3/3 - 10*t**2 + 60*t - 255. Find r such that o(r) = 0.
-6, 2
Let p(s) = 2*s**3 + s**2 - s - 1. Let f(i) = i + 1. Let w(k) = 4*f(k) + 4*p(k). Factor w(h).
4*h**2*(2*h + 1)
Suppose -1 + 13 = 3*l. Factor 31*j**l + 223*j**2 + 8*j**3 + 16*j**5 - 5*j**4 - 255*j**2 - 24*j - 4 + 10*j**4.
4*(j - 1)*(j + 1)**3*(4*j + 1)
Let c(i) = -3*i**3 + 5*i**3 + 1 - 3*i**3. Let m(r) = 3*r**3 - r**2 + r - 3. Let n(p) = -8*c(p) - 3*m(p). Solve n(g) = 0.
1
Suppose 7*n - 48*n - 16*n = 0. Factor 18/13*c + 12/13*c**2 + 2/13*c**3 + n.
2*c*(c + 3)**2/13
Let q(t) = 5*t**2 + 5*t + 1. Let l be q(-3). Let c = 63/2 - l. Solve -c*j**2 + 0*j + 3/4*j**3 + 0 = 0.
0, 2/3
Factor 0 - 3/2*n**5 + 0*n**2 - 3/2*n**3 + 3*n**4 + 0*n.
-3*n**3*(n - 1)**2/2
Let l(n) = -n**3 - 6*n**2 - 11*n - 2. Let c(s) = -2*s**2 + 23*s - 16. Let b be c(11). Let h(d) = -1. Let a(q) = b*l(q) - 20*h(q). Factor a(w).
5*(w + 1)*(w + 2)*(w + 3)
Let t = 22143 + -110703/5. Determine b, given that -12/5*b**2 + 4/5*b**3 - 4/5*b + t = 0.
-1, 1, 3
Suppose -5*j + 8*j = 15. Suppose -a = -4*h + 6, 3*a + h - 3 = j. Factor -36*v**2 - 4 + 27*v - a - 6*v**3 + 21*v**3.
3*(v - 1)**2*(5*v - 2)
Determine a so that 2*a**3 + 183 - 183 + 4*a + 4*a**2 - a**4 - 3*a**3 = 0.
-2, -1, 0, 2
Let k(r) be the first derivative of 1/4*r**2 + 0*r + 3/8*r**3 + 3/16*r**4 + 1/40*r**5 + 8. Suppose k(l) = 0. What is l?
-4, -1, 0
Suppose -330 + 0 = 5*x + g, -5*g = -2*x - 132. Let u = x + 66. Solve -1/2*y + 1/2*y**2 + u = 0.
0, 1
Let p(f) be the second derivative of -1/84*f**4 - 1/210*f**5 + 0 - 6*f - 9/2*f**2 + 0*f**3. Let a(t) be the first derivative of p(t). Factor a(w).
-2*w*(w + 1)/7
Let v(n) be the third derivative of 0*n - 1/140*n**6 - 1/84*n**4 + 9*n**2 + 0 + 0*n**3 - 1/70*n**5 - 1/735*n**7. Let v(x) = 0. Calculate x.
-1, 0
Let b(s) be the second derivative of -2*s - 14/3*s**3 - 4*s**2 + 58/5*s**5 + 2*s**7 + 124/15*s**6 + 4*s**4 + 0. Find w, given that b(w) = 0.
-1, -2/7, 1/3
Let d(b) be the third derivative of b**7/42 - 3*b**6/8 + 5*b**5/4 - 35*b**4/24 + 92*b**2. Factor d(j).
5*j*(j - 7)*(j - 1)**2
Suppose -4*n - 26 + 62 = 0. Let f(m) = -m**2 + 9*m + 2. Let p be f(n). Factor -1/4*q + 1/2 - 1/4*q**p.
-(q - 1)*(q + 2)/4
Factor 12*q**3 + 216*q - 63*q**2 + 6*q**2 - 69*q**2 + 2*q**4.
2*q*(q - 3)**2*(q + 12)
Let v = 98527511/363 - 271426. Let r = -2/121 - v. Find g, given that -r - 1/3*g**3 - g**2 - g = 0.
-1
Let h be 708/1180 - (48/(-70) + 1). Factor 16/7*r + 32/7 + h*r**2.
2*(r + 4)**2/7
Let j be (2 + -4)/(-2)*1. Let i(v) = -v - 1. Let x(h) = -h**2 + h + 3. Let g(m) = j*x(m) + 3*i(m). Suppose g(t) = 0. What is t?
-2, 0
Let c(g) be the second derivative of -54*g**2 - 1/4*g**4 + 3*g + 0 - 6*g**3. Determine w, given that c(w) = 0.
-6
Let c(f) be the third derivative of -f**7/2100 + 7*f**6/1200 - 3*f**5/200 - 9*f**4/80 + 9*f**3/10 + 5*f**2 + 6. Factor c(o).
-(o - 3)**3*(o + 2)/10
Suppose -3*i + 4 = -2*i. Let v = -1313 - -3941/3. Factor 0*x**2 + 0*x + v*x**3 + 2/3*x**i + 0.
2*x**3*(x + 1)/3
Factor 8/3*g - 10/3*g**2 - 2/3 + 4/3*g**3.
2*(g - 1)**2*(2*g - 1)/3
Suppose 4*d - 184 = -5*f, -4*d + 148 = f + 3*f. Let u be ((-8)/(-15))/(-4)*f/(-8). Let -u - 3/5*z**2 - 6/5*z = 0. What is z?
-1
Factor -2/7*d**2 + 20/7*d - 32/7.
-2*(d - 8)*(d - 2)/7
Let q(i) be the first derivative of i**3/3 - i**2 + 21. Suppose q(c) = 0. Calculate c.
0, 2
Let o = -2112/5 - -19048/45. Solve -2/9*j**4 + 4/9*j + o*j**3 - 10/9*j**2 + 0 = 0 for j.
0, 1, 2
Let r(w) be the third derivative of 3/140*w**5 + 11*w**2 - 1/56*w**4 + 1/490*w**7 + 0*w - 3/280*w**6 + 0 + 0*w**3. What is a in r(a) = 0?
0, 1
Let m(p) = p**4 - 209*p**3 - 5615*p**2 - 3. Let i(j) = -2*j**4 + 628*j**3 + 16846*j**2 + 8. Let z(c) = -3*i(c) - 8*m(c). Let z(f) = 0. What is f?
-53, 0
Let z(y) be the second derivative of -1/2*y**3 + 0*y**5 - 1/20*y**6 + 0*y**2 + 3/8*y**4 + 0 + 15*y. Factor z(g).
-3*g*(g - 1)**2*(g + 2)/2
Determine y so that 20/7*y - 8/7 + 4*y**2 = 0.
-1, 2/7
Let c(r) be the first derivative of 23 + 27/4*r**2 + 12*r + 1/2*r**3. Suppose c(x) = 0. Calculate x.
-8, -1
Let j(h) be the third derivative of h**8/16800 - h**7/3150 - 7*h**4/24 + h**2. Let v(k) be the second derivative of j(k). Factor v(i).
2*i**2*(i - 2)/5
Let n(q) be the second derivative of 1/15*q**5 + 9/2*q**2 - 4/3*q**3 - 3*q + 0 - 1/6*q**4. Let b(h) be the first derivative of n(h). Factor b(u).
4*(u - 2)*(u + 1)
Let n(c) be the second derivative of c**5/60 - 43*c**4/36 + 161*c**3/6 - 147*c**2/2 + 92*c - 1. Suppose n(p) = 0. Calculate p.
1, 21
Let -111/2*v - 54 - 3/2*v**2 = 0. What is v?
-36, -1
Let f(h) be the first derivative of h**9/12096 + h**8/2240 - h**7/3360 - h**6/480 - 4*h**3/3 + 11. Let z(i) be the third derivative of f(i). Factor z(y).
y**2*(y - 1)*(y + 1)*(y + 3)/4
Suppose 2*k - 5*t + 17 = 0, 0 = 2*k + t - 13. Factor 24*l**2 - 4 - 10*l**3 - 22*l**3 - 5*l**4 + 17*l**k.
4*(l - 1)**3*(3*l + 1)
Let u = -6 - -14. Factor 34*a**5 + 32*a**5 + u*a**3 + 16*a**3 - 12*a**2 - 15*a**4 - 63*a**5.
3*a**2*(a - 2)**2*(a - 1)
Let r(g) = -3*g + 109. Let o be r(36). Let s be (100/8)/5 + o + -1. What is k in 6*k**2 - 9/2*k + 1 - s*k**3 = 0?
2/5, 1
Let n(x) be the second derivative of -7*x**4/90 - 32*x**3/45 - 16*x**2/15 + 3*x - 18. Find y, given that n(y) = 0.
-4, -4/7
Let h(z) be the first derivative of 2*z**3/9 - z**2/3 - 4*z + 45. Determine m, given that h(m) = 0.
-2, 3
Let h(g) be the first derivative of -4/21*g**6 + 8/7*g - 13/14*g**4 - 18 + 32/35*g**5 - 22/21*g**3 + 8/7*g**2. What is n in h(n) = 0?
-1/2, 1, 2
Let k be (6/8 - 1) + (-8)/(-8). Let c be 13/4 + 3*(-5 + 4). Factor -k*m**3 - 1/4*m**4 - c*m - 3/4*m**2 + 0.
-m*(m + 1)**3/4
Let u = 1548 - 1545. Suppose 0*r**u + 0 + 8/7*r**2 + 4/7*r**5 - 8/7*r**4 - 4/7*r = 0. What is r?
-1, 0, 1
Let w(h) = h**2 + 11*h. Let d be w(-12). Let n = d + -8. What is c in n*c + c**3 + 14*c**4 + 0*c**3 - 14*c**2 - 5*c**3 = 0?
-1, 0, 2/7, 1
Let j be 5800/8120 + (3/(-7))/((-39)/(-9)). Let -20/13 - 82/13*q - j*q**2 = 0. Calculate q.
-10, -1/4
Let i(m) be the second derivative of -3*m**5/20 + m**4 - 3*m**3/2 + 98*m. Factor i(z).
-3*z*(z - 3)*(z - 1)
Let i = -14932/119 - -880/7. Solve -i + 8/17*p**3 + 0*p**4 - 2/17*p**5 + 4/17*p**2 - 6/17*p = 0 for p.
-1, 1, 2
Find k such that -14*k - 2/7*k**3 - 48/7 - 52/7*k**2 = 0.
-24, -1
Let j = -63 - -78. Suppose -23*q**3 + 2*q + q**2 - j*q**3 + 2*q**2 + 39*q**3 = 0. Calculate q.
-2, -1, 0
Let b(s) be the second derivative of s**9/60480 - s**8/13440 - s**7/10080 + s**6/1440 + 13*s**4/12 + 2*s. Let u(a) be the third derivative of b(a). Factor u(o).
o*(o - 2)*(o - 1)*(o + 1)/4
Factor -4*n**2 - 16/3*n + 4/3*n**3 + 0.
4*n*(n - 4)*(n + 1)/3
Let f(z) = z + 2. Let p be f(1). Let -4*q**4 - q - p*q**4 + 3*q**4 + q**3 + 5*q**4 - q**2 = 0. Calculate q.
-1, 0, 1
Suppose -41*x + 255 + 73 = 0. Solve -x*i**4 + 0*i + 6*i**3 + 0*i**2 + 0 + 8/3*i**5 = 0.
0, 3/2
Let d(r) be the second derivative of 4*r**7/315 - 8*r**6/225 + r**5/150 + 7*r**4/90 - r**3/9 + r**2/15 + 74*r. What is p in d(p) = 0?
-1, 1/2, 1
Let l(y) be the second derivative of 36*y - 1/30*y**6 + 1/4*y**5 + 0 + 0*y**2 + 2/3*y**3 - 2/3*y**4. Let l(b) = 0. Calculate b.
0, 1, 2
Suppose -10 - 5 = -5*v. Let m be v + -7 + (-98)/(-21). Let 0 - 2*s + m*s**2 = 0. What is s?
0, 3
Suppose 3*y - 2 = 2*y. Let v(s) be the second derivative of 1/60*s**5 - 7*s - 1/36*s**4 + 0 + 2/3*s**y - 2/9*s**3. Let v(q) = 0. Calculate q.
-2, 1, 2
Let 0 + 4*g + 1/3*g**2 = 0. What is g?
-12, 0
Let t(y) = y + 6. Let i be t(-2). Let -5*z**2 + 2*z + 2*z**4 + 155*z**3 - 157*z**3 + i - z**2 = 0. Calculate z.
-1, 1, 2
Let t(d) be the first derivative of -182*d**3 + 68*d**2 - 8*d + 658. Factor t(l).
-2*(13*l - 2)*(21*l - 2)
Let u(p) be the third derivative of p**7/42 + p**6/2 + 7*p**5/4 + 25*p**4/12 + 156*p**2. Factor u(s).
5*s*(s + 1)**2*(s + 10)
Determine c, given that 300 - 36*c - 600 + 300 + 3*c**2 = 0.
0, 12
Let i = -1 - 3. Let g(s) = s**3 + 3*s**2 - 5*s - 2. Let r be g(i). Factor 3 + 6*p**2 - 111*p + 105*p - 3*p**r.
3*(p - 1)**2
Suppose f + 18 - 35 = 0. Find b, given that f*b - 3 + 6 + 15*b**2 - 1 = 0.
-1, -2/15
Let j(g) be the second derivative of -3*g**5/20 - 5*g**4/4 - 3*g**3/2 + 27*g**2/2 - 2*g - 12. Factor j(q).
-3*(q - 1)*(q + 3)**2
Let i be (287/123 - (0 + 2))*12. Determine d, given that 2/5*d**i + 2/5 + 8/5*d + 8/5*d**3 + 12/5*d**2 = 0.
-1
Let b(h) be the third der