)/114. Let d(t) be the third derivative of -3*t**2 + 0*t**3 + 0*t**4 + 0 + 1/90*t**6 + 0*t + o*t**5. Factor d(v).
4*v**2*(v + 2)/3
Let w = -257/153270 + 5/1179. Let g(i) be the third derivative of 1/1365*i**7 + 0 + 1/390*i**6 - i**2 + 0*i - 1/78*i**4 - w*i**5 + 0*i**3. Factor g(t).
2*t*(t - 1)*(t + 1)*(t + 2)/13
Suppose 2*j - 6*j = -112. Suppose -2*p = 5*t + 7, -4*p + 4*t + j = -0*p. Factor -4*k + p*k**3 - 14 - 2*k**2 + 2*k**4 + 14.
2*k*(k - 1)*(k + 1)*(k + 2)
Let o = 272/10185 - 5/291. Let q(l) be the second derivative of -6*l - 2/35*l**5 - 5/42*l**4 + 0*l**2 - 2/21*l**3 + 0 - o*l**6. Factor q(s).
-2*s*(s + 1)**2*(s + 2)/7
Let j be (-6)/8 + 65/(-4). Let u(i) = -2*i**2 + 43*i + 11. Let w(t) = -t**2 + 15*t + 4. Let y(o) = j*w(o) + 6*u(o). Let y(a) = 0. Calculate a.
-1, 2/5
Let r = 2118 + -2115. What is a in 3*a + 9/2*a**2 + 3/2*a**r + 0 = 0?
-2, -1, 0
Let 4*j**2 - 8*j + 1/2*j**4 + 0 + 7/2*j**3 = 0. Calculate j.
-4, 0, 1
Let c(a) be the second derivative of 3*a**5/40 - 7*a**4/4 + 8*a**3 + 96*a**2 + a + 33. Suppose c(i) = 0. What is i?
-2, 8
Suppose -4*l - 5*i = -2*i - 19, 4*l + i = 9. Let c be (1 - -1 - 2)/((-1)/l). Factor c*s**2 + 0 + 0*s**4 + 0*s + 0*s**3 + 2/7*s**5.
2*s**5/7
Let g(w) = -w - 8. Let k be g(-7). Let x = k + 3. Suppose -9*o + 92*o**x - 80*o**2 - 2*o**3 - o**3 = 0. What is o?
0, 1, 3
Let y(l) be the third derivative of -l**8/672 + l**7/70 - l**6/48 + 69*l**2. Factor y(p).
-p**3*(p - 5)*(p - 1)/2
Let c = -2042 - -2044. Suppose -24/11*f**c - 18/11*f**4 + 48/11*f**3 + 0 + 0*f = 0. Calculate f.
0, 2/3, 2
Let z(o) be the second derivative of -o**6/6 + 5*o**5/4 - 35*o**4/12 + 5*o**3/2 + 4*o - 35. Determine r, given that z(r) = 0.
0, 1, 3
Factor -5*t**3 - 25*t + 6 - 4 - 6 - 9*t**2 - 11*t**2 - 6.
-5*(t + 1)**2*(t + 2)
Let l(v) = -64*v**3 - 568*v**2 - 1640*v - 28. Let m(d) = 7*d**3 + 63*d**2 + 182*d + 3. Let t(o) = -3*l(o) - 28*m(o). Factor t(i).
-4*i*(i + 4)*(i + 11)
Let a(l) = -l**3 - 3*l**2 - 2*l - 1. Let o(w) = -5*w**3 + 9*w**2 - 8*w - 4. Let f(n) = 12*a(n) - 3*o(n). Solve f(v) = 0 for v.
0, 21
Suppose 2*u**2 + 1/4*u**3 + 9/4*u - 9/2 = 0. What is u?
-6, -3, 1
Let p(n) be the first derivative of n**4/38 - 62*n**3/57 + 30*n**2/19 + 22. Factor p(m).
2*m*(m - 30)*(m - 1)/19
Let r be 33/264 - 111/(-8). Let n be 0*(2 + (-21)/r). Determine m so that n + 1/2*m - 1/2*m**2 = 0.
0, 1
Let k(a) be the third derivative of -a**4/12 + 11*a**3 + 8*a**2. Let x be k(0). Suppose 9 + 8*z**3 - 6*z - 12*z**2 + 69*z**4 - x*z**4 - 2*z**3 = 0. Calculate z.
-3, -1, 1
Let z(h) be the first derivative of -h**4/30 + 482*h**3/15 - 58081*h**2/5 + 27995042*h/15 - 370. What is x in z(x) = 0?
241
Let q(c) = -3*c**3 - 6*c**2 + 20*c + 6. Let x(g) = -g**3 - 2*g**2 + 7*g + 2. Let p(z) = 6*q(z) - 17*x(z). Let p(s) = 0. Calculate s.
-2, -1, 1
Let o(r) be the second derivative of -4/15*r**3 + 4/5*r**2 + 0 - 4*r + 1/30*r**4. Factor o(z).
2*(z - 2)**2/5
Let j(d) be the second derivative of 0*d**3 + 0 + 0*d**2 - 1/110*d**5 + 1/231*d**7 - 1/33*d**4 + 5*d + 2/165*d**6. Solve j(k) = 0 for k.
-2, -1, 0, 1
Let p(u) be the second derivative of u**7/1260 + u**6/120 + u**5/30 - 14*u**4/3 + 6*u. Let n(v) be the third derivative of p(v). Solve n(m) = 0 for m.
-2, -1
Let t(r) = 18*r**2 + 4*r - 18. Let c(f) = -1. Let w(i) = 36*c(i) - 2*t(i). Factor w(m).
-4*m*(9*m + 2)
Let b be ((-27)/18)/(1/(-6)). Let x = b + 3. Suppose x*f**5 + 7 - 3*f**3 + 19*f**3 + 1 + 17*f**2 - 32*f**4 + 7*f**2 - 28*f = 0. What is f?
-1, 2/3, 1
Let x(l) = -l**2 + 33*l + 10. Let c(u) = 2*u**2 - 98*u - 28. Let r(d) = -5*c(d) - 14*x(d). Factor r(o).
4*o*(o + 7)
Suppose 0 = 2*v + 2*v, 2*y + 4*v - 8 = 0. Let g(m) be the second derivative of 0 + 9/7*m**2 - 2*m - 2/7*m**3 + 1/42*m**y. Factor g(c).
2*(c - 3)**2/7
Let z(j) be the first derivative of -j**7/2940 - j**6/630 - j**5/420 + 4*j**3/3 - 10. Let y(u) be the third derivative of z(u). Factor y(x).
-2*x*(x + 1)**2/7
Suppose 4*u - 16 = i - 11, 2*i - 12 = -3*u. Factor 0 + 8/7*z**3 - u*z**2 - 4/7*z.
2*z*(z - 2)*(4*z + 1)/7
Let t(n) be the second derivative of 0*n**3 + 0*n**2 + 0 - 1/27*n**4 - 1/135*n**6 + 1/30*n**5 - 2*n. Factor t(g).
-2*g**2*(g - 2)*(g - 1)/9
Let l(p) = -p**3 + p**2 + 1. Let n be l(1). Let k be 2/(-2) + n + 2. Solve -6*w - 157*w**k - w - 4*w**5 + 11*w**3 + 164*w**2 - 2 - 5*w**4 = 0.
-2, -1, -1/4, 1
Factor 17*y**2 - 198*y - 2*y**3 - 30 - 3*y**2 + 184*y.
-2*(y - 5)*(y - 3)*(y + 1)
Let w(p) be the third derivative of -2*p**2 + 1/5*p**5 + 3/70*p**7 - 3/20*p**6 + 0 + 0*p**4 - 1/224*p**8 + 0*p**3 - 20*p. Factor w(y).
-3*y**2*(y - 2)**3/2
Let v be (-1 - -1)/(546/78). Determine i so that -8/7*i**3 + 8/7*i - 20/7*i**2 + v + 20/7*i**4 = 0.
-1, 0, 2/5, 1
Let j(v) = 2*v**2 - 531*v + 34848. Let k(z) = 4*z**2 - 1061*z + 69696. Let q(d) = -5*j(d) + 3*k(d). What is w in q(w) = 0?
132
Let t(i) be the second derivative of -7*i**5/60 + 23*i**4/24 - i**3 - 13*i**2/2 - 18*i. Let z(y) be the first derivative of t(y). Let z(l) = 0. What is l?
2/7, 3
Let r(k) = k**2 - 245*k + 244. Let n(m) = -m**2 + 488*m - 487. Let b(p) = 4*n(p) + 7*r(p). Factor b(t).
3*(t - 1)*(t + 80)
Let z(r) be the second derivative of -25*r**7/441 + 2*r**6/21 + 61*r**5/210 - 11*r**4/63 - 4*r**3/7 - 8*r**2/21 - r + 61. Let z(k) = 0. Calculate k.
-1, -2/5, 1, 2
Let c = 19 - 7. Suppose -5*h + 20 = 5*j, -4*h + 15 = -0*h + 3*j. Factor 2*a**h - 2*a - 2*a**2 + c*a**2 - 9*a**2 - a**4.
-a*(a - 2)*(a - 1)*(a + 1)
Let -26/11*z**3 - 144/11 - 24/11*z + 2/11*z**4 + 92/11*z**2 = 0. What is z?
-1, 2, 6
Let m(b) be the first derivative of 2*b**6/3 - 4*b**5 + 8*b**4 - 16*b**3/3 - 189. Factor m(g).
4*g**2*(g - 2)**2*(g - 1)
Let s(l) be the first derivative of l**5/45 + l**4/3 + 2*l**3 + 7*l**2 - 13. Let u(g) be the second derivative of s(g). Suppose u(c) = 0. Calculate c.
-3
Let j = -11333/2 - -79431/14. Suppose j*n - 102/7*n**4 - 148/7*n**2 - 6/7 + 188/7*n**3 + 18/7*n**5 = 0. Calculate n.
1/3, 1, 3
Let p(b) be the third derivative of b**8/3360 + b**7/420 - b**5/15 - 17*b**4/24 + 4*b**2. Let s(d) be the second derivative of p(d). Factor s(f).
2*(f - 1)*(f + 2)**2
Let l(p) be the first derivative of p**7/2100 - p**6/180 + p**5/100 + 3*p**4/20 + 14*p**3/3 + 18. Let o(j) be the third derivative of l(j). Factor o(b).
2*(b - 3)**2*(b + 1)/5
Let a(g) be the second derivative of -2*g**7/21 - 4*g**6/15 + 3*g**5/5 + 114*g. Factor a(l).
-4*l**3*(l - 1)*(l + 3)
Let b(w) be the second derivative of -10*w - 1/90*w**6 + 0 - 3/2*w**3 - 1/10*w**5 + 0*w**2 + 0*w**4. Let y(z) be the second derivative of b(z). Factor y(u).
-4*u*(u + 3)
Let w be (9/1)/3 + -3. Let z = 2 + w. Determine i so that 5 - 2 + 5*i**z - 7*i + 69*i**3 - 70*i**3 = 0.
1, 3
Let z = 11 + -5. Let p be -2*2/(z/((-12)/4)). Factor -3/5*r**3 + 3/5*r - 3/5*r**p + 0 + 3/5*r**4.
3*r*(r - 1)**2*(r + 1)/5
Let s = -84 - -84. Let m be (-3)/(-3)*(-1 + 2). What is k in -3*k + 2*k + s*k**2 - m - k**3 + 2*k + k**2 = 0?
-1, 1
Suppose -4*p - 8 = q, -q - 5*p + 4*p = -1. Let y(u) be the third derivative of 3*u**2 + 1/60*u**5 + 0 + 0*u**3 - 1/24*u**q + 0*u. Factor y(w).
w*(w - 1)
Let u(k) = 2*k**2 + 6*k - 6. Suppose -q - 10 = -3*q. Let o(b) = b**2 + 7*b - 5. Let w(j) = q*u(j) - 6*o(j). Solve w(y) = 0.
0, 3
Suppose 3*x = l + 14, x + 3*l = 6*l + 18. Let r(j) be the second derivative of 0 + 0*j**2 + 0*j**x + 0*j**4 + 1/90*j**5 - j. What is h in r(h) = 0?
0
Let b(w) be the third derivative of w**6/660 - w**4/44 + 2*w**3/33 + 23*w**2. Factor b(p).
2*(p - 1)**2*(p + 2)/11
Solve 7*r**2 - 17*r**2 + 24*r + 12*r**2 = 0.
-12, 0
Let j(w) be the second derivative of 0*w**3 + 0 - 33*w + 1/20*w**6 + 0*w**2 + 3/20*w**5 + 0*w**4. Let j(z) = 0. Calculate z.
-2, 0
Determine g so that -3*g - 179*g**4 - 161*g**4 + 382*g**4 + 22*g**2 - 52*g**3 - 9*g**5 = 0.
0, 1/3, 1, 3
Let k(u) be the first derivative of u**2 + 7/120*u**6 + 0*u**3 - 3 - 1/12*u**4 + 0*u - 1/12*u**5. Let v(a) be the second derivative of k(a). Solve v(w) = 0.
-2/7, 0, 1
Let r(x) be the first derivative of -x**7/5460 + x**6/260 - 9*x**5/260 + 9*x**4/52 + x**3/3 + 9. Let q(t) be the third derivative of r(t). Factor q(c).
-2*(c - 3)**3/13
Determine l so that 15/2*l**3 + 111/2*l - 9 - 54*l**2 = 0.
1/5, 1, 6
Let a be 13/52*4*2. Let k(b) be the third derivative of 1/168*b**4 - a*b**2 - 1/210*b**5 + 0*b + 1/21*b**3 - 1/840*b**6 + 0. Let k(i) = 0. What is i?
-2