- 1)*(u + 2)**3*(5*u + 2)/2
Let f(p) = -3*p**2 - p - 1. Let n(g) = 2*g**2 + 1113*g - 309135. Let i(k) = f(k) + n(k). Determine d, given that i(d) = 0.
556
Let r = 164 + -120. Suppose 34 - r*x + 0*x**2 - 5*x**2 - 7*x**2 + 42 - 60 = 0. What is x?
-4, 1/3
Let y(b) be the second derivative of b**5/5 - 19*b**4/3 + 200*b**3/3 - 264*b**2 + 3*b - 211. Suppose y(x) = 0. Calculate x.
2, 6, 11
Let s(g) be the first derivative of -77*g**4 + 620*g**3/3 - 4*g**2 + 1445. Factor s(c).
-4*c*(c - 2)*(77*c - 1)
Suppose -158*h + 36 = -3*u - 151*h, -3*u = -h. Let -14/11*t - 18/11*t**3 - 5/11*t**4 - 3/11 - 24/11*t**u = 0. Calculate t.
-1, -3/5
Let s be ((-8)/(-90304))/((-3)/(-3678)). Let k = s - -3/332. Solve 4/17 - 6/17*y + k*y**2 = 0 for y.
1, 2
Suppose 5*o - 32 - 93 = -5*c, -4*o + 108 = -4*c. Suppose -6*i - 14 + o = 0. Factor 0 - 2/7*x - 2/7*x**i.
-2*x*(x + 1)/7
Suppose v - 2 = -l, -4*l - 3*v - 1 = -9. Suppose -i = -2*u - 5, 0*u + l*i = -2*u + 10. Suppose 5/3*d**4 - 5*d**3 + 0*d + 10/3*d**2 + u = 0. Calculate d.
0, 1, 2
Let y(z) = -108*z**3 - 105*z**2 + 48*z + 53. Let p(d) be the second derivative of -d**4/12 - d**3/6 - d**2/2 + 98*d. Let l(o) = -3*p(o) - y(o). Factor l(n).
(3*n - 2)*(6*n + 5)**2
Let b = 100014 + -100014. Suppose 0 = 4*h - 36 + 12. Factor -3/5*v + b - h*v**2.
-3*v*(10*v + 1)/5
Factor 0 - 3/4*n**3 - 25/2*n**2 + 17/4*n.
-n*(n + 17)*(3*n - 1)/4
Suppose -2*i + 2 = -2. Let x = 1176 + -1156. Factor 12*b**4 - 5*b**2 - x*b**4 + 0*b**i + 13*b**4.
5*b**2*(b - 1)*(b + 1)
Suppose 5*q - 216 = -191. Suppose 5*z - q*c = -c - 20, 4*z = 4*c - 20. Factor 0 - 32/17*n**2 + 16/17*n**3 - 2/17*n**4 + z*n.
-2*n**2*(n - 4)**2/17
Let v(t) be the first derivative of -45 + 9/2*t**4 - 3/5*t**5 + 0*t - 5*t**3 + 0*t**2. Factor v(k).
-3*k**2*(k - 5)*(k - 1)
Let x(o) be the first derivative of -o**6/8 - 9*o**5/20 + 15*o**4/16 + 3*o**3/4 - 3*o**2/2 + 738. Determine c so that x(c) = 0.
-4, -1, 0, 1
Let i(z) be the second derivative of 2*z**6/15 + 2*z**5 + 13*z**4/3 - 16*z**3 + 1439*z. Suppose i(a) = 0. What is a?
-8, -3, 0, 1
Let m be 82/(-8) + 394295/32956. Factor 60/7 - m*a**2 - 114/7*a.
-6*(a + 10)*(2*a - 1)/7
Let l(k) = -2 + 1 - 1 + 5*k - 22*k**2 + 21*k**2. Let b be l(4). Solve 12 + 4*z**b - z**2 - 5*z + 3*z - 5*z**2 = 0 for z.
-3, 2
Suppose -27 = 4*z + 5*c, 3*z - 5*c + 1647 = 1688. Factor 3/2*o**z - 9 - 3/2*o.
3*(o - 3)*(o + 2)/2
Let r = -58184 - -58186. Factor l - 1/3 + 1/3*l**r - l**3.
-(l - 1)*(l + 1)*(3*l - 1)/3
Suppose 3*m + 9 = -5*z, 14 = 2*z + 110*m - 111*m. Factor 0*w**2 - 3/5 + 6/5*w - 6/5*w**z + 3/5*w**4.
3*(w - 1)**3*(w + 1)/5
Let a(v) be the first derivative of 6*v**2 + 1/6*v**4 + 2 - 1/30*v**6 + 0*v + 2/3*v**3 - 1/15*v**5. Let s(p) be the second derivative of a(p). Factor s(t).
-4*(t - 1)*(t + 1)**2
Let u be (-4)/(-8) - 2/12. Let q = -5/3723 - -417/2482. Find b, given that 1/6 + u*b + q*b**2 = 0.
-1
Suppose 2*i = 4*i - 4*w - 6, w = 0. Let d(v) = 2*v**2 - 6*v + 2. Let o be d(i). Solve p + 0*p**3 - 5*p + 3*p**3 - 9*p**o + 13*p - 3 = 0.
1
Let z(r) = 90*r**2 + 490*r - 60. Let j(a) = a**2 - 2*a. Let s(y) = 5*j(y) - z(y). Let s(b) = 0. Calculate b.
-6, 2/17
Factor 343/4 - 1/4*q**2 - 171/2*q.
-(q - 1)*(q + 343)/4
Let k(r) be the second derivative of r**4/108 + r**3/9 - 3857*r. Let k(c) = 0. Calculate c.
-6, 0
Let m(c) be the third derivative of -1/12*c**5 - 25/24*c**4 - 5*c**3 + 0 + 142*c**2 + 0*c. Let m(n) = 0. Calculate n.
-3, -2
Let 693*y**2 + 696 + 2781/2*y - 3/2*y**3 = 0. Calculate y.
-1, 464
Let g = -263392 - -263395. Solve 111/4*y**2 + 12*y**g + 6 - 3*y**5 - 45/4*y**4 - 63/2*y = 0.
-4, -2, 1/4, 1
Let k(d) be the second derivative of -3*d**5/100 - 9*d**4/20 - 23*d**3/10 - 9*d**2/2 + 446*d. Factor k(v).
-3*(v + 1)*(v + 3)*(v + 5)/5
Let l(r) be the first derivative of r**5/210 - r**4/14 - r**2/2 + r - 44. Let p(a) be the second derivative of l(a). What is d in p(d) = 0?
0, 6
Let a = 100 - 98. Let -11 + 30*j + 51 + 160*j**2 - 15*j**3 - 215*j**a = 0. What is j?
-4, -2/3, 1
Factor 2/7*o**3 + 240/7*o**2 - 576 - 1544/7*o.
2*(o - 8)*(o + 2)*(o + 126)/7
Let r = 10 - 32. Let x = r - -24. Factor 2 - 26*m**3 + 52*m**3 + m**4 + m - 3*m**x - 27*m**3.
(m - 2)*(m - 1)*(m + 1)**2
Let n(b) be the first derivative of -b**3/9 - 6*b**2 + 37*b/3 - 526. Factor n(o).
-(o - 1)*(o + 37)/3
Let o(w) be the first derivative of w**4 + 44*w**3 - 452*w**2 + 1248*w - 1019. Solve o(q) = 0.
-39, 2, 4
Let w(p) be the first derivative of 7*p**3/12 + 711*p**2/2 + 203*p + 3105. Factor w(t).
(t + 406)*(7*t + 2)/4
Let s(r) be the second derivative of -r**4/3 + 281*r**3/12 - 35*r**2/4 - 2396*r. Solve s(f) = 0 for f.
1/8, 35
Let g = 38 - 39. Let a be (-2 - -3) + 1 - g. Factor 4*u**2 - a*u**2 - u + u.
u**2
Suppose 29*w = 23*w + 546. Let -45 - 24*j**3 + w - 93*j**2 - 34 - 84*j = 0. Calculate j.
-2, 1/8
Let i(v) = -v**3 + 296*v**2 - 15. Let u(l) = -296*l**2 + 12. Let t(n) = -4*i(n) - 5*u(n). Factor t(m).
4*m**2*(m + 74)
Determine d so that -60 + 2*d**2 + 26*d + 16*d - 26 - 6 = 0.
-23, 2
Let n be (-24)/32 + 26502/(-9016). Let a = -75/23 - n. Solve -3/7*p**4 + 16/7*p**3 + 16/7*p - 26/7*p**2 - a = 0.
1/3, 1, 3
Let g(o) be the first derivative of 0*o - 1/120*o**4 + 0*o**5 + 7 + 5*o**3 + 0*o**2 + 1/1800*o**6. Let t(a) be the third derivative of g(a). Factor t(j).
(j - 1)*(j + 1)/5
Let g(f) be the first derivative of -f**3/6 + 125*f**2/4 + 3294. Factor g(m).
-m*(m - 125)/2
Let v be (6*(60/8)/5)/(-1). Let j be (-2 - v/4) + 330/24. Factor j + 4*t**2 - 16*t + 3 - 1.
4*(t - 2)**2
Let d(b) be the third derivative of b**9/20160 - b**7/1680 - b**5/60 - b**3/6 - 62*b**2. Let q(c) be the third derivative of d(c). Let q(m) = 0. What is m?
-1, 0, 1
Let t(n) be the first derivative of -n**6/42 - n**5/35 + 13*n**4/14 + 26*n**3/21 - 25*n**2/14 - 25*n/7 + 251. Let t(j) = 0. What is j?
-5, -1, 1, 5
Let v = -113133/5 + 22629. Factor 2/5*r**4 + 22/5*r**2 + 0 + 12/5*r**3 + v*r.
2*r*(r + 1)*(r + 2)*(r + 3)/5
Let n(t) = -11*t**4 + 3*t**3 + 17*t**2 - 17*t + 28. Let p(v) = -v**4 + v**2 + v + 1. Let m(l) = -n(l) + 10*p(l). Solve m(y) = 0 for y.
-3, 1, 2, 3
Suppose -s - 4*h + 46 = 0, -h + 1128 - 1113 = 2*s. Factor 4 + 3*j + 1/2*j**s.
(j + 2)*(j + 4)/2
Let f(k) be the second derivative of -40*k + 0 + 0*k**2 + 2/5*k**3 - 2/5*k**4 + 9/50*k**6 - 9/100*k**5. Suppose f(u) = 0. What is u?
-1, 0, 2/3
Let b be 4/(-6) + 3/(-9). Let s(w) = -w**2 + w + 3*w - 4*w. Let q(l) = -35*l**2 - 20*l. Let n(i) = b*q(i) + 30*s(i). Factor n(z).
5*z*(z + 4)
Suppose -98*x - 86*x + 324*x - 280 = 0. Factor -3/4*v**x + 21/4*v + 6.
-3*(v - 8)*(v + 1)/4
Let c = 10639 - 42553/4. Let j(v) be the second derivative of 4/3*v**3 - 1/60*v**6 - 5/4*v**2 - c*v**4 + 1/5*v**5 + 13*v + 0. Factor j(g).
-(g - 5)*(g - 1)**3/2
Let o(u) be the second derivative of u**6/600 - 11*u**5/100 + 21*u**4/40 + 3*u**3 + 2*u**2 + u + 267. Let a(c) be the second derivative of o(c). Factor a(t).
3*(t - 21)*(t - 1)/5
Let o(p) = -2*p**3 + p**2 - p - 1. Let y(u) = u**2 + 27*u - 18. Let z be y(-28). Let v(s) = 3*s**3 - 3*s**2 + 7*s - 1. Let f(k) = z*o(k) + 5*v(k). Factor f(d).
-5*(d - 1)**2*(d + 3)
Let m(f) be the second derivative of -f**5/150 - f**4/45 + 7*f**3/45 - 4*f**2/15 - 1103*f. Factor m(c).
-2*(c - 1)**2*(c + 4)/15
Factor -4*q**4 - 9 + 8*q + 0 - 12*q**3 + 8 + 4*q**2 + 4*q**5 + 1.
4*q*(q - 2)*(q - 1)*(q + 1)**2
Let b(h) be the third derivative of h**5/330 + 5*h**4/22 + 221*h**3/33 - 190*h**2 - 2*h. Find r, given that b(r) = 0.
-17, -13
Let i(g) be the second derivative of -g**6/90 + 7*g**5/10 - 13*g**4/12 - 41*g**3/9 - 759*g. Let i(j) = 0. Calculate j.
-1, 0, 2, 41
Let v(j) be the second derivative of j**5/80 + 313*j**4/48 + 155*j**3/3 + 309*j**2/2 + 10505*j. Solve v(m) = 0.
-309, -2
Let q(d) be the second derivative of 5*d**9/3024 - d**8/336 - d**7/84 - 4*d**3 - 2*d + 14. Let j(x) be the second derivative of q(x). Solve j(m) = 0.
-1, 0, 2
Let k = -1/1946 + 985/23352. Let t(h) be the second derivative of -1/2*h**2 - 16*h - 1/12*h**3 + 0 + k*h**4. Factor t(p).
(p - 2)*(p + 1)/2
Let r(v) be the second derivative of -v**4/66 - 2752*v**3/33 - 1893376*v**2/11 - v - 943. Suppose r(u) = 0. What is u?
-1376
Factor -1/4*r**4 + 0 + 61/4*r**3 - 240*r**2 + 225*r.
-r*(r - 30)**2*(r - 1)/4
Let b = 11924/5 + -2976. Let n = b + 592. Factor -28/5*q + n + 49/5*q**2.
(7*q - 2)**2/5
Let o(l) be the third deri