- c. Find i, given that 4*i**3 + i + 6*i**4 + 2*i - 7*i - 2*i**5 - n*i**2 + 6 + 2*i = 0.
-1, 1, 3
Let d be (-4)/(-10)*(26 + -31). Let b(s) = -s + 1. Let y(p) = -p + 7. Let z be y(8). Let t(x) = -x**2 + 5*x - 4. Let u(n) = d*b(n) + z*t(n). Factor u(v).
(v - 2)*(v - 1)
Let t(m) be the first derivative of -121*m**4 - 47 - 208*m**2 - 836/3*m**3 - 64*m. Factor t(c).
-4*(c + 1)*(11*c + 4)**2
Let -2 + 598*h**3 - 83*h**4 + 11*h**4 - 80*h + 42*h**4 + 44*h**2 + 2 = 0. What is h?
-2/5, 0, 1/3, 20
Let k be 90/(-81) - (196/(-63) + 2). Let h(d) be the third derivative of 1/12*d**5 + k*d**6 + 0*d**4 + 6*d**2 - 1/42*d**7 + 0 + 0*d + 0*d**3. Factor h(u).
-5*u**2*(u - 1)*(u + 1)
Suppose 91*b - 1260 - 115 = -184*b. Let 10/11*w**4 + 2/11*w**b + 0*w - 18/11*w**2 + 0 + 6/11*w**3 = 0. Calculate w.
-3, 0, 1
Factor 1/4*p**3 - 18 + 13/2*p**2 + 45/4*p.
(p - 1)*(p + 3)*(p + 24)/4
Let o(q) be the second derivative of -7*q**6/216 + q**5/8 - 5*q**4/36 + 20*q**3/3 - 48*q. Let n(z) be the second derivative of o(z). Factor n(i).
-5*(i - 1)*(7*i - 2)/3
Let o(k) be the third derivative of 0*k - 10*k**3 - 1 - 115/24*k**4 + 12*k**2 - 5/6*k**5 + 1/24*k**6. Determine m, given that o(m) = 0.
-1, 12
Let u(b) be the first derivative of b**6/1440 + 13*b**5/480 + 34*b**3/3 - 2*b + 10. Let k(y) be the third derivative of u(y). Let k(j) = 0. What is j?
-13, 0
Let m(v) be the third derivative of v**5/20 + 191*v**4/8 + 95*v**3 - 72*v**2. Determine d, given that m(d) = 0.
-190, -1
Let b be 80/(-24) + 3 + (-37)/(-3). Suppose -17*w - b*w = -11*w. Find d such that 2/5*d**3 + 0*d + w*d**2 + 0 = 0.
0
Factor -5*a**4 + 0*a**4 - 55*a**3 - 187*a + 31*a - 24*a - 179044*a**2 + 178864*a**2.
-5*a*(a + 2)*(a + 3)*(a + 6)
Let a(x) be the first derivative of -x**4/30 + 8*x**3/45 + x**2/3 + 1222. Factor a(i).
-2*i*(i - 5)*(i + 1)/15
Let h(r) be the first derivative of -2*r**5/5 + 77*r**4/2 + 7657. Solve h(n) = 0.
0, 77
Let k be (177/(-57) - -3)*(69 + 1). Let d = 738/95 + k. Factor 2/5*u - d*u**3 + 2/5 - 1/10*u**4 - 3/10*u**2.
-(u - 1)*(u + 1)*(u + 2)**2/10
Suppose 9*r + 31 = 67. Let u(p) be the second derivative of 0*p**3 - 9*p + 0 - 1/12*p**2 + 1/72*p**r. Factor u(b).
(b - 1)*(b + 1)/6
Let l(c) be the second derivative of c**4/3 + 7*c**3/3 + 6*c**2 - 5*c + 37. Factor l(g).
2*(g + 2)*(2*g + 3)
Factor 10*a**4 - 14*a**2 - 10*a**2 + 7*a**4 + 3*a**3 + 5*a**3 - 15*a**4.
2*a**2*(a - 2)*(a + 6)
Let k = 3220558/3 - 1073508. Factor -k + 12*o - 2/3*o**2.
-2*(o - 17)*(o - 1)/3
Let i(n) be the third derivative of n**5/30 - 911*n**4/3 + 3319684*n**3/3 + 181*n**2 - 2*n + 1. Factor i(u).
2*(u - 1822)**2
Let h(f) = 5*f**2 + 2*f + 1. Let n be h(-1). Let p be 203/(-29) + (-10)/(-1). Factor 17*i**3 - 7*i**p - 2*i**2 + 3*i**3 - 11*i**n.
-i**2*(i - 1)*(11*i - 2)
Find g, given that 5*g**5 + 775*g**2 - 2995*g + 200*g**3 + 12160 + 3184*g**2 + 5419*g + 13976*g + 2441*g**2 - 200*g**4 = 0.
-2, 8, 38
Let x(n) be the second derivative of -136 + 2*n + 47/3*n**3 + 1/12*n**4 + 2209/2*n**2. Suppose x(k) = 0. What is k?
-47
Let w(o) = o**2 + 564*o - 20330. Let t be w(34). Solve -1/2*p**5 + 0*p**t + 0*p + p**3 + 0 + 1/2*p**4 = 0 for p.
-1, 0, 2
Let i(g) be the third derivative of 0*g**4 + 0*g - 1/42*g**7 + 0*g**3 - 7/12*g**5 - 1/3*g**6 + 0 + 30*g**2. Suppose i(p) = 0. Calculate p.
-7, -1, 0
Let c(r) be the third derivative of -1936/21*r**3 - 22/21*r**4 - 1/210*r**5 - 107*r**2 + 0 + 0*r. Factor c(z).
-2*(z + 44)**2/7
Let z(p) = p**2 - 14*p + 20. Let o be z(14). Let a be (-8)/12 - (-41)/3. Factor 40 - 33*h + 5*h**3 + a*h + 0*h**3 - 50*h**2 + 5*h**5 + o*h**4.
5*(h - 1)**2*(h + 2)**3
Let s(w) be the third derivative of 0*w - 1/140*w**5 + 12*w**2 - 225/14*w**3 + 15/28*w**4 - 2. Solve s(l) = 0.
15
Let p(t) = 60*t**3 - 12070*t**2 - 136655*t - 404965. Let m(z) = 7*z**3 - 1342*z**2 - 15184*z - 44996. Let n(r) = -35*m(r) + 4*p(r). Factor n(x).
-5*(x + 6)**2*(x + 250)
Let -96*d**3 - 192*d**2 - 120*d**4 - 67*d**3 - 16*d - 364*d**4 - 497*d**3 = 0. What is d?
-1, -2/11, 0
Let t(l) be the first derivative of 5*l**4/4 - 470*l**3/3 + 1375*l**2/2 - 910*l + 1171. Find k such that t(k) = 0.
1, 2, 91
Let z(j) be the third derivative of 0 - 1/120*j**6 + 1/3*j**4 - 1/48*j**8 - 2*j**2 - 1/2*j**5 - 49*j + 1/7*j**7 + 0*j**3. Find y such that z(y) = 0.
-1, 0, 2/7, 1, 4
Let k(f) be the third derivative of 3*f**8/728 - 19*f**7/455 + 133*f**6/780 - 9*f**5/26 + 25*f**4/78 + 795*f**2. Determine m so that k(m) = 0.
0, 1, 5/3, 2
Let o(z) be the first derivative of z**6/21 - 2*z**5/35 - 3*z**4/7 - 488. Factor o(b).
2*b**3*(b - 3)*(b + 2)/7
Factor -844*g + 5959*g**3 - 984 - 28*g**2 - 61*g**2 - 95*g**2 - 5963*g**3.
-4*(g + 2)*(g + 3)*(g + 41)
Let o(h) be the first derivative of h**7/273 - h**6/195 - h**5/65 + 2*h - 14. Let i(r) be the first derivative of o(r). Factor i(q).
2*q**3*(q - 2)*(q + 1)/13
Let -18/7*z**3 + 90/7 + 183/7*z + 75/7*z**2 = 0. What is z?
-1, -5/6, 6
Let i(w) be the first derivative of 3*w**4/20 + 223*w**3/15 + 729*w**2/5 - 1072*w/5 + 9507. Let i(f) = 0. What is f?
-67, -8, 2/3
Suppose 0 = 5*j + 5*k - 15, -2*j - 5*k + 10 = 1. Factor 45 + 60*x - 60*x - 5*x**j.
-5*(x - 3)*(x + 3)
Let d(p) be the second derivative of p**4/12 + 23*p**3 + 405*p**2/2 - 7619*p. Factor d(q).
(q + 3)*(q + 135)
Factor 8860*g**2 - 900*g**3 - 2461*g**4 - 54080 + 1017*g**4 + 1039*g**4 + 10400*g.
-5*(g + 4)**2*(9*g - 26)**2
Suppose -3*j + 19 = 13. Let y(v) = -3 + 2 + 115*v**2 - 114*v**j. Let x(m) = -10*m**3 + 20*m**2 + 2*m - 12. Let t(o) = -2*x(o) + 12*y(o). Solve t(p) = 0 for p.
-3/5, 1
Let f = 60360/19 + -301762/95. Let 2/5*q**4 + 0 + 0*q - 4/5*q**3 + f*q**5 + 0*q**2 = 0. Calculate q.
-2, 0, 1
Factor -379/3 + 1/3*l**2 + 126*l.
(l - 1)*(l + 379)/3
Let u = 70782 - 70774. Factor 24/5 + 18/5*r**2 + 2/5*r**3 + u*r.
2*(r + 1)*(r + 2)*(r + 6)/5
Let i be (62/(-527)*-17)/3. What is k in 92/3*k**4 + 68/3*k**2 - 115/3*k**3 - 28/3*k**5 - 19/3*k + i = 0?
2/7, 1/2, 1
Let o(d) be the first derivative of -d**4/24 + 5*d**3/6 - 21*d**2/4 - 4*d - 1. Let f(j) be the first derivative of o(j). Factor f(k).
-(k - 7)*(k - 3)/2
Let 150*l - 674*l**2 - 674*l**2 + 394*l + 36992 + 1350*l**2 = 0. What is l?
-136
Let k(r) = r**3 + 21*r**2 + 49*r - 22. Let i be k(-19). Let u = 3007/13 + i. Find m such that -6/13*m - 2/13*m**2 - u = 0.
-2, -1
Let c(j) = -5*j - 98. Let y be c(-20). Factor 5 + 2*i**y + i**2 - 4 - 18*i + 15 - i**2.
2*(i - 8)*(i - 1)
Suppose 212 = 240*f - 242*f. Let o = 1168/11 + f. Factor 16/11*i**3 + 64/11*i - 32/11 - o*i**4 - 48/11*i**2.
-2*(i - 2)**4/11
Let p(x) = -30*x - 570. Let f be p(-19). Let q(j) be the first derivative of -7/2*j**4 + f*j + 6*j**2 + 38/3*j**3 - 27. Find m, given that q(m) = 0.
-2/7, 0, 3
Suppose -z - 40 = -21*z. Solve -25 - 56 + 5*y**z - 15 - 19 + 110*y = 0.
-23, 1
Let d be 1/(-3)*4/8*(-4 - -4). Let r(z) be the first derivative of -1/5*z**2 + 4/15*z**3 + 11 + d*z - 1/10*z**4. Suppose r(c) = 0. What is c?
0, 1
Let c = 174887/4 - 43721. What is h in -1/4*h**2 - 1/2 + c*h = 0?
1, 2
Find l, given that -2/11*l**2 + 312/11 - 98/11*l = 0.
-52, 3
What is q in 4/3*q**2 - 197/3*q + 49/3 = 0?
1/4, 49
Let i be (126/(-12) + 7)/(1007/(-76) + 8). Let -2*b**2 - 28/3*b - 16/3 + i*b**4 + 8/3*b**3 = 0. What is b?
-4, -1, 2
Let u(t) = -3*t**4 - 18*t**3 + 9. Let h(k) = -k**4 - 9*k**3 + 4. Let i be -14 - (0 + -5 + 0). Let a(r) = i*h(r) + 4*u(r). Let a(o) = 0. What is o?
0, 3
Suppose -2951*g + 2943*g + 88 = 0. Suppose 9*a - 25 = 2*a - w, 0 = a + 2*w - g. Factor 2/5*c**4 + 4/5 + 2/5*c - 2/5*c**a - 6/5*c**2.
2*(c - 2)*(c - 1)*(c + 1)**2/5
Let w(n) be the first derivative of -n**6/30 - 8*n**5/25 + 62*n**3/15 + 97*n**2/10 + 42*n/5 - 2062. Find s, given that w(s) = 0.
-7, -2, -1, 3
Suppose 0*l = 4*l - 12. Suppose -17*r + 0 = -8 - 26. Find s, given that -l*s**3 - 1318*s**4 + 18 + 1315*s**4 + 35*s**r - 14*s**2 + 39*s = 0.
-2, -1, 3
Let l be (13 + (-11506)/880)/(2/(-30)). Let y(i) be the first derivative of l*i**2 - 19 + 9/8*i**3 + 3/8*i. Determine m so that y(m) = 0.
-1/3
Let w(h) = -8*h**3 + 42*h**2 + 3*h + 5. Let u(f) = -7*f**3 + 36*f**2 + 3*f + 4. Let v(x) = -7*u(x) + 6*w(x). Factor v(z).
(z - 1)**2*(z + 2)
Let a(y) be the third derivative of 1/30*y**5 + 4/3*y**3 + 2*y**2 - 1/105*y**7 + 0*y + 1/12*y**6 - 1/168*y**8 - 27 - 2/3*y**4. Factor a(p).
-2*(p - 1)**3*(p + 2)**2
Let r(c) be the second derivative o