.
-1, 21
Determine q, given that -255*q + 225*q**2 + 50 + 199*q**3 + 195*q**3 + 199*q**3 - 613*q**3 = 0.
1/4, 1, 10
Let b be (2/225)/((-48)/18). Let s = b + 1807/2100. Suppose -16/7*z**3 - 4/7*z - 2*z**2 + 0 - s*z**4 = 0. What is z?
-1, -2/3, 0
Let k(q) be the first derivative of q**6/45 + q**5/30 - q**4/18 - q**3/9 + 10*q + 3. Let f(p) be the first derivative of k(p). Factor f(w).
2*w*(w - 1)*(w + 1)**2/3
What is x in -8*x**3 - 39*x**2 - 2*x**5 + 13*x**5 + 19*x**4 + 15*x**3 + 9*x - 7*x**5 = 0?
-3, 0, 1/4, 1
Let a(b) be the third derivative of b**6/210 - b**5/21 + 4*b**4/21 - 8*b**3/21 + 93*b**2. Factor a(r).
4*(r - 2)**2*(r - 1)/7
Factor -135/4*a + 3/4*a**4 + 51/4*a**3 + 0 + 81/4*a**2.
3*a*(a - 1)*(a + 3)*(a + 15)/4
Suppose -3*y - 3 = 3*n, -3*y + 3*n + 7 = 4*n. Suppose 2*r**2 - 4*r - y*r**2 + 6*r + 3*r**2 = 0. Calculate r.
-2, 0
Factor 2/5*z**3 + 18/5*z - 4*z**2 + 0.
2*z*(z - 9)*(z - 1)/5
Let l(m) be the first derivative of m**6/18 - m**5/3 + m**4/3 + 110. What is p in l(p) = 0?
0, 1, 4
Let a(s) = -s**2 - 9*s + 7. Let c be a(-9). Factor 10*k + 11*k**2 - c*k**2 + 4 + 0*k**2 - 2*k.
4*(k + 1)**2
Let v(g) be the second derivative of g**8/13440 + g**7/420 + g**6/30 + 4*g**5/15 - g**4/6 - 5*g. Let z(k) be the third derivative of v(k). Factor z(w).
(w + 4)**3/2
Let y(t) = 6*t + 0 + 18*t**2 - 19*t**2 + 4. Let u be y(5). Find n, given that 23*n**3 - 12*n**3 - 4*n**4 + 29*n**3 - 20*n**2 - 10*n**5 + u*n**4 = 0.
-2, 0, 1/2, 2
Let l = 4 + -6. Let w(q) = -q**3 - 2*q**2 - 2*q. Let n be w(l). Let 2/3*g**3 + 1/3 - 4/3*g**5 + 7/3*g**n + 2/3*g - 8/3*g**2 = 0. Calculate g.
-1, -1/4, 1
Let r be -14*1 - (-4 + 6). Let s = r + 18. Factor 8*u**3 - 9*u**4 - 3*u**2 - s*u**3 - 6*u + 2*u**4 + 10*u**4.
3*u*(u - 1)*(u + 1)*(u + 2)
Let o(v) be the third derivative of -v**5/105 + 116*v**4/21 - 26912*v**3/21 - 27*v**2. Find k, given that o(k) = 0.
116
Let o(d) be the second derivative of 24*d - 3/2*d**3 + 1/8*d**4 + 15/4*d**2 + 0. Determine t, given that o(t) = 0.
1, 5
Let y(u) = -u**3 - u**2 - 1. Let n(g) = -2*g**3 - 26*g**2 - 52*g - 34. Let r(q) = n(q) - 6*y(q). Solve r(o) = 0 for o.
-1, 7
Let c(x) be the first derivative of 2*x**5/5 - 8*x**3/3 + 80. What is b in c(b) = 0?
-2, 0, 2
Let y(w) be the first derivative of w**5 - 5*w**4/4 - 20*w**3/3 + 10*w**2 + 168. Factor y(g).
5*g*(g - 2)*(g - 1)*(g + 2)
Suppose -5*o + 331 = -59. Let x = o + -78. Factor 0*h + 4/5*h**3 + x + 0*h**2.
4*h**3/5
Let j(n) be the third derivative of -13*n**5/10 + n**4/6 + 45*n**2. Factor j(a).
-2*a*(39*a - 2)
Let d(s) be the second derivative of -s**4/60 - 7*s**3/10 + 165*s. Suppose d(p) = 0. What is p?
-21, 0
Let o(m) = 668*m + 10023. Let h be o(-15). Determine f so that 0*f**h + 0*f + 2/5*f**4 - 4/5*f**2 + 2/5 = 0.
-1, 1
Suppose 37 + 14 = 17*o. Let x(l) be the first derivative of -6 - 1/9*l**o - 3*l + l**2. Factor x(q).
-(q - 3)**2/3
Let j(p) be the first derivative of 33*p**3/7 - 96*p**2/7 - 12*p/7 + 478. Factor j(w).
3*(w - 2)*(33*w + 2)/7
Let y(h) be the third derivative of h**6/600 - h**5/50 + 3*h**4/40 - 2*h**3/15 - h**2 - 4. Determine i, given that y(i) = 0.
1, 4
Let j = 44 + -31. Let x be j + -10 - (-3 + 2). Determine o, given that -2*o**3 + 0 - 2/3*o**2 + 2/3*o**x + 2/3*o + 4/3*o**5 = 0.
-1, 0, 1/2, 1
Let d(o) be the second derivative of 2/3*o**3 + 1/15*o**6 + 0 - o**2 - 1/5*o**5 + 18*o + 0*o**4. Solve d(n) = 0 for n.
-1, 1
Let w(u) be the third derivative of -u**7/1260 - 7*u**6/720 - 17*u**5/360 - 17*u**4/144 - u**3/6 + 471*u**2. Solve w(p) = 0.
-3, -2, -1
Let w(q) = -2*q**3 - 3*q**2 - q - 2. Let n be w(-2). Solve f**4 + 2 + 2*f - 2*f**3 - n + 1 = 0 for f.
-1, 1
Let j be ((-19)/(798/(-36)))/((-5)/(-7)). Factor 9/5*i + j*i**2 + 3/5.
3*(i + 1)*(2*i + 1)/5
Let x(d) = -12*d**5 - 12*d**4 + 24*d**3 + 40*d**2 - 84*d + 36. Let c(l) = l**5. Let k(h) = -8*c(h) - x(h). Determine s so that k(s) = 0.
-3, 1
Suppose -1976 + 716 = -15*u. Let y = -81 + u. Suppose -1/3*z**4 - 7/6*z**y - z**2 + 1/6*z + 1/3 = 0. Calculate z.
-2, -1, 1/2
Factor -2/3 + 8/15*x + 2/15*x**2.
2*(x - 1)*(x + 5)/15
Suppose 145 + h**2 - 6*h**2 + 56*h + 51 + 9*h**2 = 0. Calculate h.
-7
Let z(q) = -q**4 + q**3 - q**2 + q + 1. Let o(r) = -4*r**5 + 12*r**4 - 13*r**3 + 5*r + 3. Let i(y) = o(y) - 3*z(y). What is g in i(g) = 0?
-1/4, 0, 1, 2
Let o(k) be the third derivative of k**4/24 + k**3/2 - 11*k**2. Let b be o(-1). Determine g, given that 3/2*g**b + 0*g + 0 - 3/2*g**3 = 0.
0, 1
Let g(v) = -19*v**2 - 59*v + 11. Let z(x) = -10*x**2 - 30*x + 6. Let f = -53 + 42. Let i(r) = f*z(r) + 6*g(r). Factor i(c).
-4*c*(c + 6)
Suppose 347 = -2*x + 357. Let n(l) be the third derivative of 1/12*l**x + 0*l**3 + 0*l + 0 + 5/24*l**4 - 12*l**2. Factor n(m).
5*m*(m + 1)
Let u(w) be the first derivative of -w**5/5 - 3*w**4/4 + w**3/3 + 3*w**2/2 + 610. Factor u(g).
-g*(g - 1)*(g + 1)*(g + 3)
Suppose 140*j = 55*j + 50*j + 62*j. Factor 2/11*a**5 + 4/11*a**4 + 0*a**3 - 4/11*a**2 - 2/11*a + j.
2*a*(a - 1)*(a + 1)**3/11
Let h(z) = -345*z**2 + 265*z - 65. Let i = -129 + 126. Let k(g) = 43*g**2 - 33*g + 8. Let o(r) = i*h(r) - 25*k(r). Suppose o(b) = 0. What is b?
1/4, 1/2
Let y = -73 + 67. Let r be (-3 - y)/3*3. Let -4/11*o + 8/11*o**r - 2/11*o**4 + 4/11*o**2 - 4/11*o**5 - 2/11 = 0. Calculate o.
-1, -1/2, 1
Let t be 7/4 - 5/(-20). Let n(r) be the first derivative of -2/9*r - 2/27*r**3 - 2/9*r**t + 6. Let n(b) = 0. What is b?
-1
Let r(y) be the first derivative of -y**6/40 - 3*y**5/4 - 75*y**4/8 - 125*y**3/2 + 7*y**2/2 + 13. Let a(k) be the second derivative of r(k). Factor a(c).
-3*(c + 5)**3
Let y be ((-544)/40)/17*6/(-4). Let p(f) be the first derivative of -1/25*f**5 - 4/5*f - 13/15*f**3 - 1 + 3/10*f**4 + y*f**2. Factor p(a).
-(a - 2)**2*(a - 1)**2/5
Let k(n) = -2*n**2 - 177*n - 4053. Let u(b) = 12*b**2 + 1061*b + 24319. Let f(m) = -38*k(m) - 6*u(m). Factor f(q).
4*(q + 45)**2
Let l(u) be the first derivative of 0*u**3 - 2/3*u - 2/3*u**2 + 1/3*u**4 + 2/15*u**5 + 20. Find p, given that l(p) = 0.
-1, 1
Let d(z) be the second derivative of -1/5*z**6 + 0 + 0*z**3 + 0*z**2 - 8/9*z**4 - 4/5*z**5 - 1/63*z**7 + 7*z. Factor d(u).
-2*u**2*(u + 1)*(u + 4)**2/3
Let f(h) be the first derivative of -h**6/3 - 2*h**5/5 + 3*h**4 - 4*h**3/3 - 5*h**2 + 6*h + 139. Solve f(v) = 0 for v.
-3, -1, 1
Let v(c) = -9*c**2 - 11*c + 3. Let g(f) = 5*f**2 + 7*f - 1. Let m(h) = -10*g(h) - 6*v(h). Find z, given that m(z) = 0.
-1, 2
Let a = 4115 + -4113. Factor 56/5*j + 4/5*j**a + 196/5.
4*(j + 7)**2/5
Let d(f) = -6*f + 5. Let z be d(2). Let h = z - -13. Factor -5*i**2 + 3*i**2 - 4*i - h*i**2 + 8*i**4 + 4*i**5.
4*i*(i - 1)*(i + 1)**3
Let k(b) = b**3 + 11*b**2 - b - 9. Let r(i) = i**3 + i**2 + 4*i + 1. Let z be r(-2). Let o be k(z). Factor -24*l - 6 - 21/2*l**o.
-3*(l + 2)*(7*l + 2)/2
Suppose 0 = -5*z + z + 104. Suppose -z = -5*d + 3*d. Factor p**2 + 7*p - d + 8*p**2 - 28*p - 5.
3*(p - 3)*(3*p + 2)
Let s be (-42)/(-36) - 18/27. Factor -3/2*l**3 + 3/2*l + s*l**2 - 1/2*l**4 + 0.
-l*(l - 1)*(l + 1)*(l + 3)/2
Let o(n) be the first derivative of n**6/30 + 2*n**5/25 - 3*n**4/5 + 14*n**3/15 - n**2/2 - 200. Factor o(x).
x*(x - 1)**3*(x + 5)/5
Let m(o) be the second derivative of -4*o + 3*o**2 - 3/8*o**4 + 1/20*o**5 + 0 + o**3. Let b(g) be the first derivative of m(g). Factor b(s).
3*(s - 2)*(s - 1)
Let o(q) = -q**2 + 26*q + 509. Let n be o(-13). Determine j so that -8/3 - 22/3*j**3 + 32/3*j - 8/3*j**4 + 2*j**n = 0.
-2, 1/4, 1
Let w(k) = 104*k**4 - 16*k**3 - 64*k**2 - 16*k - 8. Let r(y) = -311*y**4 + 49*y**3 + 192*y**2 + 48*y + 22. Let b(s) = -4*r(s) - 11*w(s). Factor b(m).
4*m*(m - 1)*(5*m + 2)**2
Let w(a) be the first derivative of -a**5/300 - a**4/30 - a**3/10 + 9*a**2/2 + 10. Let t(j) be the second derivative of w(j). Let t(k) = 0. What is k?
-3, -1
Let c(g) be the third derivative of g**9/70560 + g**8/70560 + g**5/12 - 3*g**2. Let o(p) be the third derivative of c(p). Determine j so that o(j) = 0.
-1/3, 0
Factor -173 + 182 + 2*u**2 - 18*u + 4*u**3 + 3*u**2.
(u - 1)*(u + 3)*(4*u - 3)
Let b(x) = 14*x**2 + 2 + 2*x - 18*x**2 - 2 + 4. Let m(h) = 21*h**2 - 9*h - 19. Let g(l) = 11*b(l) + 2*m(l). Factor g(r).
-2*(r - 3)*(r + 1)
Let v = 35 - 33. Factor -3*g**v - 147 + 147 + 9*g.
-3*g*(g - 3)
Let j(i) be the second derivative of 0 - 5*i + 1/21*i**4 + 1/70*i**5 - 1/105*i**6 + 0*i**3 + 0*i**2. Let j(x) = 0. Ca