6*f**3/21 + 4*f**2/7 + 10*f + 15. Let d(r) be the first derivative of p(r). Factor d(m).
2*(m - 2)*(m + 2)*(4*m - 1)/7
Let j(s) be the second derivative of 0 + 1/14*s**7 - 7/10*s**6 + 4*s**3 + 27/10*s**5 - 5*s**4 - 11*s + 0*s**2. Factor j(z).
3*z*(z - 2)**3*(z - 1)
Let w = -35 - -37. Let d(y) = -y**4 - 7*y**3 - 9*y**2 - y - 2. Let n(z) = -z**3 - z**2 + z - 1. Let t(g) = w*n(g) - d(g). Factor t(b).
b*(b + 1)**2*(b + 3)
Let t(l) be the first derivative of l**5/25 + 7*l**4/5 + 74*l**3/5 + 182*l**2/5 + 169*l/5 - 165. Determine d so that t(d) = 0.
-13, -1
Let r(c) be the second derivative of c**7/315 - c**6/75 - 3*c**5/25 + 16*c**4/45 + 32*c**3/15 + 2*c - 13. Determine y, given that r(y) = 0.
-3, -2, 0, 4
Let u(g) be the first derivative of -1/5*g**5 + 4/3*g**3 + 1/2*g**2 - 10 + 0*g - 1/16*g**4. Find c such that u(c) = 0.
-2, -1/4, 0, 2
Let q = 40 + -37. Solve 9*u**4 + 2*u**3 - q*u**5 - 33*u**2 - 11*u**3 + 36*u**2 = 0.
0, 1
Determine u, given that 71 + 202 - 5*u**2 - 23 - 101 - 75*u + 351 = 0.
-20, 5
Let d(h) be the third derivative of h**6/72 - h**5/3 - 65*h**4/72 + 25*h**2 - 3*h. Solve d(l) = 0 for l.
-1, 0, 13
Suppose -2*z - 12 = -5*z. Suppose -3*k + z*d + 24 = 6, -3*d - 7 = k. Find r, given that -9 - 18*r**k + 4*r + 9 + 14*r**3 = 0.
0, 2/7, 1
Let v(y) be the first derivative of -13*y**3 + 19 + 3/4*y**4 - 108*y + 72*y**2. Factor v(t).
3*(t - 6)**2*(t - 1)
Let h(x) = -x**2. Let v(d) = 17*d**2 - 23*d + 20. Let t(p) = -3*h(p) + v(p). Let y(f) = 7*f**2 - 8*f + 7. Let r(b) = -6*t(b) + 17*y(b). Factor r(l).
-(l - 1)**2
Let d(j) be the first derivative of j**4/18 + 2*j**3/27 - j**2/9 - 2*j/9 + 121. Factor d(u).
2*(u - 1)*(u + 1)**2/9
Let p be (7 + 0)/(4 + -3). Let y(i) = 3*i + 0*i - 2 - 10*i**2 - p*i. Let v(w) = -w**2 - w. Let m(k) = -8*v(k) + y(k). Suppose m(d) = 0. What is d?
1
Let n(u) = u**2 - 3*u + 5. Let f be n(2). Let -6 - 3*p**4 - 3*p - 11*p**2 - 3*p**5 + 3 + 6*p**f + 17*p**2 = 0. Calculate p.
-1, 1
Let n(q) be the third derivative of 2/35*q**7 - 1/15*q**5 + 0 + 3/4*q**4 - 4/3*q**3 - 58*q**2 - 2/15*q**6 - 1/168*q**8 + 0*q. Solve n(m) = 0.
-1, 1, 4
Let w = -126/2209 - -8090/19881. Let l = w + -6/47. Factor 4/9*v + l*v**2 + 2/9.
2*(v + 1)**2/9
Let c(f) = 79 + 3*f**3 - 80 - f**3. Let m(v) = 3*v**3 + 25*v**2 - 35*v + 11. Let j(i) = 4*c(i) - m(i). Factor j(r).
5*(r - 3)*(r - 1)**2
Let g = 107 - 104. Let q(r) be the first derivative of 3/5*r**5 - 9/8*r**4 - 3/8*r**2 - 1/8*r**6 + r**3 + 0*r + g. Factor q(z).
-3*z*(z - 1)**4/4
Let h(q) be the second derivative of -1/60*q**6 - 1/6*q**3 + 1/8*q**4 + 2*q + 0*q**2 - 1 + 0*q**5. Factor h(b).
-b*(b - 1)**2*(b + 2)/2
Let u(h) = -h**3 + h**2 + 2*h - 2. Let y be ((-1)/2)/((-5)/10). Suppose 3 - 1 = 2*t. Let m(n) = n**4 - n**3 - n**2 + 1. Let b(g) = t*u(g) + y*m(g). Factor b(z).
(z - 1)**3*(z + 1)
Suppose 0 = 89*y - 99*y + 20. Let m(r) be the second derivative of 0 - r**4 - 3*r + 3/2*r**y - 3/2*r**3. Solve m(u) = 0.
-1, 1/4
Let z be (-6)/48 - (-41)/8. Let p(n) be the third derivative of 0 + 0*n - 4*n**2 - 1/20*n**z - 1/2*n**3 + 1/4*n**4. Suppose p(r) = 0. Calculate r.
1
Factor -6*r**3 - 8*r**2 + 36 + 4*r**3 + 6*r - 8*r**3 + 8*r**3.
-2*(r - 2)*(r + 3)**2
Suppose 1151*j - 1180*j = 0. Factor 2/13*k**4 - 2/13*k**2 + 0*k**3 + j + 0*k.
2*k**2*(k - 1)*(k + 1)/13
Let m(j) be the first derivative of j**5/30 + j**4/12 - j**3/6 - 401. Let m(s) = 0. What is s?
-3, 0, 1
Let m = 781 + -781. Let q(l) be the second derivative of 0*l**2 + l + 0*l**5 - 1/60*l**6 + m*l**3 + 1/24*l**4 + 0. Let q(a) = 0. Calculate a.
-1, 0, 1
Suppose -4*u + 4*w = 2*w + 8, 4*u - 3*w + 12 = 0. Let x(p) be the second derivative of 0*p**2 + 1/9*p**3 - 1/36*p**4 - 7*p + u. Factor x(d).
-d*(d - 2)/3
Let r = 21 - 19. Factor 7*n - 3 + 7 + 14 + 2*n**r + 5*n.
2*(n + 3)**2
Let w(f) = -f**3 - 5*f**2 - 3. Suppose 4*i = 17 - 5. Let d(l) = 5 + 1 + 4*l**i + 21*l**2 + 7. Let x(n) = -6*d(n) - 26*w(n). Determine q, given that x(q) = 0.
-2, 0
Solve 3/5*x**5 - 27/5*x**3 - 12/5*x + 0 - 33/5*x**2 - 3/5*x**4 = 0 for x.
-1, 0, 4
Suppose 2 = -6*x + 7*x. Let o(n) = n**3 + 15*n**2 - n - 9. Let u be o(-15). Let -u*y**4 - y**3 + y**2 + 7*y**3 - 7*y**x + y + 5*y**3 = 0. What is y?
0, 1/3, 1/2, 1
Let g(q) be the first derivative of -q**4/2 + 2*q**3 + 6*q**2 - 16*q - 906. Factor g(z).
-2*(z - 4)*(z - 1)*(z + 2)
Let o be 2/30*(357/153 + 1/6). Factor 1/2 + 5/6*i - o*i**3 + 1/6*i**2.
-(i - 3)*(i + 1)**2/6
Suppose -2*m - 156 = -5*f + 349, -88 = -f + 3*m. Let p = f + -99. Factor 0 - 6/5*u**p + 0*u**3 + 3/5*u**5 - 3/5*u + 6/5*u**2.
3*u*(u - 1)**3*(u + 1)/5
Let o be (-8)/(24/(-15)) + -6. Let l be o/(-15)*12 + (-6)/45. Suppose -2/3*y**5 + 4/3*y**3 - 2/3*y**4 + 4/3*y**2 - 2/3*y - l = 0. Calculate y.
-1, 1
Let p(w) = w**2 - 11*w + 20. Let b be p(8). Let i be 6*b/32*-2. Factor i*g**4 - 2*g + 2*g**3 - g**2 - 1/2.
(g - 1)*(g + 1)**2*(3*g + 1)/2
Let u(n) be the first derivative of -1/15*n**5 - 1/4*n**4 + 0*n**2 + 1 + 0*n - 2/9*n**3. Let u(x) = 0. Calculate x.
-2, -1, 0
Let f(a) = 7*a**3 + 181*a**2 + 4421*a + 4227. Let c(j) = -3*j**3 - 91*j**2 - 2210*j - 2114. Let u(m) = -5*c(m) - 2*f(m). Factor u(g).
(g + 1)*(g + 46)**2
Let d(k) be the first derivative of -11/9*k**3 + 0*k + 41 + 1/3*k**2 + 7/12*k**4 + 4/3*k**5. Suppose d(n) = 0. Calculate n.
-1, 0, 1/4, 2/5
Let r(x) be the third derivative of 24*x**2 + 0*x - 1/3*x**4 + 0 + 4*x**3 - 1/30*x**5. Let r(p) = 0. Calculate p.
-6, 2
Suppose -6 = 5*h - 1. Let x be 4 + (h - 0) + -3. Factor -j**3 - 2/5*j + 7/5*j**2 + x.
-j*(j - 1)*(5*j - 2)/5
Let d(i) be the second derivative of i**6/5 + i**5 + i**4/2 - 4*i**3 - 4*i**2 - 4*i + 12. Find h such that d(h) = 0.
-2, -1/3, 1
Factor 0 + 3/4*r**4 + 6*r**3 + 0*r - 15*r**2.
3*r**2*(r - 2)*(r + 10)/4
Let h be -25*(22/(-5) + 4). Let x be (15/h)/((-3)/(-4)). Solve d**2 - d**x + 3*d - 6*d + 3*d**2 = 0.
0, 1
Let r be (-4 - (12 + -20))*2/14. Factor -2/7*o**4 - 4/7*o**3 - 2/7 + 2/7*o + 2/7*o**5 + r*o**2.
2*(o - 1)**3*(o + 1)**2/7
Let t(c) be the second derivative of -c**5/10 + 31*c**4/6 - 29*c - 3. Solve t(b) = 0 for b.
0, 31
Suppose 9 + 0 = 3*s - 2*m, -12 = -4*s - 4*m. Let 3/2*d - 1/2*d**2 - 5/6*d**s + 0 - 1/6*d**4 = 0. Calculate d.
-3, 0, 1
Let n(y) be the third derivative of y**8/33600 + y**7/6300 - y**6/3600 - y**5/300 + y**4/12 + 11*y**2. Let k(h) be the second derivative of n(h). Factor k(m).
(m - 1)*(m + 1)*(m + 2)/5
Suppose 2 = 12*l - 11*l. Factor -24*x**3 + 37*x**2 + 27*x**l + 33*x - 19*x**2 - 48 + 3*x**4 - 9*x.
3*(x - 4)**2*(x - 1)*(x + 1)
Let k be (1088/(-264))/17*3/2. Let a = 32/33 - k. Factor -8*h**2 + a*h + 35/3*h**3 + 0.
h*(5*h - 2)*(7*h - 2)/3
Let d be (-110)/264*(-3)/5 + 0. Determine h, given that -3/4*h**2 + 0*h + 1 - d*h**3 = 0.
-2, 1
Let f(q) be the second derivative of q**7/14 + 2*q**6/5 - 3*q**5/20 - q**4 - 4*q + 36. Factor f(m).
3*m**2*(m - 1)*(m + 1)*(m + 4)
Let p(o) be the third derivative of -o**5/80 + o**4/32 + 3*o**3/2 + 7*o**2. Factor p(m).
-3*(m - 4)*(m + 3)/4
Suppose -10*p + 643 = 2893. Let n be (-8 + -1)*45/p. Factor 2/5 - n*q**2 - q**4 + 13/5*q**3 - 1/5*q.
-(q - 1)**3*(5*q + 2)/5
Let u(n) be the first derivative of 5*n**9/3024 - n**7/84 + n**5/24 + 8*n**3 - 26. Let z(f) be the third derivative of u(f). What is w in z(w) = 0?
-1, 0, 1
Suppose 5*k - 30 = -5*n, -3707*n + 18 = -3705*n + 4*k. Factor 36/5*b**4 + 0 - 78/5*b**n - 24/5*b + 72/5*b**2 - 6/5*b**5.
-6*b*(b - 2)**2*(b - 1)**2/5
Let p = -35 - -39. What is h in -3*h**3 - 7*h**2 + 7*h**2 + 11*h**3 + 4*h**4 - 8*h - p = 0?
-1, 1
Let g be (-1)/5 + (-8)/10. Let d be -2*((-3 - -3) + g). Find h such that 4*h**2 - h**d - 2*h**3 - h**3 + 5*h**4 + 3*h - 8*h**4 = 0.
-1, 0, 1
Let n(y) be the third derivative of -y**5/100 - 3*y**4/8 + 513*y**2 - 2*y. Factor n(i).
-3*i*(i + 15)/5
Let o(w) be the second derivative of 0 + 1/30*w**4 + 23*w + 0*w**2 + 0*w**3 - 1/75*w**6 + 0*w**5. Let o(l) = 0. What is l?
-1, 0, 1
Let v be (-2)/(-7) + 234/(-3465). Let s = v + 2/11. Determine x so that -6/5*x**2 + 4/5*x + 0 + s*x**3 = 0.
0, 1, 2
Let j be 9/(81/30) + (-5 - -2). Let u(d) be the first derivative of j*d**3 - 2/7*d + 3 - 5/14*d**2. Factor u(r).
(r - 1)*(7*r + 2)/7
Let w(m) be the first derivative of -17 - 3/2*m - 1/6*m**3 + m**2. Find x, given that w(x) = 0.
1, 3
Let s(t) be the first derivative of t**4/4 + 4*t**3/3 - 7*t**2/2 - 6*t + 4. Let d be s(-5). Factor