(y) + 9*v(y). Factor k(h).
-2*(h - 3)**3
Suppose 0 = -7*f + 9 + 12. Let h(q) be the second derivative of 12*q + 1/12*q**5 - 1/18*q**4 + 1/126*q**7 + 0*q**f - 2/45*q**6 + 0 + 0*q**2. Factor h(a).
a**2*(a - 2)*(a - 1)**2/3
Let p(h) be the third derivative of -h**5/30 - 7*h**4/48 + h**3/6 - 64*h**2. Factor p(s).
-(s + 2)*(4*s - 1)/2
Let j = -55 + 61. Let -2*l**2 + 2 - j*l + 5*l**2 + 6*l**2 - 5*l**2 = 0. Calculate l.
1/2, 1
Let d = -157/2 - -2673/34. Let b = -1775 + 1775. Solve d*k + 4/17*k**2 + b + 2/17*k**3 = 0.
-1, 0
Let u(s) = 21*s - 36. Let r be u(2). Let g(o) be the first derivative of -o**3 + r*o + 3/2*o**2 - 7. Factor g(n).
-3*(n - 2)*(n + 1)
Let x be 4/10 + (-72)/(-20). Let g(r) = -r + 14. Let n be g(12). Determine y so that -x*y + y**2 + n*y + 0*y**2 = 0.
0, 2
Let x(j) be the second derivative of j**8/1680 + j**7/280 + j**6/120 + j**5/120 - 17*j**3/6 + 47*j. Let l(t) be the second derivative of x(t). Factor l(o).
o*(o + 1)**3
Let l be (-29)/(-84) - (-342)/(-3591). Factor -z - 1/4*z**4 - z**3 - 3/2*z**2 - l.
-(z + 1)**4/4
Let m(l) = 3*l**2 - 39*l. Let n be m(13). Let i(r) be the second derivative of -7/3*r**4 + 49/20*r**5 + 0 - 2*r + 2/3*r**3 + n*r**2. Factor i(x).
x*(7*x - 2)**2
Let l(t) = -t**3 - 7*t**2 + 2*t + 11. Let z be l(-7). Let w(b) = 28*b**2 + 36*b + 11. Let c(h) = -1. Let s(o) = z*c(o) - w(o). What is m in s(m) = 0?
-1, -2/7
Let s(p) be the third derivative of p**6/600 - 7*p**5/300 - p**4/24 + 5*p**3/2 + 384*p**2. Suppose s(w) = 0. Calculate w.
-3, 5
Factor 1/8*m**3 - m**2 + 2*m + 0.
m*(m - 4)**2/8
Let g be (0 - 12)/(-1*5/(-10)). Let t be (g/(-70))/((-60)/(-200)). Let -6/7 - t*s - 2/7*s**2 = 0. What is s?
-3, -1
Factor 0*l**2 + 2/3*l**4 + 0 - l**3 + 0*l + 1/3*l**5.
l**3*(l - 1)*(l + 3)/3
Suppose -4*d = 3*f - 27 - 20, -5*d - 55 = -5*f. Suppose -f = -6*r - 7. Find c such that -9/2*c - 11/2*c**2 + r = 0.
-1, 2/11
Let i = 120348/11 - 10940. Determine a, given that 2/11*a**4 - i*a**2 + 0*a + 0 - 8/11*a**3 + 2/11*a**5 = 0.
-2, -1, 0, 2
Suppose -3*x - 2*g + 3*g = 63, 0 = -4*g + 12. Let o be -2*(1 - x/(-8)). Factor 3*d**o - 3/4 + 3/4*d**2 - 3*d.
3*(d - 1)*(d + 1)*(4*d + 1)/4
Let d = 8328/5155 + -16/1031. Let 0 - d*i + 2/5*i**2 = 0. What is i?
0, 4
Let p(u) be the first derivative of -2*u**5/65 + 5*u**4/13 - 14*u**3/13 - 36*u**2/13 + 216*u/13 - 387. Solve p(r) = 0.
-2, 3, 6
Determine y, given that 26/9*y - 2/9*y**3 + 4/3 + 14/9*y**2 - 2/9*y**4 = 0.
-2, -1, 3
Suppose -67 + c**2 + 41 - 3*c**2 - 5*c - 23*c = 0. Calculate c.
-13, -1
Let a be 2 + 1 - (0 - -65). Let d be a/(-14) - 6/14. Factor -39*v + d + 37*v - 3 + v**2.
(v - 1)**2
Suppose 3*z = a + 41, -4 = -4*a - 24. Suppose y - z = 4. Let y*n**2 - 18*n**4 + 8*n - 6*n**3 - 3*n**4 - 2*n**4 + 5*n**4 = 0. What is n?
-2/3, 0, 1
Factor 2/3*t**4 - 16/3*t**2 + 0*t - 4/3*t**3 + 0.
2*t**2*(t - 4)*(t + 2)/3
Let l(y) be the third derivative of 5*y**8/336 + y**7/42 - 5*y**6/6 + 971*y**2. Factor l(b).
5*b**3*(b - 4)*(b + 5)
Let j(y) = 17*y - 23. Let b be j(-6). Let c be (-16)/64 - (2 - b/(-52)). Let 0 - c*q**3 - 2/13*q - 4/13*q**2 = 0. Calculate q.
-1, 0
Let c = 151/24570 + -1/1170. Let m(x) be the second derivative of 1/27*x**4 + 0*x**5 + 0*x**2 - x - 2/135*x**6 - 1/27*x**3 + 0 + c*x**7. What is d in m(d) = 0?
-1, 0, 1
Let y(x) = x**3 + x**2 + x + 1. Suppose 8 = 4*p - 4*r, -4 = 3*p + 5*r - 2. Let k(i) = 4*i**3 + 36*i - 8. Let n(a) = p*k(a) - 8*y(a). Let n(w) = 0. What is w?
-4, 1
Factor 4320/13*c + 74/13*c**3 + 2/13*c**4 + 72*c**2 + 3456/13.
2*(c + 1)*(c + 12)**3/13
Factor 1323/4*l + 3/4*l**3 + 0 - 63/2*l**2.
3*l*(l - 21)**2/4
Let o(j) = 4*j**3 - 32*j**2 + 20*j + 8. Let s(d) = 6 - 1 - 21*d**2 - 959*d + 3*d**3 + 972*d. Let c(v) = 5*o(v) - 8*s(v). Factor c(m).
-4*m*(m - 1)**2
Find s, given that -1965*s**2 - 2402 - 4675*s - 542 - 5*s**4 - 336 - 185*s**3 + 390 = 0.
-17, -2, -1
Let a(t) be the third derivative of -t**6/900 + t**4/15 + 5*t**3/6 + 3*t**2. Let r(u) be the first derivative of a(u). Let r(g) = 0. What is g?
-2, 2
Let a be 0/(-5 + 6)*1. Let v(r) be the second derivative of a*r**4 - 3*r + 2/15*r**6 + 0*r**2 + 1/5*r**5 + 0 + 0*r**3. Find k such that v(k) = 0.
-1, 0
Suppose -9/5 - 37/5*z - 4/5*z**2 = 0. Calculate z.
-9, -1/4
Let i(x) be the first derivative of -x**4/108 + x**3/3 - 9*x**2/2 + 28*x + 13. Let v(k) be the first derivative of i(k). Factor v(j).
-(j - 9)**2/9
Let w(n) = -n**3 + 160*n**2 - 165*n**2 + 13*n + 3*n**3. Let x(v) = v**3 - 3*v**2 + 6*v. Let s(i) = -2*w(i) + 5*x(i). Determine m, given that s(m) = 0.
0, 1, 4
Let i(y) be the first derivative of y**4/26 + 10*y**3/13 + 72*y**2/13 + 224*y/13 + 241. Solve i(h) = 0.
-7, -4
Let g = -101142/29 - -3488. Let k = g - -28/87. Suppose 2 - 4/3*j - k*j**2 = 0. Calculate j.
-3, 1
Let f(b) be the first derivative of 2*b**3/11 + 78*b**2/11 + 1014*b/11 - 35. Factor f(p).
6*(p + 13)**2/11
Let b = -7 + 9. Let s(z) = -34*z - 136. Let i be s(-4). What is f in 1/3*f**b + 0*f + i = 0?
0
Let s be (-4)/5*25/60*6*-1. Solve -54/5*h**5 - 2/5 - 18*h**4 - 20*h**s + 36*h**3 + 14/3*h = 0 for h.
-3, 1/3
Let g be 5 - (2 + -2 + -2). Let q be 4/7*g/2. Suppose 2*o**5 + 6*o**3 - 4*o - 2*o - 8*o**q - 2*o + 8*o**4 = 0. Calculate o.
-2, -1, 0, 1
Let u(o) be the third derivative of -o**7/210 + 4*o**6/15 - 3*o**5/2 + 11*o**4/3 - 29*o**3/6 + 246*o**2. Determine b, given that u(b) = 0.
1, 29
Let r(s) = -2*s. Let i(n) = 3*n**3 + 12*n**2 - 8*n - 48. Let c(a) = i(a) + 2*r(a). What is h in c(h) = 0?
-4, -2, 2
Let n be 6/(((0 - 9) + 8)*-2). Factor 0*l**n + 0*l + 3/4*l**4 - 3/4*l**2 + 0.
3*l**2*(l - 1)*(l + 1)/4
Find l such that -10/3*l**2 + 8/3*l + 0 + 2/3*l**3 = 0.
0, 1, 4
Let r = 11 - 21. Let h = -4 - r. Factor -h*i + 4*i**2 + 64 - 52 + 22*i.
4*(i + 1)*(i + 3)
Suppose u - 1 = 3*u + s, 5*u = -4*s - 10. What is a in -u*a**2 + 952 - 476 - 464 - 10*a = 0?
-6, 1
Suppose 2*g = 2*j - j - 2, 3*g = 4*j + 7. Let h be (g/2)/(6/(-396)). Factor 20*s + 3*s**3 + s**3 - h - 16*s**2 + 91.
4*(s - 2)*(s - 1)**2
Let r = -12754/5 - -2552. Solve -r*a**2 + 6/5*a - 2/5 + 2/5*a**3 = 0.
1
What is r in -96/5 - 4/5*r**2 - 20*r = 0?
-24, -1
Let s = -1/488 - -245/488. Let d(z) be the first derivative of 1 + s*z**3 + 3*z - 9/4*z**2. Determine a so that d(a) = 0.
1, 2
Let o be ((-4)/(-34))/((-28)/(-476)). Let z(f) be the second derivative of 0*f**3 + 0 + 0*f**o - 1/5*f**5 + 0*f**4 - 7*f. Factor z(k).
-4*k**3
Let p(s) be the second derivative of -s**6/90 - s**5/20 + s**4/3 + 26*s**3/9 + 8*s**2 + 28*s - 2. Factor p(z).
-(z - 4)*(z + 2)**2*(z + 3)/3
Let a be (2 + 0)/(2/(-4) + 1). Suppose -6*p = a*p. Factor 2*i**2 + p + 2/7*i**5 + 10/7*i**4 + 18/7*i**3 + 4/7*i.
2*i*(i + 1)**3*(i + 2)/7
Let u(j) = 101*j**2 - 110*j + 5. Let f(v) = v**2. Let r(w) = 4*f(w) + u(w). What is b in r(b) = 0?
1/21, 1
Factor 28/3*j - 5*j**2 + 4/3.
-(j - 2)*(15*j + 2)/3
Let r(w) = -w**3 + 11 + 16*w**2 + 1 + 2*w**3. Let i be r(-16). Find f, given that -f**2 + 12 - i - f = 0.
-1, 0
Let q be (-54)/(-26) - (-19)/(-247). Factor -48 - 1/3*x**q + 8*x.
-(x - 12)**2/3
Let m(q) be the second derivative of q**6/40 + q**5/60 - 14*q**3/3 - 26*q. Let f(h) be the second derivative of m(h). Let f(k) = 0. What is k?
-2/9, 0
Let i(v) be the first derivative of -2*v**3/9 + 80*v**2/3 - 3200*v/3 + 195. Suppose i(c) = 0. Calculate c.
40
Factor -200 + 3*r + 200 + 3*r**3 + r**4 + 3*r**2 - 2*r.
r*(r + 1)**3
Let v = 1 + 21. Find a, given that -9*a**4 - v - 3*a**5 - 2*a**2 + 22 + 14*a**2 = 0.
-2, 0, 1
Let t be (-3)/(-2) + 215/(-170). Factor -4/17 + t*d**2 + 2/17*d - 2/17*d**3.
-2*(d - 2)*(d - 1)*(d + 1)/17
Let n(s) be the third derivative of -1/210*s**6 + 1/21*s**3 + 0*s + 1/42*s**4 + 4*s**2 - 1/735*s**7 + 0*s**5 + 0. Find k such that n(k) = 0.
-1, 1
Let n(s) be the second derivative of s**5/130 + 35*s**4/78 + 323*s**3/39 + 289*s**2/13 - 925*s. Solve n(c) = 0 for c.
-17, -1
Suppose -5*y = 5*h - 10, -3*h + 1 = y - h. Let c = -8/13 + 29/26. Solve -6*p**2 - 32 - 24*p - c*p**y = 0.
-4
Let r(h) be the third derivative of -h**6/240 + 3*h**5/40 - 9*h**3 - 145*h**2. Factor r(p).
-(p - 6)**2*(p + 3)/2
Let g be 3 + ((-6)/(-9))/((-2)/3). Let v be (g/((-32)/18))/((-30)/40). Factor -9/4*n + 0*n**2 + 3/4*n**3 - v.
3*(n - 2)*(n + 1)**2/4
Let u(x) be the first derivative of -100*x**3 - 5 + x**4 - 2*x**4 + 100*x**3 + 2*x**2. Find z, given that u(z) = 0.
-1, 0, 1
Let n(t) be the fir