e ((-20)/175)/2*-5. Let -4/7 - 6/7*y + n*y**3 + l*y**2 = 0. Calculate y.
-1, 2
Let v(l) be the second derivative of l**6/90 - l**5/20 - 67*l**4/36 - 71*l**3/6 - 33*l**2 - 5*l + 17. Determine w so that v(w) = 0.
-3, -2, 11
Let r = 624 - 624. Let c(i) be the second derivative of 7/165*i**6 - 9/110*i**5 - 10*i + 1/33*i**4 + 0*i**2 + r + 0*i**3. Factor c(a).
2*a**2*(a - 1)*(7*a - 2)/11
Let p(s) = s - 7. Let i be p(10). Factor -22*g**i + 0*g**2 - 3*g**2 + 8*g**4 - 6*g**2 + 3*g**2.
2*g**2*(g - 3)*(4*g + 1)
Let f(o) be the first derivative of -5*o**2 - 25 - 25*o - 1/3*o**3. Factor f(x).
-(x + 5)**2
Suppose -s - 70 + 73 = 0. Suppose 2*z - 6 - 4 = -t, 2 = -z + 3*t. Factor -6*f**s - z + 1 - 39*f**4 + 42*f**4 + 6*f.
3*(f - 1)**3*(f + 1)
Let f(n) be the first derivative of 1/3*n**4 + 0*n + 8/9*n**3 + 11 + 2/3*n**2. Factor f(t).
4*t*(t + 1)**2/3
Let w(m) = -m + 2. Let t be w(0). Factor -3 - 5*j + 0*j + t*j + 3*j**2 + 3*j**3.
3*(j - 1)*(j + 1)**2
Suppose -g + 4 = 1. Factor -4*k**2 + 2*k + 0*k**2 + k**2 + g + 2*k**2.
-(k - 3)*(k + 1)
Let f(x) be the third derivative of x**5/420 - 5*x**4/28 + 75*x**3/14 - 54*x**2. Factor f(q).
(q - 15)**2/7
Let x(d) = -9*d + d + 0*d**2 + 7*d - 2*d**2. Let p be x(0). Factor -1/2*m**3 + 3/2*m + p*m**2 - 1.
-(m - 1)**2*(m + 2)/2
Let h(r) be the third derivative of -r**5/20 + 25*r**4/8 - 23*r**3 - 8*r**2 + 2. Factor h(y).
-3*(y - 23)*(y - 2)
Let l(i) = i**3 + 39*i**2 - 812*i - 106. Let o be l(-54). Solve 6/7*d**4 - 3/7*d**3 - 3/7*d**5 + 0 + 0*d**o + 0*d = 0 for d.
0, 1
Let d(w) be the second derivative of 0*w**3 + 0 - 1/2*w**2 - 1/4*w**4 + 1/20*w**5 - 2*w. Let x(o) be the first derivative of d(o). Factor x(b).
3*b*(b - 2)
Suppose 240*z - 225*z = 90. Let y(m) be the third derivative of 0 + 1/240*m**z + 10*m**2 + 0*m + 1/20*m**5 + 0*m**3 + 3/16*m**4. Find x, given that y(x) = 0.
-3, 0
Let j(b) = -3*b**3 + 5*b**3 + b**2 - 4*b**2 + 1 + 0*b**2. Let o be j(2). Find f, given that -f**5 + 4*f**2 + 3*f**4 - 1 - 2*f - f**5 - o*f**4 - 1 + 4*f**3 = 0.
-1, 1
Factor 1/3*z**3 - 5/3 + 11/3*z - 7/3*z**2.
(z - 5)*(z - 1)**2/3
Let c(j) = 560*j**3 + 8195*j**2 + 26740*j - 8330. Let y(g) = 33*g**3 + 482*g**2 + 1573*g - 490. Let z(w) = -2*c(w) + 35*y(w). Solve z(p) = 0 for p.
-7, 2/7
Suppose 1 = -2*z + 3. Let c be (-42)/(-24) + z/4. Solve -4*a**2 + 2*a**2 - c*a**3 + 0*a**3 = 0 for a.
-1, 0
Let f(u) = -3*u**3 - 3*u**2 - u + 3. Let p(i) = 7*i**3 + 6*i**2 + 3*i - 6. Let x(q) = -q + 9. Let a be x(4). Let l(c) = a*f(c) + 2*p(c). Solve l(g) = 0 for g.
-3, -1, 1
Let t(q) be the third derivative of -q**9/22680 + q**8/1120 - q**7/252 - 5*q**6/216 + 3*q**4/8 + 4*q**2. Let i(j) be the second derivative of t(j). Factor i(p).
-2*p*(p - 5)**2*(p + 1)/3
Suppose 3*w - 10 = w. Let f(j) = -j + 9. Let c be f(w). What is l in -4*l**3 - 3*l**3 - l**3 - c*l**4 + 12*l**2 = 0?
-3, 0, 1
Let m be (4/10)/((-4)/(-140)). Let k = 19 - m. Factor -4*y + 3*y - 2*y**2 + k*y**2 - 2*y**2.
y*(y - 1)
Let s(q) be the third derivative of q**7/1050 - q**6/225 - q**5/150 + q**4/15 + 2*q**3 + 4*q**2. Let a(b) be the first derivative of s(b). Solve a(t) = 0 for t.
-1, 1, 2
Let j = 55 - 39. Suppose 3 = -15*d + j*d. Factor 2/5*o - 4/5*o**2 + 2/5*o**d + 0.
2*o*(o - 1)**2/5
Let t be 0/((-13 - -39)/(-13)). Suppose -3/10*h**4 + t - 1/10*h**5 + 0*h**2 + 0*h + 0*h**3 = 0. What is h?
-3, 0
Let h(z) be the first derivative of z**6/6 - 138*z**5/5 + 4621*z**4/4 + 3220*z**3 + 2450*z**2 - 418. Solve h(c) = 0 for c.
-1, 0, 70
Let h(d) = -d**2 + 9*d + 13. Let o be h(10). What is x in -101*x**2 + 104*x**2 + 0 - o = 0?
-1, 1
Let x(u) be the second derivative of u**9/113400 - u**8/25200 - u**7/18900 + u**6/2700 - 5*u**4/2 + 25*u. Let v(l) be the third derivative of x(l). Factor v(n).
2*n*(n - 2)*(n - 1)*(n + 1)/15
Let p(n) = -42*n**3 + 9*n**3 - 89*n + 14*n - 105*n**2 - 18 - 21*n**4. Let s(u) = -u**4 - 1. Let o(t) = -p(t) + 18*s(t). Factor o(w).
3*w*(w + 1)*(w + 5)**2
Suppose 4*o + 4*u - 164 = 0, u - 94 = -2*o - 4*u. Suppose 0 = 3*t - o + 37. Factor 2/13*b**2 - 2/13 + t*b.
2*(b - 1)*(b + 1)/13
Suppose 384/11*o - 60/11*o**2 + 2/11*o**3 + 1024/11 = 0. Calculate o.
-2, 16
Let l be (3/((-27)/(-24)))/(184/276). Factor 4/7*d + 0 + 2*d**l + 22/7*d**2 + 32/7*d**3.
2*d*(d + 1)**2*(7*d + 2)/7
Suppose -15*i - 660 + 660 = 16*i. Solve -4/3*y**2 + 4/3 + i*y = 0 for y.
-1, 1
Let f(w) be the second derivative of w**6/120 - w**4/8 - 4*w**3/3 - 15*w. Let p(a) be the second derivative of f(a). Factor p(j).
3*(j - 1)*(j + 1)
Let i(s) be the second derivative of s**6/75 + s**5/50 + 2*s - 113. Determine y so that i(y) = 0.
-1, 0
Suppose -3*r + 104*n = 107*n + 21, -4*n - 28 = 0. Factor r*b - b**3 - 1/3*b**4 - 2/3*b**2 + 0.
-b**2*(b + 1)*(b + 2)/3
Let j(w) = w**3 - 2*w**2 + 5*w. Let f(u) = 2*u**3 - 3*u**2 + 10*u. Let n be ((-11)/22)/(37/18 + -2). Let h(z) = n*j(z) + 4*f(z). Factor h(t).
-t*(t - 5)*(t - 1)
Let s(c) be the second derivative of -c**7/5880 - c**6/560 - c**5/140 - 19*c**4/12 - 6*c. Let i(g) be the third derivative of s(g). Factor i(l).
-3*(l + 1)*(l + 2)/7
Let v = 3 - 0. Let n(w) be the first derivative of 0*w**v + 6 + 12*w - 6 + 6*w**2 + w**3 + 4. Determine z so that n(z) = 0.
-2
Factor -519 - 5*b**4 - 1280*b**2 + 519 - 160*b**3.
-5*b**2*(b + 16)**2
Factor -7 - 6 - 6 - 10*p**2 - 7 - 36*p.
-2*(p + 1)*(5*p + 13)
Find t, given that -8/9*t**5 - 74/9*t**3 - 64/9*t**2 - 40/9*t**4 - 26/9*t - 4/9 = 0.
-2, -1, -1/2
Suppose 12/5*l**3 - 2/5*l**4 + 8/5*l - 18/5*l**2 + 0 = 0. Calculate l.
0, 1, 4
Let k be (((-68)/5)/4 - -4)*5. Let x(f) be the first derivative of 2 - 8*f - 28/3*f**k - 9/10*f**5 + 12*f**2 + 4*f**4 + 1/12*f**6. Factor x(l).
(l - 2)**4*(l - 1)/2
Let m = -28 - -24. Let c(r) = -4. Let p(k) = -k**2 + 1. Let q(s) = m*p(s) - c(s). Factor q(i).
4*i**2
Suppose 0 = -4*o + 20, p - 15 = -2*o + 6. Let k = 35 - -13. Factor -4*q**5 - k*q**4 - p*q**3 + 17*q**3 - 24*q**5 + 10*q**3.
-4*q**3*(q + 2)*(7*q - 2)
Suppose 7/2*k**2 + 0 - 10/3*k**3 + 0*k - 1/6*k**4 = 0. Calculate k.
-21, 0, 1
Factor -22*o**2 + 17*o**2 - 33*o**2 + 113*o**2 + 5*o**2 - 4*o.
4*o*(20*o - 1)
Solve 2*g**4 - 26*g**2 + 30 + 0*g**4 - 9*g + 101*g + 122*g**2 + 36*g**3 = 0.
-15, -1
Let w = -14171 + 14176. Find s, given that -w + 85*s - 1445/4*s**2 = 0.
2/17
Determine b so that -69/7 + 1/7*b**2 + 68/7*b = 0.
-69, 1
Let r(m) be the second derivative of 14*m + 1/66*m**4 + 3/11*m**2 + 0 - 4/33*m**3. Factor r(a).
2*(a - 3)*(a - 1)/11
Let s(o) be the third derivative of o**8/210 + o**7/21 + 11*o**6/150 - 2*o**5/15 - 13*o**4/30 - o**3/3 - 528*o**2. Determine q so that s(q) = 0.
-5, -1, -1/4, 1
Let d(g) = 2*g**2 - 2*g - 9. Let c be d(-6). Factor 60*y + 6 + 14 - c*y - 5*y**2.
-5*(y - 1)*(y + 4)
Let o(h) = -5*h - 21. Let z be o(-5). Let l(v) be the second derivative of 0 + 5*v - 1/10*v**5 - v**3 + 0*v**2 + 2/3*v**z. Factor l(j).
-2*j*(j - 3)*(j - 1)
Let b(z) be the second derivative of -z**7/2520 - z**6/240 - z**4/6 - 27*z. Let l(k) be the third derivative of b(k). Find y, given that l(y) = 0.
-3, 0
Let d(f) be the third derivative of -f**6/360 + 19*f**5/36 - 2303*f**4/72 + 2209*f**3/18 - 118*f**2. Factor d(a).
-(a - 47)**2*(a - 1)/3
Let k(o) be the third derivative of -o**7/1680 + 13*o**4/8 + 30*o**2. Let z(v) be the second derivative of k(v). Factor z(c).
-3*c**2/2
Let m(u) be the third derivative of u**6/120 + 3*u**5/20 - 7*u**4/8 + 11*u**3/6 + 2*u**2 - 126*u. Factor m(g).
(g - 1)**2*(g + 11)
Let y(c) be the first derivative of 2*c**3/3 + 7*c**2 + 20*c + 65. Suppose y(n) = 0. Calculate n.
-5, -2
Find t such that 21/4 - 1/4*t**2 + 5*t = 0.
-1, 21
Suppose 4*a + 2*n = -2*n - 12, 0 = 4*n + 4. Let l be 5/20 + a/(-4). Solve l + 0*z - 3/4*z**2 = 0 for z.
-1, 1
Suppose 5*u - 2 - 23 = -3*d, 5*d = -4*u + 33. Let w(n) be the first derivative of -d + 5/7*n**2 - 8/7*n - 2/21*n**3. Factor w(x).
-2*(x - 4)*(x - 1)/7
Solve 19*y**3 - 72 + 14*y**3 + 21*y - 43*y**3 - 28*y**2 + 78*y + 11*y**3 = 0.
1, 3, 24
Suppose 9*n - 4*n - 35 = 0. Factor 11*v**3 - 5*v**2 - v**4 + 3*v - 8*v**3 - n*v**3 - 5*v.
-v*(v + 1)**2*(v + 2)
Let c(v) = v - 2. Let p be c(17). Factor 109*k**3 + 5*k + 15*k**2 - p*k**4 - 104*k**3 - 15*k + 5*k**5.
5*k*(k - 2)*(k - 1)**2*(k + 1)
Let y = -13 - 146. Let w = y - -478/3. Factor 0*c + w*c**2 + 0 - 4/3*c**4 - c**3.
-c**2*(c + 1)*(4*c - 1)/3
Let m be 16/92 + 9/1242*12. Determine a, given 