n. Factor -5/4*r**2 + 5 + n*r.
-5*(r - 2)*(r + 2)/4
Suppose 5*y = -4*j + 32, -y - 183*j + 19 = -178*j. Let h(d) be the second derivative of 13*d + 0 - 3*d**3 + 2/3*d**y + 2*d**2. Factor h(s).
2*(s - 2)*(4*s - 1)
Let w(u) be the second derivative of -u**4/6 - 137*u**3 + 826*u**2 + 168*u. Solve w(q) = 0.
-413, 2
Let m(o) be the third derivative of 1/12*o**6 + 1/3*o**4 + 0*o + 3 - 6*o**2 + 0*o**3 - 4/15*o**5 - 1/105*o**7. Factor m(r).
-2*r*(r - 2)**2*(r - 1)
Factor 204*g**2 + 5*g**4 - 445*g - 235*g**3 - 37*g**2 - 220*g + 270*g**2 + 238*g**2 + 220.
5*(g - 44)*(g - 1)**3
Let k = 392 + -398. Let v be (-56)/176 - 3/k. Factor 6/11*n**3 + 4/11*n - v*n**5 + 10/11*n**2 - 2/11*n**4 + 0.
-2*n*(n - 2)*(n + 1)**3/11
Let y be 11 + -12 + -5 + 8. Suppose -5*h = 4*z - 5, 78*z = 80*z - y*h - 16. Let -18/7*l**3 - 6/7*l**z - 48/7*l + 142/7*l**2 - 38/7*l**4 - 32/7 = 0. Calculate l.
-4, -1/3, 1
Let y be 1*((-187)/22 - (-4)/(-8)). Let l(w) = 6*w**2 + 63*w + 93. Let r(a) = 3*a**2 + 32*a + 45. Let d(j) = y*r(j) + 4*l(j). Factor d(z).
-3*(z + 1)*(z + 11)
Let t(s) be the third derivative of 5/96*s**4 - 1/4*s**3 + 0*s - 1/240*s**5 + 2*s**2 - 19. Factor t(q).
-(q - 3)*(q - 2)/4
Let o(x) be the second derivative of 5*x**7/42 - x**6/6 - 17*x**5/4 + 35*x**4/4 + 30*x**3 + 4*x - 192. Solve o(y) = 0.
-4, -1, 0, 3
Let l = -70805/4 - -17702. Let v(q) be the first derivative of 8 - 1/3*q**3 - 3/2*q**2 + l*q**4 - 1/5*q**5 + 2*q. Factor v(k).
-(k - 2)*(k - 1)**2*(k + 1)
Let q(p) be the third derivative of 5*p + 3*p**2 + 2*p**3 + 5/3*p**4 + 1/20*p**5 + 1/210*p**7 + 1/112*p**8 - 9/40*p**6 + 0. Suppose q(d) = 0. What is d?
-3, -1, -1/3, 2
Let x be 6*(-7)/(-84)*0. Let t(w) be the second derivative of 0*w**5 + 0*w**4 + 6*w + x + 0*w**2 + 1/210*w**6 + 0*w**3 - 1/294*w**7. Factor t(d).
-d**4*(d - 1)/7
Factor 7 - 4*u**2 + 67 - 234 - 25 + 25 - 164*u.
-4*(u + 1)*(u + 40)
Let m(w) be the second derivative of w**6/120 - 13*w**5/40 - 1067*w. Suppose m(o) = 0. Calculate o.
0, 26
Solve -83/4*y**2 - 3/4 + 17/2*y + 9*y**4 - 21*y**3 = 0 for y.
-1, 1/6, 3
Let q(s) be the third derivative of -s**8/1176 - 2*s**7/245 - 3*s**6/140 - 2*s**5/105 - 166*s**2. Factor q(i).
-2*i**2*(i + 1)**2*(i + 4)/7
Let k = 1 - -15. Let d be (248/k)/(1/2). Find p such that -28*p - d*p - 3*p**2 + 3*p**3 + 53*p = 0.
-1, 0, 2
Let c = -106 - -109. Determine h, given that h**3 - 13*h + 0*h**c - 7*h**2 - 10 + 5*h**2 = 0.
-2, -1, 5
Let d = 580 - 576. Let a be d/((-2)/6*126/(-21)). Suppose -a*c**2 + 2/3*c**4 + 0*c - 4/9*c**3 + 8/9 = 0. Calculate c.
-1, 2/3, 2
Let a(n) be the first derivative of -n**7/280 + n**6/96 + n**5/120 + 291*n**2/2 - 129. Let r(c) be the second derivative of a(c). Factor r(q).
-q**2*(q - 2)*(3*q + 1)/4
Suppose 2*z + 2*z + v - 896 = 0, -5*z + 1120 = -v. Let 115 + 1058*x**3 + 384*x + 10*x**5 + 2252*x**2 - z*x**4 - 723 + 32 = 0. Calculate x.
-1, 2/5, 12
Let t(q) be the second derivative of 123*q + 12*q**2 + 39/10*q**3 - 1/20*q**4 + 0. Factor t(z).
-3*(z - 40)*(z + 1)/5
Let i = 9/108620 - -271541/108620. Find b, given that 1/4*b**2 + 25/4 - i*b = 0.
5
Let d(u) be the first derivative of -u**4/10 - 18*u**3/5 - 48*u**2 - 280*u - 1997. Factor d(z).
-2*(z + 7)*(z + 10)**2/5
Let c(a) be the first derivative of 11*a**7/105 - 4*a**6/15 + 7*a**5/50 + a**4/15 - 21*a - 61. Let j(f) be the first derivative of c(f). Factor j(s).
2*s**2*(s - 1)**2*(11*s + 2)/5
Determine q so that -119*q + 1/2*q**2 + 705/2 = 0.
3, 235
Let p(h) = h**4 - h**3 - 2*h**2 + 3*h + 5. Let f(t) = 12*t**4 - 3*t**3 - 94*t**2 + 193*t - 57. Let w(b) = 5*f(b) - 55*p(b). Solve w(i) = 0.
-14, 2
Suppose 0 = 8*c - 5*c - 5*c. Let g be (-44)/14 + -1*(-4 + c). Let 2/7*d**2 - 4/7*d - g = 0. Calculate d.
-1, 3
Determine j, given that 39*j**4 - 186*j**2 - 3*j**5 + 4*j**3 - 102*j**4 + 611*j**4 - j**5 - 362*j**2 = 0.
-1, 0, 1, 137
Let p be 100 - 9 - 5 - 2. Let k be (15/(-20))/(p/(-98)). Factor 0 + 23/8*l**2 - k*l**3 - 3/4*l.
-l*(l - 3)*(7*l - 2)/8
Let s = 127339/35 - 4842/5. Let p = -2663 + s. What is b in p*b**2 + 0 - 16/7*b - 20/7*b**3 = 0?
0, 2/5, 2
Let o(z) be the first derivative of -55 + 22*z**2 - z**4 - 24*z - 16/3*z**3. Suppose o(h) = 0. What is h?
-6, 1
Factor 1/12*o**3 - 19/3 + 20/3*o - 23/12*o**2.
(o - 19)*(o - 2)**2/12
Suppose 0 = -6*l - 19*l + 11*l. Let y(b) be the second derivative of 0 + l*b**3 + 0*b**4 + 1/30*b**6 - 1/84*b**7 + 27*b + 0*b**2 + 0*b**5. Factor y(c).
-c**4*(c - 2)/2
Let z be 13 - (12 - 6) - (4 + 1). Suppose -p - 6 = -3*t, 19*p - 21*p = t - z. Solve 3/2*l + 0*l**3 - 9/4*l**t + 0 + 3/4*l**4 = 0 for l.
-2, 0, 1
Let d(p) be the second derivative of p**6/12 + p**5/2 - 35*p**4/4 - 275*p**3/3 - 875*p**2/4 - 253*p. Factor d(z).
5*(z - 7)*(z + 1)*(z + 5)**2/2
Suppose 0 - 13/9*y**3 + 1/9*y**4 + 0*y + 0*y**2 = 0. Calculate y.
0, 13
Let f(w) = -4*w**2 - 11*w - 10. Let t be f(-2). Let y be (-13)/2*t/91. Factor 8/7*a**3 - 8/7*a + 10/7 - 12/7*a**2 + y*a**4.
2*(a - 1)**2*(a + 1)*(a + 5)/7
Factor 4/3*z**3 - 124/3*z**2 - 140 - 548/3*z.
4*(z - 35)*(z + 1)*(z + 3)/3
Let q be (-3 - (-45)/12) + 79/(-4). Let l = q - -22. Find u such that l*u - u**2 + 16 - u**2 - 7*u**2 - 3*u**3 - 7 = 0.
-3, -1, 1
Let u(o) be the first derivative of -o**4/11 + 455*o**3/33 - 6441*o**2/11 - 3249*o/11 + 717. Factor u(n).
-(n - 57)**2*(4*n + 1)/11
Let i be (20/46)/(40472/232714). Solve 1/6*p**3 + 18 + i*p**2 + 12*p = 0 for p.
-6, -3
Let h(a) = -8*a**3 + 12*a**2 + 57*a + 52. Let o(v) = -7*v**3 + 12*v**2 + 57*v + 50. Suppose 3*b = 1 + 14. Let q(k) = b*o(k) - 4*h(k). Factor q(s).
-3*(s - 7)*(s + 1)*(s + 2)
Let h(z) be the third derivative of z**5/80 + 37*z**4/32 + 161*z**3/4 + 2*z**2 + 1671. Factor h(p).
3*(p + 14)*(p + 23)/4
Let h(c) be the third derivative of -16/3*c**3 - 1/30*c**5 + 0*c + 4*c**2 - 31 - 2/3*c**4. Factor h(t).
-2*(t + 4)**2
Find i such that -40525*i + 39 + 87 + 40649*i - 2*i**2 = 0.
-1, 63
Suppose c = 7*l - 2*l - 135, 4*l - c - 109 = 0. Let r = l + -25. Suppose j**2 - 5*j**2 - 10*j - r + 5*j = 0. What is j?
-1, -1/4
Let k(w) be the first derivative of w**5 + 145*w**4/4 + 130*w**3/3 - 140*w**2 + 14343. Factor k(d).
5*d*(d - 1)*(d + 2)*(d + 28)
Let h be (-3 + 0 + -1)/(97 - 111 - -11). Solve -32/3*n - h*n**3 + 16/3 + 20/3*n**2 = 0 for n.
1, 2
Suppose -4*i + 25 = 3*g, 0 = 4*i - 3*g + 3 - 34. Suppose -6*v + 19 = i. Suppose -c**2 + 7*c**2 - 4*c**2 + 2 + 0*c**v - 4*c = 0. Calculate c.
1
Determine t so that 104*t**4 - 55696 - 161*t**3 - 309*t**3 + 110920*t - 105*t**4 - 43223*t**2 - 11530*t**2 = 0.
-236, 1
Let y = -176281/3 - -705145/12. Let -1/4*q**2 + y - 3/2*q = 0. Calculate q.
-7, 1
Let y(u) = -3*u + 4 + 13 + u. Let c be y(7). Factor 7*q**2 - 6*q**3 - 10*q**2 + q - c*q - 5*q**2.
-2*q*(q + 1)*(3*q + 1)
Let g(k) be the third derivative of -k**5/60 - 5*k**4/8 + 38*k**3/3 + 1029*k**2. What is t in g(t) = 0?
-19, 4
What is w in 408 - 1221/2*w - 4089/4*w**2 - 15/4*w**3 = 0?
-272, -1, 2/5
Solve 112/3 - 6*q**3 + 1028/3*q**2 - 374*q = 0 for q.
1/9, 1, 56
Suppose 0*w + 5*w - 176 = 4*h, 0 = 3*w. Let l = h - -46. Factor 4*u**2 + 3*u**2 + l - 3*u + 2*u**2 - 8*u**2.
(u - 2)*(u - 1)
Let o(j) be the first derivative of -j**5/5 + 27*j**4/4 - 39*j**3 - 203*j**2/2 + 294*j + 3827. Suppose o(w) = 0. What is w?
-2, 1, 7, 21
Let s = -708 + 706. Let j(i) = 12*i**3 - 234*i**2 - 7716*i + 14. Let x(c) = c**3 + c**2 - 2*c + 1. Let q(p) = s*j(p) + 28*x(p). Factor q(u).
4*u*(u + 62)**2
Let p = -284 + 288. Suppose -8*c + p*o + 20 = 3*o, 4*c + 3*o = -4. Solve -1/4*z**3 - 2*z - 1 - 5/4*z**c = 0.
-2, -1
Let y(t) = 7*t**2 + 9*t. Let x = 9 + -26. Let o(r) = -20*r**2 - 26*r. Let n = 953 + -959. Let i(b) = n*o(b) + x*y(b). Solve i(q) = 0.
-3, 0
Suppose 5*b - 2*i = 6, -5*b - 49 + 57 = -i. Factor -3/5 - 1/5*k**b - 4/5*k.
-(k + 1)*(k + 3)/5
Let t(y) = 15*y**2 + 171*y + 6. Suppose 4*s + 5*c - 5 = 0, 2*c + 26 = 3*s + s. Let v(l) = -13*l**2 - 170*l - 5. Let p(q) = s*t(q) + 6*v(q). Factor p(f).
-3*f*(f + 55)
Let h = -2578/2505 + 183/167. Let t(f) be the second derivative of 1/30*f**4 - 2/5*f**2 - h*f**3 - 14*f + 0. Find n, given that t(n) = 0.
-1, 2
Let b(z) = z**4 + 2*z - 1. Let x(m) = -27*m - 5*m**3 + 306 - 13*m**4 + 21*m + 40*m**3 + 5*m**4 - 303. Let i(g) = -3*b(g) - x(g). Find p such that i(p) = 0.
0, 7
Let j(m) = m**3 + 4551*m**2 + 6758997*m + 3381754498. Let f(t) = -t**3 - 4567*t**2 - 6758995*t - 3381754497. L