3. Factor 0*w - 1/2*w**3 + 0 + a*w**2.
-w**2*(w - 3)/2
Let h(f) be the third derivative of -f**6/240 + 7*f**5/240 - f**4/24 + 4*f**3 - 11*f**2. Let w(d) be the first derivative of h(d). Factor w(z).
-(z - 2)*(3*z - 1)/2
Let t be (2 - 18/(-60)) + 39/(-26). Factor 0*h**4 - 4/5*h**5 + 0*h**2 + 8/5*h**3 + 0 - t*h.
-4*h*(h - 1)**2*(h + 1)**2/5
Let h(w) = -38*w**2 + 89*w - 95. Let b(f) = 7*f**2 - 18*f + 19. Let o(i) = -22*b(i) - 4*h(i). Suppose o(k) = 0. Calculate k.
1, 19
Let w(o) = o**3 - o**2 + 1. Let s(p) = -4*p**3 + 20*p**2 - 8*p - 2. Suppose 0 = 6*j + j + 7. Let g(a) = j*s(a) + 6*w(a). Solve g(h) = 0.
-2/5, 1, 2
Let j(a) be the third derivative of -a**7/1260 + a**6/120 + 5*a**4/12 + 21*a**2. Let w(g) be the second derivative of j(g). Factor w(u).
-2*u*(u - 3)
Let q be 15/9*(-288)/(-120). Let m(b) be the second derivative of 1/21*b**q + 0 + 0*b**2 + 7*b + 1/7*b**3 - 1/70*b**5. Find k, given that m(k) = 0.
-1, 0, 3
Let h(y) be the second derivative of y**6/90 - y**5/12 - 31*y**4/36 - 43*y**3/18 - 3*y**2 + y - 4. Suppose h(q) = 0. What is q?
-2, -1, 9
Suppose 0 = o - 2 - 1. Factor -3*n**4 - 42*n**o - 2 + n + n**4 + 40*n**3 + n**5 + 4*n**2.
(n - 2)*(n - 1)**2*(n + 1)**2
Suppose -q + 16*a - 19*a = 15, -2*a = -11*q + 80. Solve 0 + 24*b**2 + 9*b**4 + q*b + 57/2*b**3 = 0 for b.
-2, -2/3, -1/2, 0
Let u(l) be the third derivative of l**5 + 8/3*l**3 + 0 + 2/105*l**7 + 13/6*l**4 + 0*l + 7/30*l**6 + 10*l**2. Factor u(h).
4*(h + 1)**3*(h + 4)
Suppose 24/5*a**3 - 24/5*a - 38/5*a**2 + 8 - 2/5*a**4 = 0. What is a?
-1, 1, 2, 10
Let a(o) be the first derivative of 0*o**2 - 44 - 1/6*o**4 - 8/3*o + 2/3*o**3. Find l, given that a(l) = 0.
-1, 2
Suppose 0 = -53*s + 75 + 31. Let v(l) be the third derivative of 0*l**4 + 0 - 5*l**s + 0*l**3 - 1/240*l**6 + 0*l - 1/120*l**5. Find c, given that v(c) = 0.
-1, 0
Suppose -4*n - 12/5*n**2 + 16/5 + 4*n**3 - 4/5*n**4 = 0. Calculate n.
-1, 1, 4
Find w, given that -23*w**3 - 10*w**3 + 38*w**3 = 0.
0
Let x(u) = -u**3 - 15*u**2 - 15*u - 12. Let l be x(-14). Suppose 0*h - 2*h - 6 = -l*a, -2*a + 1 = 3*h. Factor 1/2*s - 1/4*s**a + 0.
-s*(s - 2)/4
Let f(o) be the third derivative of o**5/60 - o**4/4 + 3*o**3/2 - 20*o**2 - 4. Find s, given that f(s) = 0.
3
Let s(f) be the first derivative of 18*f**5/35 + 19*f**4/7 + 106*f**3/21 + 4*f**2 + 8*f/7 - 233. Solve s(y) = 0.
-2, -1, -2/9
Let q be (-660)/(-320) - 2/32. Factor -2/7*h**q + 0 + 2/7*h**3 - 4/7*h.
2*h*(h - 2)*(h + 1)/7
Let j(w) be the first derivative of 0*w + 2/3*w**3 - 6*w**2 + 17. Factor j(z).
2*z*(z - 6)
Let j(x) = x**4 - x**3 - x**2 - x - 3. Let o(k) = -10*k**4 - 30*k**3 - 20*k**2 + 160*k + 165. Let t(h) = -5*j(h) - o(h). Find w, given that t(w) = 0.
-5, -3, -1, 2
Let g = -39248 - -117745/3. Determine w, given that 0 - 4/3*w + w**3 - g*w**2 = 0.
-1, 0, 4/3
Let t(a) = -5*a**3 + 7*a**2 + 2*a + 2. Let w(u) = -66*u**3 + 90*u**2 + 27*u + 27. Let i(s) = -27*t(s) + 2*w(s). What is h in i(h) = 0?
0, 3
Let m(c) be the third derivative of c**6/75 - 3*c**5/25 + 13*c**4/30 - 4*c**3/5 - 34*c**2 + 1. Solve m(f) = 0 for f.
1, 3/2, 2
Let r = -5 - -9. Let k(u) = u**2 - 3*u - 4. Let c be k(r). Factor 0 - 3/7*a**2 + c*a.
-3*a**2/7
Let g(n) be the first derivative of n**5/20 + n**4/6 - n**3/6 - n**2 + 46*n + 23. Let t(c) be the first derivative of g(c). What is i in t(i) = 0?
-2, -1, 1
Suppose 2*r = -3*r + 45. Let a = r - 4. Factor 1 - 1 + 11*v - a*v - 3*v**2.
-3*v*(v - 2)
Let c(r) be the first derivative of -8*r**3/3 - 54*r**2 + 248*r - 165. Suppose c(q) = 0. What is q?
-31/2, 2
Let b(z) be the second derivative of -z**4/18 - z**3/3 - 2*z**2/3 - 64*z. Let b(j) = 0. What is j?
-2, -1
Suppose 200 = -23*i + 28*i. Factor 2*v**2 + 86 - i*v + 137 - 23.
2*(v - 10)**2
Let k(j) be the second derivative of -j**5/15 - 11*j**4/9 - 68*j**3/9 - 16*j**2 + 124*j - 1. Find w, given that k(w) = 0.
-6, -4, -1
Let n(p) be the first derivative of 0*p + 10 + 5/4*p**2 + 10/3*p**3. Factor n(b).
5*b*(4*b + 1)/2
Let w = -10004/15 - -667. Let d(g) be the third derivative of 7*g**2 + 32/3*g**3 + 0*g + 0 - 4/3*g**4 + w*g**5. Factor d(p).
4*(p - 4)**2
Let r(g) = g**2 - 1. Suppose 39 - 74 = 35*w. Let n(b) be the first derivative of 8*b**3/3 - b**2 - 6*b - 1. Let v(o) = w*n(o) + 6*r(o). Factor v(d).
-2*d*(d - 1)
Let z(g) = -2*g**2 + 0*g**2 + 14 - 4*g + g**2. Let u be z(-6). Find t, given that 14*t**u + 4*t - 2 - 8*t**4 + 2 - 4*t**5 - 6*t**2 = 0.
-1, 0, 1
Let a(q) be the first derivative of -q**4/18 + 32*q**3/27 - 65*q**2/9 + 100*q/9 + 277. Factor a(s).
-2*(s - 10)*(s - 5)*(s - 1)/9
Let o(m) be the third derivative of -7*m**2 + 1/360*m**6 + 0 + 0*m - 5/72*m**4 + 1/180*m**5 + 1/6*m**3. Suppose o(h) = 0. Calculate h.
-3, 1
Let d(h) be the first derivative of 2/27*h**3 - 1/9*h**2 - 1 - 4/9*h. Factor d(p).
2*(p - 2)*(p + 1)/9
Let h(y) be the second derivative of -1/39*y**4 + 10*y + 1/130*y**5 + 1/39*y**3 + 0*y**2 + 0. Factor h(v).
2*v*(v - 1)**2/13
Solve 1/2 - 32*b**3 + 15/2*b + 24*b**2 = 0 for b.
-1/8, 1
Let u(x) be the second derivative of x**8/1008 + x**7/630 + 17*x**2 - 29*x. Let h(q) be the first derivative of u(q). Find n such that h(n) = 0.
-1, 0
Let w = 373/5 - 56313/755. Let s = w + 147/302. Find n such that -1/2*n - s*n**2 + 1/2*n**3 + 1/2 = 0.
-1, 1
Let m be (-6 - 4) + (-2)/(-2). Let g be 13/6 + m/(-18). Find p, given that g - 8/3*p + 2/3*p**2 = 0.
2
Determine x so that -12*x + 21/4*x**2 - 15 + 9/4*x**3 = 0.
-10/3, -1, 2
Let a = 98 + -90. Factor 30*r**2 + r**3 + r - 25*r**2 - a*r**4 - 2*r**3 - 1 - 4*r**5.
-(r + 1)**3*(2*r - 1)**2
Let v(s) = -3*s**3 - s**2 - s - 1. Let d be v(-2). Factor a**4 + a**4 - 23*a**3 + d*a**3.
2*a**3*(a - 1)
Suppose 3*h + n = 77, 5*h - 5 = 3*n + 128. Suppose 6*o = h - 8. Solve 0 - 1/2*a**4 + 1/2*a**2 + 1/2*a**o + 0*a - 1/2*a**5 = 0.
-1, 0, 1
Let q be 3*(3 + 4 + -1). Suppose 0 = -4*a + 5*z + 6, a + 4 = -5*z + q. Factor -4 + a*b - b**2 - 2 + 2.
-(b - 2)**2
Let o be 135/81 + 0 + (-2)/(-6). Determine h so that o*h**5 + 2*h**5 + 0*h**3 + h**5 - 5*h**3 = 0.
-1, 0, 1
Factor -12/5*l**4 + 16/5*l**3 + 32/5*l**2 + 2/5*l**5 + 64/5 - 96/5*l.
2*(l - 2)**4*(l + 2)/5
Let u(y) = y**3 - 5*y**2 + 8*y - 14. Let n be 5/(10/(-6)) + (5 - -2). Let j be u(n). Suppose 3 - 3/2*k - 3/2*k**j = 0. What is k?
-2, 1
Suppose 0*q = -2*q + 2*a - 8, 0 = 3*q - 4*a + 11. Let l(p) = 5*p**2 - 5. Let y(t) = -7*t**2 + 7. Let g(v) = q*y(v) - 8*l(v). Factor g(k).
-5*(k - 1)*(k + 1)
Let k(c) be the second derivative of -c**7/112 - 19*c**6/80 - 417*c**5/160 - 485*c**4/32 - 50*c**3 - 375*c**2/4 - 14*c. Suppose k(n) = 0. Calculate n.
-5, -2
Let j = -451 - -451. Let s(i) be the third derivative of 1/24*i**5 + 1/420*i**7 + 1/60*i**6 + 2*i**2 + 0 + 0*i + 1/24*i**4 + j*i**3. Let s(q) = 0. Calculate q.
-2, -1, 0
Determine r, given that 1/11 - 1/11*r**2 + 1/11*r**3 - 1/11*r = 0.
-1, 1
Suppose -172*f + 508 + 254 = 209*f. Let p = -1 + 4. Determine v so that -16*v - 8*v**p - 1/5*v**5 + f*v**4 + 16*v**2 + 32/5 = 0.
2
Suppose 57*j - 74*j + 65*j + 51 - 3*j**2 = 0. What is j?
-1, 17
Let r = 71 + -71. Let k(a) = a**3 + 2*a. Let w be k(r). Factor 0*g + 1/4*g**2 + w - 1/4*g**3.
-g**2*(g - 1)/4
Let d(g) be the third derivative of 1/330*g**5 + 0*g - 5*g**2 + 0 + 1/660*g**6 + 0*g**4 + 0*g**3. Factor d(j).
2*j**2*(j + 1)/11
Factor -20/3*h**2 - 39*h - 54 - 1/3*h**3.
-(h + 2)*(h + 9)**2/3
Factor 0*a**4 - 6*a**4 - 11*a**4 + 80*a**3 + 9*a**4 - 4*a**5 - 96*a**2.
-4*a**2*(a - 2)**2*(a + 6)
Let d(o) be the second derivative of o**7/210 + o**6/45 + o**5/30 - o**3/3 + 8*o. Let z(r) be the second derivative of d(r). Let z(h) = 0. What is h?
-1, 0
Let w(z) = 2*z**5 + 6*z**4 - 10*z**3 - 22*z**2 - 18*z - 2. Let m(f) = -4*f**5 - 12*f**4 + 23*f**3 + 43*f**2 + 37*f + 5. Let r(i) = 2*m(i) + 5*w(i). Factor r(g).
2*g*(g - 2)*(g + 1)*(g + 2)**2
Determine l so that -84/5*l - 18*l**3 - 171/5*l**2 + 0 - 3/5*l**4 = 0.
-28, -1, 0
Let s(q) be the second derivative of q**4/120 - 37*q**3/60 - 19*q**2/10 + 115*q. Determine m so that s(m) = 0.
-1, 38
Let v(h) = h**2 + 4*h - 37. Let t be v(5). Suppose t = -0*n + 4*n. Factor 4/7*z - 2/7 - 2/7*z**n.
-2*(z - 1)**2/7
Let q = 326 - 260. Let x = 135/2 - q. Factor -x*f**3 + 3*f**2 - 3 + 3/2*f.
-3*(f - 2)*(f - 1)*(f + 1)/2
Let q(g) be the third derivative of 0*g - 8/3*g**3 - 34*g**2 + 1/60*g**6 + 0 - 1/5*g**5 + g**4. Factor q(y).
2*(y - 2)**3
Let a 