 - 2)*(f - 1)/9
Let j(p) be the second derivative of -p**5/40 + p**4/8 - p**3/6 - 6*p. Factor j(i).
-i*(i - 2)*(i - 1)/2
Let y = 8 - 5. Suppose -y - 5 = -4*b. Factor -2/7 - 4/7*c - 2/7*c**b.
-2*(c + 1)**2/7
Solve -16/3*a + 44/3*a**3 - 16*a**2 - 28/3*a**5 + 0 + 16*a**4 = 0.
-1, -2/7, 0, 1, 2
Let p be 4 - (2184/18)/(-7). Find n such that 30*n**2 - p*n + 54*n**3 + 8/3 = 0.
-1, 2/9
Let c(i) be the second derivative of -i**7/11340 - i**6/3240 + i**4/4 + i. Let u(n) be the third derivative of c(n). Solve u(d) = 0 for d.
-1, 0
Let s(r) be the third derivative of 0*r + 0*r**3 + 1/1848*r**8 + r**2 + 2/165*r**5 + 1/132*r**4 + 1/110*r**6 + 0 + 4/1155*r**7. Find k such that s(k) = 0.
-1, 0
Let m(h) be the second derivative of h**7/2520 - h**6/180 + h**5/30 - h**4/6 - 2*h. Let q(y) be the third derivative of m(y). Solve q(u) = 0 for u.
2
Let u(a) be the first derivative of -a**4/10 + 4*a**3/15 - a**2/5 + 21. Factor u(p).
-2*p*(p - 1)**2/5
Suppose 24 = 4*k + k + 4*y, -5*k - y + 21 = 0. Suppose -13*f**2 + 3 + 31*f**2 + f + 3*f**k + 12*f**3 + 11*f = 0. Calculate f.
-1
Suppose -5*t + 70 = h - 59, -2*t + 3*h = -38. Find w, given that -2*w**2 - 6*w + 25 - t = 0.
-3, 0
Factor 2 - q**2 + 2*q**2 - 5*q**2 + 2.
-4*(q - 1)*(q + 1)
Let s be ((-1)/8)/(1/(-2)). Let o be 8/(-4)*2/(-16). Factor 1/4*z**3 + 1/4 - o*z**2 - s*z.
(z - 1)**2*(z + 1)/4
Suppose 0*c + 3*c - 6 = 0. Let m = c - 0. Suppose v**5 - 3*v**3 + v**4 + v**2 + 2*v**3 - m*v**2 = 0. What is v?
-1, 0, 1
Let u(z) = 18*z**4 - 25*z**3 + 2*z**2 + 8*z + 3. Let n(q) = -53*q**4 + 75*q**3 - 7*q**2 - 23*q - 8. Let t(l) = -3*n(l) - 8*u(l). Factor t(y).
5*y*(y - 1)**2*(3*y + 1)
Let r(v) = -2*v**5 + 3*v**4 + 10*v**3 - 6*v**2 - 2*v. Let p(l) = -l**5 - l**3 + l**2. Let q(t) = -3*p(t) - r(t). Find c such that q(c) = 0.
-1, -2/5, 0, 1
Let g(y) be the third derivative of y**7/525 - y**6/150 - 2*y**2. Factor g(q).
2*q**3*(q - 2)/5
Let z(o) = -o**2 + 18*o + 35. Let j(q) = q**2 - 12*q - 23. Let d(u) = 8*j(u) + 5*z(u). Factor d(r).
3*(r - 3)*(r + 1)
Let p(d) be the first derivative of d**4 + 4*d**3 + 4*d**2 - 3. Solve p(v) = 0.
-2, -1, 0
Let x = 3 - -8. Let j(p) = -2*p**3 - 20*p**2 - 92*p - 132. Let i(t) = -6*t**3 - 61*t**2 - 277*t - 395. Let g(k) = x*j(k) - 4*i(k). Factor g(h).
2*(h + 4)**3
Let b(h) = h - 15. Let i be b(18). Factor 2/7*g**i + 0 + 2/7*g + 4/7*g**2.
2*g*(g + 1)**2/7
Let m(x) = -16*x**4 - 9*x**3 + 9*x**2 + 2*x + 7. Let s(r) = -5*r**4 - 3*r**3 + 3*r**2 + r + 2. Let j(i) = 2*m(i) - 7*s(i). Find o, given that j(o) = 0.
-1, 0, 1
Suppose -m + 5*m - 55 = -a, 4*a - 292 = 2*m. Suppose 73*x - a*x = 4. Factor -4*z**x + 0 + 2/5*z + 32/5*z**5 + 66/5*z**3 - 16*z**4.
2*z*(z - 1)**2*(4*z - 1)**2/5
Let j(w) be the third derivative of -4*w**2 - 1/20*w**5 + 0*w + 0 - 1/2*w**3 + 1/4*w**4. Suppose j(c) = 0. Calculate c.
1
Let n(z) = 50*z**2 + 10*z. Let u(p) = p**2. Let f(m) = -n(m) + 15*u(m). Factor f(j).
-5*j*(7*j + 2)
Let n(a) be the second derivative of -a**5/30 - 7*a**4/6 - 49*a**3/3 - 343*a**2/3 - 5*a - 5. Factor n(q).
-2*(q + 7)**3/3
Let l(t) be the first derivative of t**4/2 - 2*t**3/3 - 2*t**2 + 31. Factor l(u).
2*u*(u - 2)*(u + 1)
Let t = 5 + -5. Let m(c) be the second derivative of 0 + t*c**2 + 3*c + 1/3*c**3 - 1/12*c**4. Factor m(g).
-g*(g - 2)
Let l(g) = g - 10. Let w be l(10). Factor n**2 + w*n**2 - 4 - 5*n - n - 3*n**2.
-2*(n + 1)*(n + 2)
Let z(y) be the first derivative of y**6/540 - y**5/45 + y**4/9 - y**3/3 + 1. Let s(u) be the third derivative of z(u). Let s(o) = 0. What is o?
2
Suppose 5*u + 4*w - 42 = 0, -w - 11 - 21 = -3*u. Let y = -7 + u. What is m in 4 - y*m - m + 6*m + 2*m**2 + 4*m = 0?
-2, -1
Let z be (-5)/(-30) + 1/2. Factor 0*u**2 + 2/3*u**4 + 0*u + z*u**3 + 0.
2*u**3*(u + 1)/3
Let i(d) = -d**3 - 3*d - 3. Let n be i(-2). Let k = n - 7. Let l**2 + l**3 - 7*l**3 + 7*l**3 - l - l**k = 0. Calculate l.
-1, 0, 1
Let o(w) = -w**4 + w - 13*w**2 - 5 + w**4 + 3*w**4 + 9*w**3. Let q(n) = -5*n**4 - 13*n**3 + 19*n**2 - n + 7. Let g(k) = -7*o(k) - 5*q(k). Solve g(c) = 0.
-1, -1/2, 0, 1
Factor -9 + 9/2*r**3 - 15/2*r + 12*r**2.
3*(r - 1)*(r + 3)*(3*r + 2)/2
Suppose 0 = -4*q + 16, 0 = 3*f - 0*q - 3*q. Factor 2*n**3 - 5*n**3 - 3*n**3 + 2*n**3 + 8*n + f*n**2.
-4*n*(n - 2)*(n + 1)
Let v(d) = 2*d**2 - 6*d - 4. Let s(k) = 3*k**2 - 7*k - 5. Let a = -20 - -16. Let u(c) = a*s(c) + 5*v(c). Suppose u(i) = 0. Calculate i.
-1, 0
Solve -69*n**3 - 38*n**4 + 11*n**4 + 75*n**3 = 0.
0, 2/9
Let i(t) be the first derivative of -3/4*t**4 + 0*t**3 + 1/2*t**6 + 0*t + 0*t**5 - 4 + 0*t**2. Determine o so that i(o) = 0.
-1, 0, 1
Let o(q) be the second derivative of 3/20*q**5 - q**3 + 0 - 4*q - 1/4*q**4 + 0*q**2. Find j such that o(j) = 0.
-1, 0, 2
Let i be 0 - (319/195)/(-1). Let a = i - -2/65. Factor -2/3 + a*h**2 + h - 2*h**3.
-(h - 1)*(2*h - 1)*(3*h + 2)/3
Let j(u) = -15*u**4 + 13*u**3 + 27*u**2 + 25*u. Let p(d) = -7*d**4 + 6*d**3 + 13*d**2 + 12*d. Let c(a) = 6*j(a) - 13*p(a). Factor c(s).
s*(s - 3)*(s + 1)*(s + 2)
Let v(m) be the second derivative of -7*m**5/180 + 2*m**4/9 - 2*m**3/9 + m**2/2 - 5*m. Let s(i) be the first derivative of v(i). Factor s(g).
-(g - 2)*(7*g - 2)/3
Factor 0 - 2/7*p + 2/7*p**3 + 0*p**2.
2*p*(p - 1)*(p + 1)/7
Let m(h) = -2*h**4 + 8*h**3 - 4*h**2 + 2. Let d(x) = -2*x**4 + 9*x**3 - 5*x**2 + x + 2. Let a(o) = -4*d(o) + 5*m(o). Factor a(z).
-2*(z - 1)**3*(z + 1)
Let c(i) be the first derivative of 8*i**6/3 - 12*i**5/5 - 13*i**4 + 4*i**3/3 + 18*i**2 + 8*i - 6. Find t such that c(t) = 0.
-1, -1/4, 1, 2
Let a(t) be the second derivative of -3*t**5/140 - t**4/14 - t**3/14 + 7*t. Let a(x) = 0. What is x?
-1, 0
Let f(c) be the second derivative of -c**5/20 + c**4/12 + c**3/6 - c**2/2 + 4*c. Factor f(h).
-(h - 1)**2*(h + 1)
Let a(s) be the third derivative of s**5/210 + s**4/21 + 4*s**3/21 + 38*s**2. Factor a(o).
2*(o + 2)**2/7
Find o, given that 38/9*o**3 + 8/9*o**4 + 16/9*o + 6*o**2 - 8/9 = 0.
-2, -1, 1/4
Let m(x) be the third derivative of -x**5/100 + x**4/20 - x**3/10 + 7*x**2. Find v such that m(v) = 0.
1
Determine g, given that 1 + 1/2*g - 1/2*g**2 = 0.
-1, 2
Let q(r) be the first derivative of 4*r**5/5 + 7*r**4/2 + 6*r**3 + 5*r**2 + 2*r - 6. Factor q(n).
2*(n + 1)**3*(2*n + 1)
Suppose -3*c = -c. Let 0 + c*v**2 - 4/7*v + 4/7*v**3 = 0. Calculate v.
-1, 0, 1
Let n be (-28)/6 + 4/(-12). Let l be ((-1)/n)/(2 - 1). Find y such that 1/5*y**3 - 1/5 - 1/5*y + l*y**2 = 0.
-1, 1
Let i(q) be the second derivative of q**8/40320 - q**7/15120 - q**6/4320 + q**5/720 + q**4/12 + 3*q. Let v(f) be the third derivative of i(f). Factor v(k).
(k - 1)**2*(k + 1)/6
Let o(j) be the first derivative of -j**6/16 - 9*j**5/40 - 3*j**4/16 - 31. Factor o(g).
-3*g**3*(g + 1)*(g + 2)/8
Let u(k) = 12*k**4 + 8*k**3 - 4*k**2. Let j(i) = -25*i**4 - 15*i**3 + 9*i**2 - i. Let o(v) = 4*j(v) + 9*u(v). Factor o(h).
4*h*(h + 1)**2*(2*h - 1)
Let j(m) be the first derivative of -1/12*m**3 - 3/4*m**2 - 9/4*m + 1. Factor j(a).
-(a + 3)**2/4
Let j = 8473/24 - 353. Let i(k) be the third derivative of 3*k**2 + 1/12*k**3 + 0 + 0*k + 1/120*k**5 - j*k**4. Factor i(s).
(s - 1)**2/2
Let d be (((-10)/(-8))/5)/1. Suppose 5*j = 3 + 17. Factor 1/4*l**j + d*l - 1/4*l**3 - 1/4*l**2 + 0.
l*(l - 1)**2*(l + 1)/4
Let c(x) = 11*x**2 - 15*x + 6. Let z(q) = -45*q**2 + 60*q - 25. Let r(i) = -25*c(i) - 6*z(i). Suppose r(n) = 0. Calculate n.
0, 3
Let q be (2/28*-9)/(1800/(-84)). Let d(j) be the second derivative of 0*j**2 - 3*j + 0*j**4 + 0 - 1/50*j**6 + 0*j**3 - q*j**5. Determine r, given that d(r) = 0.
-1, 0
Suppose -4*n - y = -3*y + 10, -5*y = 3*n + 1. Let s = 2 + n. Solve s + 2/3*d - 2/3*d**2 = 0 for d.
0, 1
Let a be (((-180)/25)/6)/(4/(-5)). Factor 21/4*f**2 + 0 + 15/4*f**3 + a*f.
3*f*(f + 1)*(5*f + 2)/4
Let p(k) = -5*k**3 - 8*k**2 - 11*k. Let f = -12 + 20. Let t(a) = -2*a**3 - 3*a**2 - 4*a. Let h(w) = f*t(w) - 3*p(w). Suppose h(q) = 0. Calculate q.
-1, 0, 1
Let m(p) = -p**5 + p**4 - p**3 + p + 1. Let f(a) = -16*a**5 + 24*a**4 - 32*a**3 - 4*a**2 + 28*a + 20. Let k(r) = -f(r) + 20*m(r). Find d, given that k(d) = 0.
-2, -1, 0, 1
Suppose 2*p - a - 36 = 3*a, 4*a + 56 = 3*p. Let k = p + -20. Factor -1/3*f - 1/3*f**3 - 2/3*f**2 + k.
-f*(f + 1)**2/3
Let t be (-3 + 2)/((-6)/24). Let h(i) be the third derivative of 0 + 1/210*i**5 + 0*i - 1/420*i**6 + i**2 + 0*i**3 + 0*i**t. Factor h(v).
-2*v**2*(v