2
Let d(g) = 6*g**3 + 21*g**2 + 36*g + 15. Let b(v) = 11*v**3 + 43*v**2 + 72*v + 25. Let h(m) = -3*b(m) + 5*d(m). Let h(w) = 0. Calculate w.
-6, -2, 0
Let f(m) = -7*m**3 - 34*m**2 - 274*m - 591. Let n(r) = -19*r**3 - 101*r**2 - 824*r - 1772. Let y(x) = -8*f(x) + 3*n(x). Let y(j) = 0. What is j?
-14, -3
Let c(n) be the third derivative of n**6/60 + 4*n**5/15 + 11*n**4/12 - 20*n**3/3 + 100*n**2 - n. Solve c(m) = 0 for m.
-5, -4, 1
Suppose 2*r = 5*o - 1041, -24*o + 4*r = -19*o - 1037. Let y = 212 - o. Let 16*q**2 - 1 + 1/2*q - 8*q**y = 0. Calculate q.
-1/4, 1/4, 2
Let m be ((-16)/(-5) + 264/(-88))/(1/20). Let c(p) be the third derivative of -1/16*p**m + 0 + 0*p**3 + 0*p + 1/120*p**5 + 33*p**2. Solve c(r) = 0.
0, 3
Let j(k) be the second derivative of 3*k**5/20 - k**4 - 29*k**3/2 - 36*k**2 - 6394*k. Suppose j(b) = 0. What is b?
-3, -1, 8
Determine v, given that -9 + 17/2*v**2 + 1/2*v**4 - 11/2*v**3 + 11/2*v = 0.
-1, 1, 2, 9
Suppose 32 = -4*j + 44. Solve m - m**3 + 2*m**4 + m - 2*m**2 - 10*m**3 + 9*m**j = 0.
-1, 0, 1
Let m(f) = -6*f**3 + 42*f**2 - 82*f + 4. Let v(w) = 7*w**3 - 43*w**2 + 81*w - 6. Let h(k) = 3*m(k) + 2*v(k). Find o, given that h(o) = 0.
0, 3, 7
Let p = 112722 - 112720. Solve -72/13 - 2/13*u**p - 24/13*u = 0 for u.
-6
Let g(b) = 5*b**4 - 70*b**3 + 365*b**2 + 6860*b + 6400. Let z(y) = 3*y**3 + y**2 - y. Let v(c) = g(c) - 20*z(c). Factor v(j).
5*(j - 16)**2*(j + 1)*(j + 5)
Let r be ((-284)/28 + 10)*7/(-9). Let h(w) be the second derivative of r*w**3 + 0 - 1/60*w**5 + 12*w - 1/36*w**4 + 0*w**2. Suppose h(o) = 0. Calculate o.
-2, 0, 1
Let o(g) be the third derivative of -g**6/320 - 147*g**5/160 - 217*g**4/32 - 18*g**3 + 10*g**2 - 4. Factor o(z).
-3*(z + 1)*(z + 2)*(z + 144)/8
Let d(a) = a**2 + 39*a + 38. Let b be d(-1). Let z(q) be the first derivative of 0*q - 7/6*q**4 + b*q**2 - 1/9*q**6 - 4 - 2/3*q**3 + 34/45*q**5. Factor z(w).
-2*w**2*(w - 3)**2*(3*w + 1)/9
Suppose 2 = 5*a - 103. Let t = -451 - -494. Find f such that -t*f**3 + 1 + a*f**3 + 3*f**2 - 3*f + 21*f**3 = 0.
1
Find q such that -241 + 356*q**3 + 369*q - 1192*q**2 - 12*q**4 + 743*q + 152*q - 175 = 0.
2/3, 1, 2, 26
Determine x so that 1800*x + 10880/3 - 5/6*x**3 + 220*x**2 = 0.
-4, 272
Let a be 8/(-48) + (-4)/(-480)*2555. Let u(y) be the third derivative of -12*y**2 - 2197/6*y**3 + 1/120*y**6 + a*y**4 + 0 - 13/20*y**5 + 0*y. Solve u(b) = 0.
13
Suppose 0 = -10*l + 6*l. Suppose -3*g = -l*g - 6. Find m such that -3*m**g + 5*m**4 - 4*m**3 + 4*m**3 - 2*m**2 = 0.
-1, 0, 1
Let o(h) be the first derivative of 35*h**6/6 - 3*h**5/2 - 185*h**4/8 - 20*h**3 - 5*h**2 - 3545. Solve o(g) = 0.
-1, -1/2, -2/7, 0, 2
Suppose 62*i - 97*i = -47*i. Let a(k) be the second derivative of i + 0*k**2 + 1/5*k**4 + 16*k + 2/5*k**3 + 3/100*k**5. Factor a(t).
3*t*(t + 2)**2/5
Solve 4*j**2 - 5*j**3 - j**4 + 1/2*j**5 + 33/2*j + 9 = 0.
-2, -1, 3
Let p(z) be the second derivative of z**7/2520 - z**6/144 - 61*z**4/12 - 64*z + 2. Let x(a) be the third derivative of p(a). Factor x(r).
r*(r - 5)
Suppose -357*h**2 + 866*h**2 + 699*h**3 + 102*h**5 - 12*h - 39*h**5 - 48 + 402*h**4 - 113*h**2 = 0. Calculate h.
-4, -1, -2/3, 2/7
Let t(b) be the second derivative of b**4/30 - 17*b**3/15 - 38*b**2/5 - 224*b. Determine q, given that t(q) = 0.
-2, 19
Solve -48*h**2 + 2/5*h**5 + 248/5*h - 96/5 - 24/5*h**4 + 22*h**3 = 0.
1, 2, 3, 4
Let k be (6/9)/(4/72). Suppose k*l - 17*l = -180. Determine q, given that -33*q**2 + 4*q**2 - 59*q**2 + 30*q**3 - l + 2*q**3 - 4*q**4 + 96*q = 0.
1, 3
Let m(f) = 13*f**2 - 386*f - 1310. Let q(b) = 19*b**2 - 582*b - 1966. Let z(d) = 7*m(d) - 5*q(d). Factor z(v).
-4*(v - 55)*(v + 3)
Suppose 2 + 2 = 4*m - 4*u, 5*u - 7 = -m. Let t be m/(-6)*480/(-50). Find p, given that -t*p - 16/5 - 4/5*p**2 = 0.
-2
Suppose -3*u + 4*q + 460 = 0, -2*q + 4*q + 630 = 4*u. Suppose 5*b - u = 115. Factor -3*o**3 + b*o**5 + 61*o**5 - 113*o**5.
3*o**3*(o - 1)*(o + 1)
Let c(z) be the third derivative of 109*z**2 - 1/80*z**6 + 0*z**4 + 0*z - 1/140*z**7 + 1/20*z**5 + 0*z**3 + 0. Solve c(d) = 0 for d.
-2, 0, 1
Let d(f) = f**5 + f**4 + 2*f**3 - 4. Let o(s) = 6*s**5 + 2*s**4 + 8*s**3 + 12*s**2 - 8*s - 20. Let p(k) = 5*d(k) - o(k). Suppose p(a) = 0. What is a?
-2, 0, 1, 2
Factor 2032*v + 20*v**3 + 1229/3*v**2 - 1/3*v**4 + 4928/3.
-(v - 77)*(v + 1)*(v + 8)**2/3
Let x(d) be the second derivative of d**5/100 - 181*d**4/20 + 361*d**3/10 - 541*d**2/10 - 5513*d. Factor x(w).
(w - 541)*(w - 1)**2/5
Let d be 3057/2 - (1 - 5)/8. Let t = d + -1526. Factor -3/7*c**t - 6 + 81/7*c - 36/7*c**2.
-3*(c - 1)**2*(c + 14)/7
Let i(n) be the second derivative of -2*n**3 + 0 + 1/600*n**6 + 12*n + 0*n**4 - 1/200*n**5 + 0*n**2. Let o(t) be the second derivative of i(t). Factor o(y).
3*y*(y - 1)/5
Suppose 0 + 0 = -15*l. Find w, given that l*w**2 + 2*w**2 + 15*w + 10 + 0*w**2 + 3*w**2 = 0.
-2, -1
Let r(w) = -9*w**4 - 97*w**3 + 102*w**2 - 4*w + 4. Let t(f) = 100*f**4 + 1070*f**3 - 1125*f**2 + 45*f - 45. Let h(p) = 45*r(p) + 4*t(p). Factor h(s).
-5*s**2*(s - 1)*(s + 18)
Let d be ((-33)/15 - -1)/((-6)/100). Solve -16*n**3 - 20 + 19*n**3 - 4*n**3 + d*n**2 - 4*n**3 + 5*n = 0.
-1, 1, 4
Factor 179*q + 1139 + 1073 - 92*q**2 + 2*q**3 + 81*q - 2300 - 82*q.
2*(q - 44)*(q - 1)**2
Let u(b) = 13*b**4 - 44*b**3 + 23*b**2 - 11*b - 6. Let k(f) = -23*f**2 + 37*f - 14*f**4 + 5 - 18*f + 43*f**3 - 10*f. Let i(l) = -5*k(l) - 4*u(l). Factor i(h).
(h - 1)**2*(3*h - 1)*(6*h + 1)
Let z(l) = -2*l**5 - 8*l**4 - 6*l + 6. Suppose -265*s - 6 = -266*s. Let j(t) = 2*t**5 + 7*t**4 + 5*t - 5. Let c(p) = s*j(p) + 5*z(p). Factor c(g).
2*g**4*(g + 1)
Let o = -17227 + 17231. Let 1/2*v**o - v**3 + 0*v + 1/2*v**2 + 0 = 0. What is v?
0, 1
Let l(n) = 5*n + 66. Let y be l(-11). Suppose y + 26 + 16*j - 19 - 2*j**2 = 0. What is j?
-1, 9
Let j(g) be the second derivative of 1/5*g**4 + g + 0 + 0*g**3 + 0*g**2 - 1/70*g**7 + 21/100*g**5 + 1/25*g**6. Solve j(f) = 0.
-1, 0, 4
Let u = -362845/4 + 90721. Factor -9/2*z**4 + 3*z + 3/4*z**5 - 9*z**2 + 0 + u*z**3.
3*z*(z - 2)**2*(z - 1)**2/4
Let m(p) be the third derivative of 1/40*p**6 + 0*p**3 + 0 - 1/4*p**4 + 54*p + 2*p**2 - 7/60*p**5. Factor m(r).
r*(r - 3)*(3*r + 2)
Let c(p) = -2*p**3 - 30*p**2 - 2*p - 24. Let y be (-15)/((-3)/1 + 4). Let h be c(y). Factor 19*d**3 - 4*d**2 - 10*d**4 - 7*d**3 + 8 - 12*d + h*d**4.
-4*(d - 2)*(d - 1)**2*(d + 1)
Let b(j) be the third derivative of -5*j**8/112 + 37*j**7/70 + 23*j**6/20 - 41*j**5/5 - 13*j**4 + 32*j**3 + 46*j**2 + 9*j - 2. Find l, given that b(l) = 0.
-2, -1, 2/5, 2, 8
Let g = 10611 - 10611. Let i(z) be the second derivative of 3/5*z**5 + g*z**4 - 8*z + 0*z**2 + 1/14*z**7 + 0*z**3 + 1/2*z**6 + 0. Determine c so that i(c) = 0.
-4, -1, 0
Suppose -62*a + 221*a - 1250 = -932. Determine j, given that -12/7*j**a + 48/7 - 8/7*j + 2/7*j**3 = 0.
-2, 2, 6
Let x(y) = -y**2 + 21*y + 72. Let m be x(-3). Let o(l) be the second derivative of 1/12*l**4 + l**2 - 29*l + m + 1/2*l**3. Factor o(z).
(z + 1)*(z + 2)
Suppose 44*o - 525 = 2*o - 133*o. Let y be ((-54)/15)/(2 - 3). Factor -3/5*z**2 + o*z - y.
-3*(z - 3)*(z - 2)/5
Let y(v) = -20*v**5 - 34*v**4 + 191*v**3 - 225*v**2 + 126*v + 19. Let p(k) = -k**5 - k**4 + 4*k**3 + 1. Let w(c) = 38*p(c) - 2*y(c). Let w(d) = 0. Calculate d.
-21, 0, 1, 2, 3
Let k(b) be the third derivative of -b**5/105 + 11*b**4/3 + 208*b**3/7 + 269*b**2. Find r such that k(r) = 0.
-2, 156
Let h = -42 + 65. Let q be h/(-69) - (-1)/(3/13). Factor 4*b**3 + 19*b**q + b**3 - 24*b**4.
-5*b**3*(b - 1)
Let k(l) be the second derivative of -l**7/49 + 41*l**6/105 - 41*l**5/35 - 37*l**4/21 + 85*l**3/21 + 33*l**2/7 - 2079*l. Find j, given that k(j) = 0.
-1, -1/3, 1, 3, 11
Let s(m) = -m + 8. Let b be s(3). Let w(o) be the third derivative of -1/12*o**b + 0 + 0*o - 12*o**2 + 1/12*o**4 + 1/2*o**3. Let w(l) = 0. What is l?
-3/5, 1
Let j(h) = -54*h**2 + 3278*h - 782. Let q(r) = 11*r**2 - 656*r + 156. Let c(n) = -3*j(n) - 14*q(n). Factor c(s).
2*(s - 81)*(4*s - 1)
Let m(x) = -x**3 - 3*x**2 + 3*x - 8. Let w be m(-4). Let k be w/(6*(-14)/6). What is l in 8/7*l**2 - 8/7*l**4 - k*l**5 - 4/7*l**3 + 6/7*l + 0 = 0?
-3, -1, 0, 1
Let o(b) = -3*b**3 + 10*b**2 - 41*b + 2. Let d(j) = -2*j**3 - j**2 + 2*j + 1. Let t(n) = 4*d(n) - 2*o(n). Factor t(v).
-2*v*(v - 3)*(v + 15)
Let g(y) be the third derivative of y**7/2520 - y**6/216 - y**5/60 - 