j - 1)/11
Let r(j) be the first derivative of 2*j**5/35 - 179*j**4/14 + 5280*j**3/7 + 8100*j**2/7 - 1071. Solve r(t) = 0 for t.
-1, 0, 90
Factor -6/5*p**3 + 5822/5*p**2 - 282658*p + 94090.
-2*(p - 485)**2*(3*p - 1)/5
Let d(g) be the first derivative of -8/15*g**3 + 0*g**2 + 92/25*g**5 + 8/5*g**6 - 3/5*g**4 - 53 + 0*g. Suppose d(i) = 0. What is i?
-2, -1/4, 0, 1/3
Let w(g) = g**2 - 75. Let p be w(9). Factor -35*a + 23*a - p*a**2 + 2*a**3 + 16*a.
2*a*(a - 2)*(a - 1)
Let c(d) be the second derivative of -d**5/4 + 1255*d**4/6 - 158750*d**3/3 + 312500*d**2 + 289*d + 3. Find h such that c(h) = 0.
2, 250
Let b = 1999617 + -1999617. Find s, given that 39/2*s + b - 3/4*s**2 = 0.
0, 26
Let d = -1434 + 1434. Let o(s) be the second derivative of 0 + 13*s + d*s**3 - 1/20*s**4 + 3/10*s**2. Find x such that o(x) = 0.
-1, 1
Let o(i) be the first derivative of 0*i + 29/2*i**2 - 212 - 1/8*i**4 + 19/2*i**3. Factor o(h).
-h*(h - 58)*(h + 1)/2
Let p(i) be the first derivative of -14*i**3/39 + 165*i**2/13 - 184*i/13 - 679. Solve p(n) = 0.
4/7, 23
Let r = -4090 + 245401/60. Let k(d) be the third derivative of 1/525*d**7 - 1/100*d**6 + 0 + 0*d**3 - r*d**4 + 0*d + 1/50*d**5 - 20*d**2. Factor k(t).
2*t*(t - 1)**3/5
Suppose 0 = 8*s + 12*s - 4300. Factor -209*o**3 + 425*o**3 + o**5 - s*o**3 - 2*o**4.
o**3*(o - 1)**2
Let y = 3091743/21590 + -11/4318. Let w = y + -2143/15. Factor -w*i**2 - 1/3 - 2/3*i.
-(i + 1)**2/3
Let b(w) be the second derivative of -w**5/70 - 47*w**4/21 - 253*w - 3. Let b(i) = 0. Calculate i.
-94, 0
Let n(q) be the third derivative of q**6/60 - 3*q**5/5 + 89*q**4/12 - 24*q**3 - 5780*q**2. Suppose n(l) = 0. What is l?
1, 8, 9
Let i(f) be the first derivative of 39 + 33/2*f**2 - f**3 - 54*f. Factor i(l).
-3*(l - 9)*(l - 2)
Let w be 250/(-15) + 21 - (1 + 3). Let -w*b**3 + 72 - 36*b + 6*b**2 = 0. What is b?
6
Let d(t) = -t**2 + 3. Let g(f) = -f**2 + 17*f - 60. Let p be g(12). Let q be d(p). Let -q*v**4 + 0 - 20/3*v**5 + 3*v**2 + 19/3*v**3 + 1/3*v = 0. Calculate v.
-1, -1/4, -1/5, 0, 1
Let q(n) = -4*n - 24. Let b be q(-7). Suppose -5*m - 16 = -b*c + 56, -2*c + 4*m + 42 = 0. Factor 4*u**2 - c*u + 19*u - u**2.
3*u*(u + 2)
Let h be (-10)/(-2*25/(-4)*39/(-195)). Let q(i) be the third derivative of -19/3*i**h + 0 + 3/5*i**5 + 44*i**2 + 0*i + 16/3*i**3. Let q(c) = 0. What is c?
2/9, 4
Let b be (72/(-60))/(4/(-330)). Let f(m) = m**3 + 1. Let g be f(1). Factor g*u**3 + 6*u**3 - 4*u**4 + 99*u - b*u.
-4*u**3*(u - 2)
Let b(u) be the third derivative of -u**9/20160 + u**8/8960 + u**7/1680 + 45*u**4/8 - 3*u**2 - 35. Let l(n) be the second derivative of b(n). Factor l(c).
-3*c**2*(c - 2)*(c + 1)/4
Let u = 12465/51251 + 2/967. Let f = u + 333/371. Factor f*o**2 + 2/7 - 10/7*o.
2*(o - 1)*(4*o - 1)/7
Let j be -36 + 1105/25 + -7. Factor -11/5*w + 6/5 + j*w**2 - 1/5*w**3.
-(w - 3)*(w - 2)*(w - 1)/5
Let d(t) be the second derivative of -3*t - 25 + 26/33*t**3 - 25/11*t**2 - 1/66*t**4. Factor d(z).
-2*(z - 25)*(z - 1)/11
Let j(k) = 2*k**4 + 23*k**3 + 149*k**2 + 324*k + 275. Let g(z) be the first derivative of -z**4/4 + z**3/3 + z - 33. Let p(u) = 5*g(u) - j(u). Factor p(y).
-2*(y + 3)**3*(y + 5)
Suppose -62*n + 25*n = -24*n. Let c(f) be the third derivative of 1/1050*f**7 + 0 + n*f - 1/100*f**5 - 2/15*f**3 - 7*f**2 + 1/15*f**4 - 1/300*f**6. Factor c(z).
(z - 2)*(z - 1)**2*(z + 2)/5
Let f be ((-130)/(-6175))/(15/1425). Let 62/3*z + 1/3*z**f + 961/3 = 0. Calculate z.
-31
Let r(m) be the second derivative of 0 + 3*m**2 - 1/2*m**4 - 1/4*m**3 - 235*m + 3/40*m**5. Let r(u) = 0. What is u?
-1, 1, 4
Let x = -669989 + 669991. Factor 3/2 - 11/4*o + 3/2*o**x - 1/4*o**3.
-(o - 3)*(o - 2)*(o - 1)/4
Let m(t) be the third derivative of -t**7/210 - t**6/30 + t**5/60 + t**4/6 + 107*t**2. Factor m(u).
-u*(u - 1)*(u + 1)*(u + 4)
Let s(v) be the first derivative of -1681*v**4/28 - 11234*v**3/7 - 1641*v**2/14 - 20*v/7 + 7707. Let s(p) = 0. What is p?
-20, -1/41
Let a = 1075716/5 - 215142. Factor a*t**3 + 18/5*t + 24/5*t**2 + 0.
6*t*(t + 1)*(t + 3)/5
Let a = 267166 + -267161. Determine w, given that 0 + 17/4*w**3 + w - w**4 - a*w**2 = 0.
0, 1/4, 2
Let q = -19221 + 19223. Let l = 494/7 + -70. Solve 4/7 + 1/7*j**q - l*j = 0 for j.
2
Let d(v) be the second derivative of -5/2*v**3 + 0 + 1/40*v**6 - 30*v + 3*v**2 + 9/8*v**4 - 21/80*v**5. Determine c, given that d(c) = 0.
1, 2
Let s(b) = -2*b**2 - 19*b - 3. Let n be s(-9). Let k = 4 + n. What is x in 7*x - k*x**2 + 8 + 13*x - 8*x**2 - 10*x**2 = 0?
-2/7, 1
Let i(m) be the first derivative of 5*m**4/4 - 25*m**3 - 180*m**2 - 380*m + 2125. Factor i(l).
5*(l - 19)*(l + 2)**2
Let s(t) = -t**3 - 11*t**2 - 11*t + 8. Let n be s(-10). What is z in 5*z**2 - 121*z - 56*z + 14*z + n*z = 0?
0, 29
Let 88/3*x - 88/3*x**3 - 448/3 + 148*x**2 + 4/3*x**4 = 0. Calculate x.
-1, 1, 8, 14
Let p = 3/57202 + 228793/286010. Factor -p*q**2 + 52/5*q + 0.
-4*q*(q - 13)/5
Let n = 107 - 86. Suppose n*g = 13*g + 80. Find y such that -g*y**3 - 85*y - 70*y**2 - 15 + 8 - 5*y**3 - 23 = 0.
-3, -1, -2/3
Let t = -330 + 332. Solve -10 + 87*m**2 + 144*m**2 - 25*m + 29*m**t = 0.
-2/13, 1/4
Let w = -282490 - -2542442/9. Factor 0 - 22/3*g**2 - 4*g**3 - w*g - 2/9*g**4.
-2*g*(g + 1)**2*(g + 16)/9
Let g(c) be the first derivative of -2*c**5/5 + 9*c**4/2 - 44*c**3/3 + 64*c - 888. Factor g(n).
-2*(n - 4)**2*(n - 2)*(n + 1)
Let y(p) = p**3 + 3*p**2 - 14*p - 10. Let b be y(-5). Suppose -4*i - i = -b. Suppose -i*t + 8*t**2 - 9*t**3 + 3*t + 11*t + 5*t**3 = 0. Calculate t.
-1, 0, 3
Let b be ((-1320)/(-168))/(-55)*(-22 - (-2)/2). Let -12/5*k**2 + 4/5*k**b + 0 + 0*k = 0. Calculate k.
0, 3
Factor 198*i - 373 - 4*i**2 - 200*i - 155*i - 255*i - 35.
-4*(i + 1)*(i + 102)
Solve 68/7 + 67/7*k - 1/7*k**2 = 0 for k.
-1, 68
Let m(q) = q**2 - 25*q - 714. Let g be m(-17). Let i(l) be the first derivative of -9 + g*l + 3/2*l**4 + 5/2*l**3 + 3/10*l**5 + 3/2*l**2. Factor i(a).
3*a*(a + 1)**2*(a + 2)/2
Determine f, given that f**4 - 9/2*f - 5/3 - 10/3*f**2 + 1/6*f**5 + 1/3*f**3 = 0.
-5, -1, 2
Find q such that -2/9*q**2 - 32/3*q - 30 = 0.
-45, -3
Let h(r) be the second derivative of 14*r**6/15 - 13*r**5/5 - 23*r**4/3 - 2*r**3 + 652*r. Factor h(a).
4*a*(a - 3)*(a + 1)*(7*a + 1)
Suppose 4*z = 20*z + 1040. Let x(s) = 7*s**2 + 10*s + 1. Let n(a) = 75*a**2 + 110*a + 10. Let l(w) = z*x(w) + 6*n(w). Factor l(j).
-5*(j - 1)**2
Let q be (17/(-15) + (-8 - -11))*21*(-9)/(-252). Factor -q*h**3 + 3/5 - 11/5*h**2 - 1/5*h.
-(h + 1)**2*(7*h - 3)/5
Let x(m) = m**3 + 12*m**2 - m - 7. Let k be x(-12). Let 71*d + d**4 - 43*d - 33*d + k*d**3 - 4 + 3*d**2 = 0. Calculate d.
-4, -1, 1
Suppose -13*b - 16*b - b + 60 = 0. Factor -76/15*o - 2/15*o**b - 722/15.
-2*(o + 19)**2/15
Suppose 12*m + 3*p = 69, -4*m + 539 = -3*p + 560. Factor 3/5*q**4 + 0*q + 24/5*q**2 - 27/5*q**m + 0.
3*q**2*(q - 8)*(q - 1)/5
Let p = -400 + 4. Let s be (-4)/26 + p/(-39). Factor 4*i**2 + i**2 + s + 154*i - 139*i.
5*(i + 1)*(i + 2)
Let i be (-1 + 37/15)*12. Let p be 5 - (48/(-32))/(-2 - (-5)/10). Factor i*j + 32/5 + p*j**2.
4*(j + 4)*(5*j + 2)/5
Suppose b = 3*c - 10, 4*c - 16 = 2*b - 2. Solve -14*j - 4 + 52 - 4*j - c*j**2 = 0.
-8, 2
Let a(n) = n**2 + 10*n. Let b be a(-10). Suppose b = -r, 10*s - 4*r - 8 = 8*s. Let -s*v**2 - 23*v**4 + 8*v**3 + 42*v**4 - 23*v**4 = 0. What is v?
0, 1
Let t(v) be the third derivative of -v**6/300 + 8*v**5/75 + 77*v**4/60 + 4*v**3 - 2342*v**2. Factor t(l).
-2*(l - 20)*(l + 1)*(l + 3)/5
Solve -49*d**3 + 14*d**3 + 336*d + 4*d**3 + 35*d**3 - 100*d**2 = 0 for d.
0, 4, 21
Let z(y) = 6*y**2 - 357*y - 354. Let u(s) = s**2 + 5*s + 5. Let x(j) = 9*u(j) - z(j). Factor x(d).
3*(d + 1)*(d + 133)
Let v(j) = j**2 + 18 - 390*j + 13 + 419*j. Let g be v(-28). Find i, given that 1/3*i**g + 4/3 + 0*i - i**2 = 0.
-1, 2
Let u(d) = -142*d**3 - 142*d**2 - 3*d + 2. Let m(x) = -x**4 - x**3 + 3*x - 2. Let z(q) = m(q) + u(q). Factor z(p).
-p**2*(p + 1)*(p + 142)
Let c be (-10 - -26) + 1792/(-196). Suppose c*f**2 - 56 + 4/7*f**3 + 12*f = 0. What is f?
-7, 2
Let k be 7*2*((-210)/20 - -11). Let s(o) be the first derivative of -30*o - k - 5/3*o**3 + 25/2*o**2. Factor s(r).
-5*(r - 3)*(r - 2)
Let l be 16 + (3477/(-12))/19. Factor -3/2*o**2 + 3/4*o**4 - 3/4*o**5 - 3/4*o + 3/2*o**3 + l.
-3*(o - 1)**3*(o + 1)**2/4
Suppose 4*g - 36 = -2*g. Let n be (g - 2) + 1/(-1). Factor 30*y - 6*y*