(b) be the second derivative of 3/4*b**3 - 1/24*b**4 + 0 + 0*b**2 - 23*b. Factor g(t).
-t*(t - 9)/2
Let g = -1326 - -1638. Let c be (g/(-637))/(4 + (-120)/28). Determine w, given that -2/7*w**2 - c + 2*w = 0.
1, 6
Let b be ((-10)/6)/(2/(-6)*1). Let o(l) = -l**2 - 32*l - 17. Let n(v) = v**2 + 22*v + 11. Let y(c) = b*o(c) + 7*n(c). Find p such that y(p) = 0.
-1, 4
Let g = -1606953/1220 + 8297156817/6293980. Let m = g + -3/938. Factor -2/11*r**2 - m*r - 18/11.
-2*(r + 3)**2/11
Let i(j) be the third derivative of -11/24*j**6 + 0*j**3 - 13/42*j**7 + 0*j + 5/4*j**4 + 0 + 5/12*j**5 + 20*j**2 - 5/112*j**8. Suppose i(l) = 0. Calculate l.
-3, -1, 0, 2/3
Factor -4*r**2 + 2/3*r**3 + 16 - 38/3*r.
2*(r - 8)*(r - 1)*(r + 3)/3
Let d be (((-600)/156)/10)/(6 - (-150)/(-24)). What is x in d*x**3 + 0 - 2/13*x**4 + 46/13*x**2 + 24/13*x = 0?
-1, 0, 12
Suppose -10*r = l - 8*r - 18, -5*r - 85 = -4*l. Suppose -2*q + l = 5*h, -19*q - h + 4 = -21*q. Factor 4/3*m**2 + 4/3*m + q.
4*m*(m + 1)/3
Suppose -2*r**3 + 1/6*r**4 - 100/3 + 37/6*r**2 + 5*r = 0. Calculate r.
-2, 4, 5
Let n(o) = -o**3 + 3*o**2 + 9*o - 4. Let c be n(4). Let a = -8 + c. Factor y**3 + 0*y**3 - a*y**3 + 2*y**3 + 5*y.
-5*y*(y - 1)*(y + 1)
Let r(h) be the first derivative of -1/9*h**2 - 5/27*h**3 - 1/12*h**4 + 0*h + 19. Determine x so that r(x) = 0.
-1, -2/3, 0
Suppose 17*b - 14 = 10*b. Solve 1284*u - 45*u**3 - 1284*u - 5*u**4 - 40*u**b = 0.
-8, -1, 0
Let i = -4 - -6. Solve -v**i + 714*v - 8*v**2 + 3*v**3 - 798*v = 0.
-4, 0, 7
Let l(v) be the third derivative of -v**6/120 - 11*v**5/60 - 13*v**4/12 - 8*v**3/3 - 1095*v**2. Let l(c) = 0. What is c?
-8, -2, -1
Find m such that -877952/5 + 2/15*m**4 + 30*m**3 + 11096/5*m**2 + 773984/15*m = 0.
-76, 3
Let x(g) be the first derivative of -g**6/2 + 54*g**5/5 - 24*g**4 - 2*g**3 + 99*g**2/2 - 48*g - 2483. Factor x(f).
-3*(f - 16)*(f - 1)**3*(f + 1)
What is l in 5*l**4 + 90*l**3 - 32892708*l + 32892708*l + 225*l**2 = 0?
-15, -3, 0
Let k(d) be the third derivative of 5/16*d**4 - 3/40*d**5 - 1/4*d**3 + 1/35*d**7 - 1/16*d**6 + 0 + 6*d**2 + 4*d. Suppose k(u) = 0. What is u?
-1, 1/4, 1
Suppose 3*f = 5*l - 16, 22 - 32 = 5*f. Suppose 125*v**5 - 127*v**5 + 6*v + 36*v**2 - 52*v**l + 12*v**3 = 0. Calculate v.
-3, 0, 1
Factor 0 - 2/5*j**4 + 0*j**3 + 4/5*j + 6/5*j**2.
-2*j*(j - 2)*(j + 1)**2/5
Let h be ((0/(-3))/(-10))/(-3). Let k(j) be the second derivative of 0 + 1/6*j**3 + 10*j + h*j**2 - 1/24*j**4. Solve k(v) = 0 for v.
0, 2
Let g = 1739 + -22577/13. Let n = 267/65 - g. Factor 9/5 + 3/5*o - 3/5*o**3 - n*o**2.
-3*(o - 1)*(o + 1)*(o + 3)/5
Let 4145*c**2 + 45*c**3 + 3624*c + 2760 + 2125*c**2 + 4507*c + 169*c = 0. What is c?
-138, -2/3
Suppose 23979*r - 24034*r = -110. Factor -123/8*a - 9/4 - 39/8*a**r.
-3*(a + 3)*(13*a + 2)/8
Solve 7875/4*a - 1323 + 17/2*a**4 + 31*a**3 - 1371/2*a**2 + 1/4*a**5 = 0.
-21, 1, 3, 4
Let i = 196 + -140. Let 111 + 0*a**2 - i - 52 - a**2 + 2*a = 0. Calculate a.
-1, 3
Let d be (-8)/(-12) - (-220)/3. Let q = 76 - d. Find c, given that 11*c**4 - 12*c**q + 8 + 3*c - c**4 + 13*c - 6*c**2 - 16*c**3 = 0.
-1, -2/5, 1, 2
Let s be (-7)/((-42)/36) - 55/10. Let w = 1793 - 3583/2. Suppose -2 + s*h**3 + w*h**2 + 0*h = 0. What is h?
-2, 1
Let b(n) be the second derivative of n**4/4 + 79*n**3 + 471*n**2/2 - 370*n - 3. Factor b(d).
3*(d + 1)*(d + 157)
Let g(k) be the second derivative of -3*k**6/50 + 287*k**5/50 + 32*k**4/15 - 17*k - 11. Suppose g(u) = 0. What is u?
-2/9, 0, 64
Let j be (-6)/(-5) + -1 - 3346/(-70). Find n such that -10187*n**2 - 35*n**3 - 4*n**4 - j*n + 11*n**3 - 16 + 10135*n**2 + 0 = 0.
-2, -1
Let q(b) be the first derivative of 2*b**3/3 - 4*b**2 - 42*b - 1035. Factor q(g).
2*(g - 7)*(g + 3)
Let w(y) be the first derivative of y**3 - 1227*y**2/2 + 2442*y - 1302. Factor w(v).
3*(v - 407)*(v - 2)
Let p = 15789 + -15785. Let v(i) be the second derivative of -1/15*i**p - 1/25*i**5 + 0 - 30*i + 2/5*i**2 + 2/15*i**3. Factor v(b).
-4*(b - 1)*(b + 1)**2/5
Suppose -4*s = 5*s - 18. Suppose 3*l - g - 17 = 0, s = 3*l - 4*g - 21. Find x such that -12 + 2*x**4 + 31*x**3 - 3*x**l - 21*x - 7*x**3 + 4*x**4 + 6*x**2 = 0.
-1, 1, 4
Factor 24834*y + 27283*y + 4*y**2 - 54365*y - 2252.
4*(y - 563)*(y + 1)
Let k(n) be the second derivative of 2 + 25/6*n**3 - 19*n + 0*n**2 + 5/12*n**4. Factor k(h).
5*h*(h + 5)
Let a be 9/(-24)*(-18464)/577. Factor 4*t**2 + 12 - a*t - 4/9*t**3.
-4*(t - 3)**3/9
Let x = -121513 - -121515. Factor 18/7*a**x + 4/7 + 2/7*a**4 - 10/7*a**3 - 2*a.
2*(a - 2)*(a - 1)**3/7
Let r(s) be the second derivative of 559*s**4/6 - 404*s**3/15 - 4*s**2/5 - 450*s. Suppose r(h) = 0. What is h?
-2/215, 2/13
Let f = -23696/3 + 7899. Let a(w) be the second derivative of 0 - f*w**2 - 1/27*w**3 + 1/18*w**4 + 1/90*w**5 + 21*w. Determine r, given that a(r) = 0.
-3, -1, 1
Let g be -7*(-220)/(-700)*(-20)/24. Factor -1/6*x**5 + 2/3 - 1/2*x**4 + g*x**2 + 2*x + 1/6*x**3.
-(x - 2)*(x + 1)**3*(x + 2)/6
Let s(y) be the third derivative of -y**5/60 + 19*y**4/12 - 37*y**3/6 + 1254*y**2. Factor s(o).
-(o - 37)*(o - 1)
Let y(r) be the first derivative of -r**5/10 + r**4/3 + 5*r**3 + 172*r - 183. Let q(t) be the first derivative of y(t). Let q(x) = 0. What is x?
-3, 0, 5
Find u such that -4/3*u**3 - 1/6*u**4 + 0 + 10/3*u**2 + 0*u = 0.
-10, 0, 2
Solve 1719/4*f**2 + 135 + 117/4*f**4 - 3/4*f**5 + 771/4*f**3 + 402*f = 0 for f.
-2, -1, 45
Let l be -65*14/35 - -26. Factor l - 10/3*c + 2/3*c**3 - 8/3*c**2.
2*c*(c - 5)*(c + 1)/3
Let i(j) = j**4 - j**2 - 13*j + 1. Let h(w) = -5*w**5 - 278*w**4 + 1490*w**3 - 2122*w**2 + 889*w + 2. Let g(v) = h(v) - 2*i(v). Determine s so that g(s) = 0.
-61, 0, 1, 3
Let y(c) be the first derivative of -5*c**4 - 26*c**2 + 1/5*c**5 + 17*c + 18*c**3 + 334. Let y(t) = 0. Calculate t.
1, 17
Let y = -150 + 174. Factor -6*v**4 + 5*v**5 - 122*v**3 - 2*v**5 + y*v**2 + 50*v**3 + 60*v**3.
3*v**2*(v - 2)**2*(v + 2)
Find o, given that -22*o**2 + 525*o**4 - 523*o**4 - 176*o + 44*o**3 + 14*o**2 = 0.
-22, -2, 0, 2
Suppose 7*g - 10*g = 0. Suppose -6 = -u + 2*k, 3*u - 4*k = -g*u + 22. Find f, given that 12*f**3 + 60*f**2 - 20*f**4 + 14 - 33*f + u - 43*f = 0.
-2, 3/5, 1
Let t(c) = -3*c**4 - c**3 + 3*c**2 + 1. Let l(a) = -40*a**4 - 24*a**3 + 816*a**2 - 4900*a + 9012. Let b(s) = l(s) - 12*t(s). Suppose b(f) = 0. Calculate f.
-18, 5
Suppose -17*y + 16*y = 15. Let u be y/(-10)*(-80)/(-12). Factor -4*w + 14*w**3 - 22*w**3 - 2*w**4 - u*w**2 + 0*w**4.
-2*w*(w + 1)**2*(w + 2)
Let h(y) = 14*y**2 - 17*y - 27. Let r be h(-17). Let v = -38732/9 + r. Factor v*k**2 - 2/9*k**5 - 16/9*k + 14/9*k**4 - 4*k**3 + 0.
-2*k*(k - 2)**3*(k - 1)/9
Let w(i) be the third derivative of -56*i**2 - 1/200*i**6 - 4/5*i**3 - 1/350*i**7 + 0 + 1/10*i**4 + 0*i + 3/50*i**5. Find k such that w(k) = 0.
-2, 1, 2
Solve -112/3*x**2 + 20/3*x**4 - 32/3*x - 8/3*x**3 + 4/3*x**5 + 128/3 = 0 for x.
-4, -2, 1, 2
Let m be (-742)/(-10865) + (-8)/10. Let i = 161/164 + m. Suppose -i*g**4 + 0*g + 0 - 1/2*g**3 - 1/4*g**2 = 0. Calculate g.
-1, 0
Let h(k) be the first derivative of 2*k**6/3 + 188*k**5/5 - 48*k**4 + 7666. Determine v, given that h(v) = 0.
-48, 0, 1
Let u(n) be the third derivative of -31*n**5/48 - n**4/48 - n**2 - 11*n. Factor u(t).
-t*(155*t + 2)/4
Suppose 2*t - m - 19 = -8, 3*t = 5*m + 13. Factor -17*v**3 + t*v**2 - 28*v + 7*v + 19*v**3 - 16 + 9*v.
2*(v - 2)*(v + 1)*(v + 4)
Let m = 8692 + -8689. Let z(i) be the third derivative of 1/3*i**4 + 0 + 2/525*i**7 - 1/25*i**5 + 16/15*i**m - 2/75*i**6 + 0*i + 20*i**2. Factor z(d).
4*(d - 4)*(d - 2)*(d + 1)**2/5
Suppose 15*x + 9 = 3*w + 17*x, 4*w = -3*x + 11. Factor 6*b**2 - w*b**4 - 1125 - 20*b**3 + 99*b**2 + 290*b + 25*b**2 + 10*b.
-5*(b - 3)**2*(b + 5)**2
Suppose -5*b + r + 153 = 0, -9*b + 14*b = 5*r + 165. Let g be b/4*(-29)/(-87). Factor -1/2*y**2 + g*y - 2.
-(y - 4)*(y - 1)/2
Let r = 8377 + -8371. Let z = -2 - -4. Factor -3*g**5 - 1 + 3*g**5 - 9*g + r*g**3 - 6*g**2 - z + 3*g**5 + 9*g**4.
3*(g - 1)*(g + 1)**4
Let h be ((-5)/(30/(-12)))/(1/(-4)). Let x be 2/(-9) - h/(-324)*-9. Factor 1/8*f**3 + x - 3/8*f**2 + 1/4*f.
f*(f - 2)*(f - 1)/8
Let k(y) = y**2 + 2*y + 7. Let f be k(-3). Let v be (16/f)/(6/30). What is h in 2*h**4 - 4*h**4 - 6*h**4 + 4*h**3 + v*h**2 + 0*h**3 - 4*h**5 = 0?
-2, -1, 0, 1
Let s(q) = 10*q**3 - 190*q**2 + 305*q + 475. Let h(u) = 11*u**3 - 194*u**2 + 305*u +