 2*p**2 - 35*p + 11*p - 6. Let m(o) = 3*h(o) + 2*v(o). Suppose m(d) = 0. Calculate d.
-2
Let m(b) be the first derivative of 1/18*b**4 - 1 + 4/3*b**2 - 4/9*b**3 - 16/9*b. Factor m(w).
2*(w - 2)**3/9
Factor 0 - 2/3*o**3 + 4*o**2 - 6*o.
-2*o*(o - 3)**2/3
Let o be 3/1 + 1 - (4 - 3). Suppose 2*f + 6 = -2, -2*f = 5*y - 12. Solve 8*j**3 - j**2 - 4*j**o + y*j + 9*j**2 = 0 for j.
-1, 0
Let u(x) = 2*x**2 + 17*x + 15. Let i(f) = f**2 + 8*f + 7. Let m(z) = z**2 - 5*z - 3. Let r be m(4). Let q(y) = r*i(y) + 3*u(y). Factor q(s).
-(s + 1)*(s + 4)
Let -q**4 + 37309*q**2 - 24*q - 37283*q**2 - q**4 = 0. What is q?
-4, 0, 1, 3
Find p such that 120*p - 52*p**2 + 7*p**2 - 24*p**3 + 3*p**4 + 75 + 63*p**2 = 0.
-1, 5
Solve -3/2*u**2 + 2*u - 1/2*u**3 + 0 = 0 for u.
-4, 0