 20*u + 1176*u**3 - 336*u**2 - 3.
-4*u*(7*u - 2)**3
Let b(l) be the third derivative of l**7/735 + l**6/60 - 5*l**5/42 - 67*l**4/84 - 12*l**3/7 - l**2 + 278. Find k such that b(k) = 0.
-9, -1, 4
Let d(i) = 10*i**2 - 10*i - 15. Let a(o) = -3*o - 5. Let w be a(0). Let m(r) = -r**2 + r + 1. Let x(z) = w*m(z) - d(z). Factor x(v).
-5*(v - 2)*(v + 1)
Let s(x) = -x**3 - 6*x**2 - 5*x**3 - 3*x + 3*x**3 - 2*x. Let d(b) = -7*b**3 - 13*b**2 - 11*b. Let o(t) = -2*d(t) + 5*s(t). Factor o(r).
-r*(r + 1)*(r + 3)
Let a(r) be the second derivative of r**8/84 - 2*r**7/105 - r**6/10 + r**5/15 + r**4/3 + 24*r**2 + 26*r. Let n(z) be the first derivative of a(z). Factor n(w).
4*w*(w - 2)*(w - 1)*(w + 1)**2
Factor -6/7*m + 0 - 2/7*m**2.
-2*m*(m + 3)/7
Let a(t) be the first derivative of 5 + 0*t**2 + 0*t**3 + 3/10*t**5 + 1/9*t**4 + 4*t. Let r(m) be the first derivative of a(m). Solve r(n) = 0 for n.
-2/9, 0
Suppose 18*g + 2 = 19*g. Factor 9*p**2 - 8*p**g + 13*p**2 + 4*p**3 + 2*p**2.
4*p**2*(p + 4)
Let k(c) be the second derivative of -27*c**4/16 - 3*c**3/2 - c**2/2 + 2*c + 198. Factor k(q).
-(9*q + 2)**2/4
Let j = -15 + 12. Let t(r) = -2*r**2 - 3*r - 3. Let s(g) be the first derivative of -g**3 - 2*g**2 - 4*g - 9. Let p(w) = j*s(w) + 4*t(w). Factor p(v).
v**2
Factor -2/3*u**2 + 160/3*u - 3200/3.
-2*(u - 40)**2/3
Let r(j) = 7*j**3 - 75*j**2 + 508*j - 428. Let h(i) = -27*i**3 + 300*i**2 - 2031*i + 1713. Let q(v) = 4*h(v) + 15*r(v). Determine n so that q(n) = 0.
1, 12
Let b(s) be the first derivative of 2/3*s**4 - 1/15*s**5 + 0*s + 3/2*s**2 - 8/3*s**3 + 6. Let q(x) be the second derivative of b(x). Factor q(m).
-4*(m - 2)**2
Let s(u) be the first derivative of 11 - 1/4*u**6 - 1/8*u**3 + 3/40*u**5 + 0*u**2 + 3/8*u**4 + 0*u. Solve s(i) = 0 for i.
-1, 0, 1/4, 1
Suppose 0*t + 5*k - 5 = 5*t, 0 = 3*t - 5*k + 11. Let d be t - 0/(6/(-3)). Factor -9*q**3 - 8*q**d + 20*q**3 - 3*q.
3*q*(q - 1)*(q + 1)
Let g be 56/(-7) + -2 + 14. Let s(l) be the second derivative of -1/3*l**g + 0 + 1/6*l**3 - 6*l + 0*l**2. Find i such that s(i) = 0.
0, 1/4
Let p(o) = 369*o - 1103. Let x be p(3). Let -68/5*r**2 + 232/5*r**3 + 10*r**5 - 44*r**x + 0 + 6/5*r = 0. What is r?
0, 1/5, 1, 3
Let b(o) be the third derivative of -o**5/100 + 9*o**4/10 - 162*o**3/5 - 4*o**2 + 1. Factor b(r).
-3*(r - 18)**2/5
Let h be -5 + 25 - (-1110)/(-60). Factor h*q**2 - 3*q + 0.
3*q*(q - 2)/2
Let a(b) be the second derivative of 7*b**6/255 + 79*b**5/170 + 151*b**4/51 + 416*b**3/51 + 96*b**2/17 + 35*b - 5. Find y, given that a(y) = 0.
-4, -3, -2/7
Suppose -3/2*q + 5 - 1/2*q**2 = 0. Calculate q.
-5, 2
Let s(d) be the first derivative of d**6/6 - 21*d**5/25 - 11*d**4/20 + 31*d**3/5 - 9*d**2/5 + 223. Suppose s(q) = 0. What is q?
-2, 0, 1/5, 3
Let q(h) be the first derivative of 52*h**3 - 315*h**2/4 + 3*h/2 + 539. Determine t, given that q(t) = 0.
1/104, 1
Suppose 68*g - 63*g = 4*p + 4, 2*g + 4*p = 24. Solve 10*m**5 - 18/5*m**3 + 0 + 0*m + 6*m**g + 2/5*m**2 = 0 for m.
-1, 0, 1/5
Let p(t) be the second derivative of t**7/280 - t**6/120 - 23*t**3/6 + 6*t. Let u(r) be the second derivative of p(r). Determine h so that u(h) = 0.
0, 1
Let x = -49 + 192. Let a = x - 73. Factor 0*o**2 + a - 6 + 4*o**2 - 32*o.
4*(o - 4)**2
Let g(s) = s**3 - 7*s**2 + 7*s + 3. Let x be g(6). Factor 4 - 9*k**3 + 3*k + 11*k**3 - x*k.
2*(k - 1)**2*(k + 2)
Let k be 2*((-37)/(-10) + -4)*-5. Factor -5 + 5*y**k + 19*y + 26*y**2 + 16*y - 51*y**2 - 10.
5*(y - 3)*(y - 1)**2
Let d(w) be the second derivative of w**4/6 - 8*w**3/3 + 12*w**2 - 78*w. Factor d(u).
2*(u - 6)*(u - 2)
Let b(r) = 5*r**4 + 6*r**3 - 7*r**2 - 8*r - 2. Let u(f) = 7*f**4 + 7*f**3 - 7*f**2 - 7*f - 3. Let p(m) = -3*b(m) + 2*u(m). Suppose p(w) = 0. Calculate w.
-5, -1, 0, 2
Suppose 3*n + 2*y = -y - 15, n - 5*y = 25. Suppose -g + 0 + 2 = n. Factor -j**3 + 0 - 1/3*j**4 - 1/3*j - j**g.
-j*(j + 1)**3/3
Suppose -4*x - 2*b = -x + 11, 4*x - 4*b = 12. Let y = 3 - x. Solve -2 + d**2 - 10*d**3 + y*d**3 + 5*d**3 + 1 + d = 0 for d.
-1, 1
Let s(h) be the third derivative of h**7/70 + h**6/40 - h**5/5 - h**4/2 - 12*h**2 - 19*h. Factor s(q).
3*q*(q - 2)*(q + 1)*(q + 2)
Factor -1369/5 - 1/5*x**2 + 74/5*x.
-(x - 37)**2/5
Suppose -8*u = u - 45. Let w(o) be the first derivative of -2/15*o**3 - 1/30*o**6 + 0*o + 2 + 0*o**4 + 2/25*o**u + 1/10*o**2. Factor w(g).
-g*(g - 1)**3*(g + 1)/5
Let b(f) be the second derivative of f**4/3 + 604*f**3/3 + 45602*f**2 - 32*f + 4. Let b(s) = 0. Calculate s.
-151
Let s(u) be the first derivative of 3*u**5/40 - 3*u**4/4 - u**3/8 + 3*u**2/2 - 61. Factor s(j).
3*j*(j - 8)*(j - 1)*(j + 1)/8
Let w(y) = y**3 + 4*y**2 - y - 2. Suppose 0 = 5*f + h + 15, -5*f = 5*h - 4 - 1. Let c be w(f). Factor -4*v**2 + 18*v - 12 - 2*v + 0*v**c.
-4*(v - 3)*(v - 1)
Let b(n) = -n**2 - 6*n - 2. Let x = -2 + -3. Let p be b(x). What is q in 7*q - q + p*q**2 - 6*q**2 = 0?
0, 2
Factor 1/6*p**4 - 2/3*p**2 + 0 - 2/3*p + 1/6*p**3.
p*(p - 2)*(p + 1)*(p + 2)/6
Let l(i) = -10*i**3 - 33*i**2. Let w(p) = -51*p**3 - 159*p**2. Let s(b) = -24*l(b) + 5*w(b). Factor s(u).
-3*u**2*(5*u + 1)
Let o(t) be the second derivative of -t**7/84 - 2*t**6/3 - 399*t**5/40 + 5*t**4/3 + 100*t**3/3 - 269*t + 2. What is j in o(j) = 0?
-20, -1, 0, 1
Let z(i) = 35*i**4 - 35*i**3 - 10*i**2 - 30*i. Let n be (-16 + 17)/(3/(-3 - 0)). Let g(h) = h**4 - h**3 - h. Let y(q) = n*z(q) + 30*g(q). Factor y(l).
-5*l**2*(l - 2)*(l + 1)
Let g(k) be the first derivative of -k**6/2 + 21*k**5/5 - 45*k**4/4 + 13*k**3 - 6*k**2 - 136. Factor g(t).
-3*t*(t - 4)*(t - 1)**3
Factor -19191/2*g**2 + 243*g**3 - 3/2*g**4 - 19926*g - 10086.
-3*(g - 82)**2*(g + 1)**2/2
Let g(v) = -2*v**3 + 3*v**2 - v - 3. Let c(k) = -4*k + 3. Let n be c(1). Let i be g(n). Find d such that -6/5*d - 57/5*d**2 - 159/5*d**i - 108/5*d**4 + 0 = 0.
-1, -1/4, -2/9, 0
Let f(p) = -p**4 + 14*p**3 + p**2 + 4*p + 6. Let j(l) = 2*l**4 - 16*l**3 - 2*l**2 - 5*l - 7. Let y(i) = -7*f(i) - 6*j(i). Factor y(v).
-v*(v - 1)*(v + 1)*(5*v + 2)
Let h(x) be the second derivative of -2*x**5/45 + x**4/18 + 4*x**3/27 - x**2/3 + 113*x. Factor h(s).
-2*(s - 1)*(s + 1)*(4*s - 3)/9
Let y be 1*3/(-2) + 2. Let a(o) = -80*o - 398. Let m be a(-5). Factor -1/6*t**m - y - 2/3*t.
-(t + 1)*(t + 3)/6
Let a(u) be the first derivative of 2*u**3/45 - 8*u/15 + 5. Solve a(y) = 0.
-2, 2
Let x(i) be the third derivative of -i**7/126 + 19*i**6/36 - 361*i**5/36 - 571*i**2. Factor x(n).
-5*n**2*(n - 19)**2/3
Let r(l) = -3*l**4 - 7*l**3 - 3*l**2 - 2*l + 5. Let i(d) = 5*d**4 + 11*d**3 + 4*d**2 + 4*d - 8. Let c(u) = -5*i(u) - 8*r(u). Suppose c(s) = 0. Calculate s.
-2, 0, 1, 2
Let b(a) be the second derivative of 2*a**7/15 - a**6/15 - 7*a**5/15 + a**4/3 - 3*a**2/2 - 15*a. Let d(u) be the first derivative of b(u). Factor d(x).
4*x*(x - 1)*(x + 1)*(7*x - 2)
Suppose -4*p + 240 = b, 2*b + 2*b = 5*p - 300. Let r = 64 - p. Suppose -2/11*d**2 - 2/11*d**3 + 2/11*d**r + 0*d + 0 + 2/11*d**5 = 0. What is d?
-1, 0, 1
Factor -36/5*h**3 - 4*h**5 + 0 + 8/5*h**2 + 0*h + 48/5*h**4.
-4*h**2*(h - 1)**2*(5*h - 2)/5
Let r(l) be the second derivative of -9/20*l**4 - 1/50*l**6 - 2/5*l**3 - 13*l + 0 + 18/5*l**2 + 9/50*l**5. Determine t, given that r(t) = 0.
-1, 2, 3
Let h(w) = 34*w**4 - 134*w**3 + 76*w**2 + 8*w + 4. Let m(u) = 32*u**4 - 137*u**3 + 77*u**2 + 8*u + 5. Let z(k) = 5*h(k) - 4*m(k). Factor z(r).
2*r*(r - 2)*(r - 1)*(21*r + 2)
Let w(c) be the third derivative of -c**6/80 + 77*c**5/20 - 305*c**4/16 + 38*c**3 + 68*c**2 + 4*c. What is k in w(k) = 0?
1, 152
Let y(j) = 2*j**2 - j + 1. Let b(l) = 20*l**2 + 70*l + 5. Let f(v) = -b(v) - 5*y(v). Let f(m) = 0. What is m?
-2, -1/6
Let q be 25/15 - (-3)/9. Factor -30*a**2 + 64*a + 85*a**q - 74*a.
5*a*(11*a - 2)
Let k(y) be the third derivative of y**5/20 + 3*y**4/4 - 7*y**3/2 + 130*y**2. Factor k(n).
3*(n - 1)*(n + 7)
Suppose 14*v - 32 + 4 = 0. Let z(x) be the second derivative of 1/12*x**4 + 0 - 1/6*x**v - 5*x - 1/9*x**3. Solve z(s) = 0.
-1/3, 1
Solve 3927*h**2 - 4*h**3 + 5184000 + h**3 - 129600*h - 2847*h**2 = 0 for h.
120
Let o be 2 - (-5)/((-20)/32). Let n be -3 + 8/(-12)*o. Solve 2*t - t**2 - 1 - n - 1 + 6 = 0.
-1, 3
Let t(y) be the second derivative of -y**5/16 - 5*y**4/6 - 25*y**3/24 + 125*y**2/4 - 79*y. Determine v, given that t(v) = 0.
-5, 2
Let q be -2 + 2 + 4*4/56. Factor q + 3/7*c + 1/7*c**2.
(c + 1)*(c + 2)/7