1/225 - i. Suppose 0 - 1/2*n**3 + b*n**2 + n = 0. What is n?
-1, 0, 2
Determine q so that -892/9 + 2380/3*q + 64/9*q**3 - 4768/3*q**2 = 0.
1/4, 223
Suppose -1155*u - 1809 = -4119. Factor -3/4*l**u - 1/4*l - 3/4*l**3 + 0 - 1/4*l**4.
-l*(l + 1)**3/4
Let x(i) be the first derivative of 8/3*i**3 - 30*i**4 + 0*i**2 + 0*i - 14/3*i**6 + 114/5*i**5 + 209. Determine g so that x(g) = 0.
0, 1/14, 2
Let b = -101933 + 611605/6. Factor 0 + b*l - 1/6*l**2.
-l*(l - 7)/6
Let g(j) be the third derivative of j**5/270 + 17*j**4/54 + 208*j**3/27 - 1371*j**2. Factor g(b).
2*(b + 8)*(b + 26)/9
Let v = -203408 + 203411. What is a in -6*a - 20/3*a**2 - 2*a**v - 4/3 = 0?
-2, -1, -1/3
Factor -216/7 + 4/7*g**3 - 198/7*g - 30/7*g**2.
2*(g - 12)*(g + 3)*(2*g + 3)/7
Factor 544/3*q**3 + 536*q**2 + 1600/3*q + 4/3*q**4 + 532/3.
4*(q + 1)**3*(q + 133)/3
Let x(q) be the second derivative of -q**5/20 + 27*q**4/2 - 891*q**3/2 + 5832*q**2 - 147*q + 16. Factor x(k).
-(k - 144)*(k - 9)**2
Let p(z) be the first derivative of -5*z**6/18 - 2*z**5 + 5*z**4/2 + 140*z**3/9 - 75*z**2/2 + 30*z - 10664. Determine l so that p(l) = 0.
-6, -3, 1
Let c(u) be the first derivative of u**6/2 - 327*u**5/5 + 5823*u**4/2 - 42106*u**3 - 340881*u**2/2 + 455877*u + 2865. Factor c(r).
3*(r - 37)**3*(r - 1)*(r + 3)
Let m = 352 - 347. Solve -4*x**2 + x**4 + 14*x**3 + x**m - 7*x**3 - 11*x**3 = 0 for x.
-2, -1, 0, 2
Let r(u) be the first derivative of -4/5*u**2 - 3/5*u - 68 + 1/25*u**5 - 2/5*u**3 + 0*u**4. Factor r(b).
(b - 3)*(b + 1)**3/5
Let u = -103 - -183. Suppose -u*v + 76*v = -8. Find b such that 4*b**v - 17*b + 100 + 35*b + 22*b = 0.
-5
Let d(f) be the first derivative of f**8/5040 - f**7/2520 - f**6/1080 + f**5/360 - 35*f**3/3 + 103. Let u(h) be the third derivative of d(h). Factor u(a).
a*(a - 1)**2*(a + 1)/3
Let j(h) be the first derivative of h**6/6 - 11*h**5/5 + 43*h**4/4 - 77*h**3/3 + 32*h**2 - 20*h + 7557. Factor j(a).
(a - 5)*(a - 2)**2*(a - 1)**2
Let a(p) be the third derivative of -169*p**5/75 + 39*p**4 - 270*p**3 - 1976*p**2. Factor a(q).
-4*(13*q - 45)**2/5
Let z(j) be the first derivative of 6*j + 1/26*j**4 - 9 + 0*j**2 + 0*j**3 - 1/130*j**5. Let w(r) be the first derivative of z(r). What is i in w(i) = 0?
0, 3
Let v(n) be the third derivative of -n**6/144 + 17*n**5/360 - n**4/24 - 44*n**2 - 23*n. Factor v(t).
-t*(t - 3)*(5*t - 2)/6
Let g = 301/342 - -269/342. Determine z so that 4/3 + 1/3*z**4 - 5/3*z**2 + g*z**3 - 4/3*z - 1/3*z**5 = 0.
-2, -1, 1, 2
Let -1/4*j**4 - 111*j - 25/4*j**3 - 89/2*j**2 - 90 = 0. Calculate j.
-15, -6, -2
Let s(o) be the third derivative of -1/20*o**5 + 0 + 0*o**4 + 0*o + 0*o**3 - 55*o**2. Factor s(c).
-3*c**2
Let b = -6547 - -6551. Let o(n) be the second derivative of 0 + 2/9*n**3 + 1/12*n**5 + 13/36*n**b - 6*n - 2/3*n**2. Solve o(d) = 0.
-2, -1, 2/5
Let u(m) be the second derivative of -m**7/14 - 3*m**6/5 - 9*m**5/5 - 5*m**4/2 - 3*m**3/2 + 100*m + 9. Factor u(x).
-3*x*(x + 1)**3*(x + 3)
Let z = 1099575 - 4398293/4. Let 5/4*o**2 - 3*o + z = 0. Calculate o.
1, 7/5
Suppose -57*b + 54*b + 33 = 0. Factor 6*x**2 - 87*x - 45*x + 37*x + 100 - b*x**2.
-5*(x - 1)*(x + 20)
Let d(k) be the third derivative of -k**8/5040 - k**7/5040 + k**6/240 - 7*k**5/60 - k**3/3 + 65*k**2. Let j(m) be the third derivative of d(m). Factor j(s).
-(s + 1)*(4*s - 3)
Let w be 46/3 - (-180)/(-15). Let i(v) be the second derivative of -5/6*v**4 - 42*v + w*v**3 + 0 - 1/4*v**5 + 20*v**2. Factor i(t).
-5*(t - 2)*(t + 2)**2
Let f(j) be the first derivative of j**3/15 - 32*j**2/5 + 63*j/5 - 941. Factor f(i).
(i - 63)*(i - 1)/5
Let w(v) be the second derivative of -1/4*v**5 + 4/5*v**2 + 7/6*v**4 + 145*v - 22/15*v**3 + 0. Factor w(i).
-(i - 2)*(5*i - 2)**2/5
Suppose 5*p - 3*p - 2 = 0. Suppose t = -p + 3. Factor 6*h**2 - 12*h + 2 + 4*h**2 + t*h - 2*h**2.
2*(h - 1)*(4*h - 1)
Let y be (20/(-12))/(7200/(-1080)). Factor -3/2 + 7/4*v - y*v**2.
-(v - 6)*(v - 1)/4
Let h(u) be the third derivative of 7*u**5/100 - 109*u**4/20 - 45*u**3/2 - 268*u**2 + u - 2. Factor h(s).
3*(s + 1)*(7*s - 225)/5
Let i(f) = -3*f**4 - 6*f**3 + 15*f**2 + 18*f - 5. Let u(l) = -1. Suppose -23*d + 144 = 29. Let j(k) = d*u(k) - i(k). Factor j(h).
3*h*(h - 2)*(h + 1)*(h + 3)
Let p(x) be the second derivative of 1/6*x**4 + 0 + 20*x**2 - 52*x - 4*x**3. What is y in p(y) = 0?
2, 10
Let y = 223 - 222. Let k(w) = w**2 - w. Let i(g) = 4*g + 20. Let v(d) = y*i(d) - 2*k(d). Let v(t) = 0. What is t?
-2, 5
Let r = -68 - -70. Suppose -l - r = -4. Determine d, given that -5*d + 9*d - 4*d**l - d**2 + d = 0.
0, 1
Let w(u) = 42*u - 496. Let l be w(12). Let z(v) be the first derivative of -8/3*v**3 - 10 - 5*v**4 + l*v + 10*v**2. Find x such that z(x) = 0.
-1, -2/5, 1
Let c(j) = -j**3 + j**2 + 2*j - 2. Let w(v) = -1 - 14*v**3 - 5*v - 1 - 17*v**3 + 36*v**3 + 2*v**2. Let k(i) = 4*c(i) + w(i). Determine q so that k(q) = 0.
-5, -2, 1
Let f(q) be the first derivative of 1/33*q**6 - 8/11*q**3 + 42 - 12/55*q**5 + 4/11*q**2 + 13/22*q**4 + 0*q. Solve f(d) = 0 for d.
0, 1, 2
Let c(u) be the third derivative of -u**7/490 + 27*u**6/280 - 44*u**5/35 - 2229*u**2. Factor c(k).
-3*k**2*(k - 16)*(k - 11)/7
Let m(y) be the third derivative of 1/6*y**6 - 5/6*y**4 + 0*y - 116*y**2 - 1/30*y**5 + 0 + 1/105*y**7 + 0*y**3. Factor m(v).
2*v*(v - 1)*(v + 1)*(v + 10)
Let p(d) = -d**3 - 11*d**2 - 29*d - 24. Let y be p(-12). Let s = y - 1403/3. Factor 4/3*z + 0 - s*z**2.
-z*(z - 4)/3
Let k(l) be the third derivative of 0*l**6 + 0*l**5 + 0*l**3 + 3*l**2 + 1/420*l**7 + 0 + 0*l**4 - 19*l. Let k(m) = 0. What is m?
0
Factor -257/9 + 1/9*m**3 - 85/3*m**2 - 57*m.
(m - 257)*(m + 1)**2/9
Let s be (28/(-18))/(-7)*18/11*(-836)/(-114). Factor 36*x - 9*x**3 + s - 2/3*x**2.
-(x - 2)*(x + 2)*(27*x + 2)/3
Let d(f) be the third derivative of 0 + 189*f**2 - 17/96*f**4 - 1/240*f**5 + 0*f - 5/4*f**3. Factor d(u).
-(u + 2)*(u + 15)/4
What is s in 0 - 48/5*s**3 + 34/5*s**2 + 14/5*s = 0?
-7/24, 0, 1
Let d(o) be the first derivative of -o**4 - 68*o**3/3 - 128*o**2 - 192*o - 8154. Factor d(t).
-4*(t + 1)*(t + 4)*(t + 12)
Factor 5*s**2 + 53*s - 281*s + 4*s**2 - 5*s**2 + 2408.
4*(s - 43)*(s - 14)
Let w(h) be the third derivative of 2*h**5/5 - 91*h**4/6 + 10*h**3 + 1815*h**2. Solve w(v) = 0 for v.
1/6, 15
Suppose -79*t + 324 = -85*t. Let j be t/(-4) - 320/32. Factor j*s**2 + 5/2*s - 1.
(s + 1)*(7*s - 2)/2
Suppose 280*c**2 + 211*c**2 - 320 - 481*c**2 - 796*c = 0. What is c?
-2/5, 80
Let l = 287757 - 287703. Factor 33/2*i**3 - 3/2*i**4 + 0 - 36*i**2 - l*i.
-3*i*(i - 6)**2*(i + 1)/2
Let -111 + 711 + 561 + 239 + 3*v**3 - 1356*v - 87*v**2 + 40 = 0. Calculate v.
-12, 1, 40
Let m(q) be the first derivative of -q**7/525 + q**6/60 - 2*q**5/75 - 41*q**2 + 2*q - 197. Let d(g) be the second derivative of m(g). What is f in d(f) = 0?
0, 1, 4
Let p(x) = -x**3 + 11*x**2 - 26*x + 4. Let o be p(-7). Let b = o + -1064. Find k such that -1/4 + 0*k + 0*k**3 + 1/2*k**2 - 1/4*k**b = 0.
-1, 1
Let t(v) be the third derivative of -v**6/180 + 17*v**5/3 - 2027*v**4/36 + 506*v**3/3 + 3433*v**2. Factor t(m).
-2*(m - 506)*(m - 3)*(m - 1)/3
Let j(n) be the second derivative of -n**5/30 + 2*n**4/3 - 5*n**3 - 51*n**2/2 + n + 7. Let a(b) be the first derivative of j(b). Let a(y) = 0. What is y?
3, 5
Let i be 14641/(-847) + 154/(42/6). Find o, given that -57/7*o**2 - 3/7*o**4 + i*o**3 + 0 + 27/7*o = 0.
0, 1, 9
Suppose 6250 = 5772*s - 909 - 4385. Factor 5/2*y + 0 - 1/8*y**4 + 7/2*y**s + 7/8*y**3.
-y*(y - 10)*(y + 1)*(y + 2)/8
Let t(f) = 2*f**3 - 44*f**2 - 45*f - 27. Let z be t(23). Let k be (-2)/((-56)/z)*-25 - 3. Factor -4/7*b**2 + k - 4/7*b + 4/7*b**3.
4*(b - 1)**2*(b + 1)/7
Solve 177*i**2 - 14*i - 533*i**2 + 185*i**2 + 105*i**3 + 176*i**2 - 66*i + 20 = 0 for i.
-1, 2/7, 2/3
Let h(i) be the first derivative of 15/7*i - 247 + 3/28*i**4 - 3/14*i**2 - 5/7*i**3. Factor h(b).
3*(b - 5)*(b - 1)*(b + 1)/7
Let c be 0/(-2) - (1 + (-51)/45). Let d(y) be the first derivative of -1/3*y**4 - 2/9*y**3 + 0*y + 1/18*y**6 - 4 + 1/2*y**2 + c*y**5. Factor d(s).
s*(s - 1)**2*(s + 1)*(s + 3)/3
Let w(f) be the second derivative of 61*f + 1/48*f**4 - 1/2*f**3 + 9/2*f**2 + 0. What is t in w(t) = 0?
6
Let f(n) = -3*n**2 + 146*n - 1127. Let j(z) = 7 + 0 - z - 8 + z**2 - z. Let t(g) = f(g) - 2*j(g). Suppose t(k) = 0. Calculate k.
15
Factor -2*x**3 - 3*x**3 - 5581 + 375