- 6*r - r.
(r - 2)*(r - 1)
Let l(u) be the third derivative of 1/80*u**6 + 0*u - 1/420*u**7 + 0 - 1/60*u**5 + 0*u**4 + 0*u**3 - 4*u**2. Factor l(w).
-w**2*(w - 2)*(w - 1)/2
Let d(q) = -4*q**5 + 7*q**4 + 11*q**3 - 8*q**2 - q + 7. Let u(k) = 8*k**5 - 15*k**4 - 23*k**3 + 16*k**2 + k - 15. Let v(x) = 7*d(x) + 3*u(x). Factor v(m).
-4*(m - 1)**3*(m + 1)**2
Let d(g) be the first derivative of 5*g**6/12 + 5*g**5/2 + 15*g**4/8 - 15*g**3/2 + 73. Factor d(n).
5*n**2*(n - 1)*(n + 3)**2/2
Let v(w) = w**3. Let f(b) = -b - 1. Let s(l) = -5*l**3 + 27*l**2 - 87*l + 75. Let x(k) = -6*f(k) + s(k). Let u(t) = 2*v(t) + x(t). Solve u(y) = 0 for y.
3
Let x(m) be the third derivative of m**7/490 + m**6/280 - m**5/140 - m**4/56 - 6*m**2. Let x(w) = 0. What is w?
-1, 0, 1
Suppose 3*i**5 + 9*i**3 - 7*i**4 + 3*i**4 - 4*i**4 - i**4 - 3*i**2 = 0. What is i?
0, 1
Let f = 42/31 + -64/93. Determine t, given that 0*t + 1/3*t**3 - f*t**4 + 1/3*t**5 + 0*t**2 + 0 = 0.
0, 1
Suppose 0 - 8/3*u + 8/3*u**3 + 2/3*u**2 - 2/3*u**4 = 0. Calculate u.
-1, 0, 1, 4
Let k(f) = 4*f**3 - 9*f**2 - 7*f + 2*f - 3*f**2 - 9 + 22*f. Let y(h) = 6*h**3 - 18*h**2 + 26*h - 14. Let c(j) = 8*k(j) - 5*y(j). Factor c(s).
2*(s - 1)**3
Suppose 0 - 9 = -3*d. Suppose a - 6*a**2 + a - 6*a**d + 3*a**3 - 5*a = 0. Calculate a.
-1, 0
Let f(r) = 2*r**4 - r**2 - 3*r + 2. Let p be (-24)/3*(-3 + 2). Let j(w) = 6*w**4 - 4*w**2 - 8*w + 6. Let z(c) = p*f(c) - 3*j(c). Factor z(o).
-2*(o - 1)**2*(o + 1)**2
Let y(u) be the first derivative of 1/2*u**2 - 2 + 1/4*u**4 - 2/3*u**3 + 0*u. Let y(f) = 0. What is f?
0, 1
Suppose 6*w + 9 = 3*w. Let q(d) = 21*d**2 + 90*d + 24. Let u(h) = -21*h**2 - 90*h - 24. Let a(k) = w*q(k) - 2*u(k). Factor a(f).
-3*(f + 4)*(7*f + 2)
Let j(r) be the second derivative of -11*r**5/60 - r**4/18 + 11*r**3/18 + r**2/3 + 2*r. Suppose j(t) = 0. What is t?
-1, -2/11, 1
Let h(i) be the third derivative of 4*i**2 + 0*i + 0 - 1/3*i**3 - 1/120*i**5 - 1/12*i**4. Determine a, given that h(a) = 0.
-2
Suppose 4*g = 3 + 9. Find j such that 2*j**5 - 6*j - 2*j**4 + 2*j - 4*j**2 - 6*j**g + 14*j**2 = 0.
-2, 0, 1
Suppose -17 = -4*a - 5. Find s, given that -s - 5*s + a + 0*s**2 - 2*s**2 + 5*s**2 = 0.
1
Let c(x) = -x**3 - 4*x**2 + 5*x + 10. Let m be c(-4). Let b = -6 - m. Factor 2/9 - 2/9*j**b - 4/9*j + 4/9*j**3 + 0*j**2.
-2*(j - 1)**3*(j + 1)/9
Let z(y) be the first derivative of 5*y**4/18 - 2*y**3/3 + y**2/3 + 2*y/9 - 23. Factor z(v).
2*(v - 1)**2*(5*v + 1)/9
Let f(p) = -5*p**3 - 5*p**2 + 5*p - 9. Let h(m) = 7 + 3 + 3*m**3 + 3*m**2 - 1 - 3*m - 4. Let u(y) = -4*f(y) - 7*h(y). Determine o, given that u(o) = 0.
-1, 1
Let s = 6 + 0. Suppose -2*u - 2 = -s. Factor -1 - u*b**2 + 2 + b**2.
-(b - 1)*(b + 1)
Let -191*j**5 + 0 + 186*j**5 + 45*j**2 - 15*j**3 - 25*j**4 + 0 = 0. Calculate j.
-3, 0, 1
Let b(x) be the first derivative of -3*x**5/10 + x**3/2 - 4. Factor b(k).
-3*k**2*(k - 1)*(k + 1)/2
Let b = 12 + -8. Suppose 4*v**3 + 0*v**b + 2*v**4 + v**5 - 6*v**3 + 3*v**3 = 0. Calculate v.
-1, 0
Let k be (-19718)/(-56) + 3/(-12). Let g = -351 + k. Suppose -4/7 - 2/7*o**2 + g*o = 0. Calculate o.
1, 2
Let l(a) = -a**3 + 0*a**2 + a**2 - 2*a + 4*a. Let t(r) = -r**2 - 4*r**3 - 3*r + 5*r**3 + r**3. Let j(p) = 5*l(p) + 3*t(p). Find d such that j(d) = 0.
-1, 0
Let m = 338 - 237. Let g = 21 + m. Factor g*q**2 + 4 + 23*q**2 + 40*q + 49*q**5 + 235*q**3 + 175*q**4 + 0*q**5.
(q + 1)**3*(7*q + 2)**2
Let i(p) be the first derivative of -p**6/120 - 11*p**5/180 - p**4/6 - 2*p**3/9 + 2*p**2 - 1. Let w(u) be the second derivative of i(u). Factor w(r).
-(r + 1)*(r + 2)*(3*r + 2)/3
Let n(h) be the second derivative of -h**4/12 + 7*h**3/6 + 5*h**2 - 2*h. Let k be n(8). Factor 0*s**k + 1 - 2*s**2 + 2 - 1.
-2*(s - 1)*(s + 1)
Let o(a) be the third derivative of a**6/180 - 2*a**5/45 + 5*a**4/36 - 2*a**3/9 - 4*a**2. Solve o(z) = 0 for z.
1, 2
Factor -3/4*z**2 - 3/4*z + 3/4*z**4 + 3/4*z**3 + 0.
3*z*(z - 1)*(z + 1)**2/4
Suppose -2*o + 2*i + 35 = 3*o, 4*o = 2*i + 28. Suppose o*g - 2*g = 20. What is a in -3/2*a**2 + 1/4*a + 0 + 3/4*a**5 - 5/2*a**g + 3*a**3 = 0?
0, 1/3, 1
Let w(y) = y**3 + y + 1. Suppose -a = -1 - 2. Let f(p) = p**3 + 5*p + 3. Let z(q) = a*w(q) - f(q). Factor z(j).
2*j*(j - 1)*(j + 1)
Let w(s) = -9*s**5 + 36*s**4 + 57*s**3 + 33*s**2 - 21. Let a(q) = 2*q**5 - 9*q**4 - 14*q**3 - 8*q**2 + 5. Let y(l) = 21*a(l) + 5*w(l). Factor y(c).
-3*c**2*(c + 1)**3
Suppose -16 = -4*i, 3*h + 2*i - 22 = -2*i. Factor -7*o**h - 7 + 3 + 4*o + 11*o**2 - 4*o**3.
-4*(o - 1)**2*(o + 1)
Let c(f) be the first derivative of 4 + 0*f**4 - 1/5*f**5 + 0*f**3 + 0*f + 0*f**2. Factor c(i).
-i**4
Let r(n) be the second derivative of -1/2*n**4 - 1/15*n**6 + 0 - 1/3*n**3 + 2*n - 3/10*n**5 + 0*n**2. Suppose r(s) = 0. Calculate s.
-1, 0
Factor -61*z - 27 - 12*z**3 + 155 - 30*z - 37*z - 88*z**2.
-4*(z + 4)**2*(3*z - 2)
Let g(z) be the second derivative of z**4/4 + z**3/2 - 7*z. Factor g(a).
3*a*(a + 1)
Let g(x) be the second derivative of -x**5/60 + x**4/36 + x**3/9 - 4*x. Factor g(l).
-l*(l - 2)*(l + 1)/3
Let b(t) be the second derivative of 3*t + 2/3*t**4 - 16/9*t**3 + 8/3*t**2 - 2/15*t**5 + 0 + 1/90*t**6. Factor b(n).
(n - 2)**4/3
Suppose 0 = 5*z + 3*t - 21, 5*t + 15 = -0*t. Let l be z/27 + 26/45. Determine g, given that -8/5*g**2 + 2*g - l + 2/5*g**3 = 0.
1, 2
Let s(m) = m + 1. Let y(o) = 3*o**2 - 3. Let v(i) = 3*s(i) + y(i). Solve v(t) = 0 for t.
-1, 0
Factor -8/17*v + 2/17*v**2 + 2/17*v**3 - 8/17.
2*(v - 2)*(v + 1)*(v + 2)/17
Let n(b) be the second derivative of b**5/300 - b**4/60 - 2*b**2 + 2*b. Let j(v) be the first derivative of n(v). Let j(k) = 0. What is k?
0, 2
Let b(j) be the first derivative of 0*j**2 + 0*j**3 + 1/9*j**6 + 2/3*j**4 - 8/15*j**5 + 0*j - 4. Factor b(n).
2*n**3*(n - 2)**2/3
Find t such that -1 + 1 - 4*t**2 - 15*t + 13*t - 2*t**3 = 0.
-1, 0
Let h be 44/8*(-1 + 5). Let i be (-126)/(-88) + h/(-121). Determine n, given that 9/4*n**4 - 7/4*n**5 + 1/2*n + 0 - 9/4*n**2 + i*n**3 = 0.
-1, 0, 2/7, 1
Let s be 32/40*(-2)/(-6). Let a(g) be the second derivative of -s*g**3 + 1/30*g**4 - 3*g + 4/5*g**2 + 0. Factor a(n).
2*(n - 2)**2/5
Suppose -6*l - 2 = -7*l. Suppose l*m + 28 = 4*y, 5*y = 4*y - m + 1. Solve -1/4*q**3 - 1/4*q**4 + 0*q + 1/4*q**y + 0 + 1/4*q**2 = 0.
-1, 0, 1
Suppose 5*o = 7*o. What is h in 1/4*h**3 + o + 1/2*h + 3/4*h**2 = 0?
-2, -1, 0
Let h(y) = -5*y**4 - 4*y**3 - 2*y + 5. Let j(k) = -15*k**4 - 13*k**3 - 4*k + 15. Let b(s) = -17*h(s) + 6*j(s). Factor b(g).
-5*(g - 1)*(g + 1)**3
Let u(d) = d + 18. Let w be u(-18). Determine h, given that 0*h + 0*h**3 + 2/9*h**4 - 2/9*h**2 + w = 0.
-1, 0, 1
Solve 3/4*m**3 - 3/4*m + 3/4 - 3/4*m**2 = 0.
-1, 1
Let b(k) be the third derivative of 0 - 1/45*k**5 + 0*k + 2*k**2 + 1/12*k**4 + 1/540*k**6 + 0*k**3. Factor b(m).
2*m*(m - 3)**2/9
Let m = -30 + 32. Suppose 4*d - n = 2, 4*d - 2*n - 4 = m*d. Factor c**2 - 5/2*c**3 + 2*c**4 + d - 1/2*c**5 + 0*c.
-c**2*(c - 2)*(c - 1)**2/2
Let z = -1496/3 + 499. Factor 8/3*s - 16/3*s**2 - z.
-(4*s - 1)**2/3
Let j = -11 + 20. Let w = -46 + 48. What is l in 21*l**5 - 21*l**3 - w*l**2 + 9*l - l**2 - j*l**5 + 3 = 0?
-1, -1/2, 1
Let y(x) = 6*x**2 - 10*x. Let z(j) = -2*j**2 - 3*j - 4. Let p(i) = 5*i**2 + 9*i + 11. Let m(t) = 4*p(t) + 11*z(t). Let n(b) = -16*m(b) - 5*y(b). Factor n(s).
2*s*(s + 1)
Let b = -133/66 - -24/11. Let k(o) be the first derivative of -1/16*o**4 - 3 - 1/2*o + b*o**3 + 1/8*o**2. Factor k(q).
-(q - 2)*(q - 1)*(q + 1)/4
Let q(d) be the second derivative of -d**5/210 - d**4/84 - 2*d**2 + 2*d. Let c(g) be the first derivative of q(g). Solve c(s) = 0.
-1, 0
Let b(p) = -12*p**5 - 11*p**4 + 12*p**3 + 22*p**2 - 11. Let c(q) = q**5 + q**4 - 2*q**2 - q + 1. Let s(n) = b(n) + 6*c(n). Suppose s(d) = 0. What is d?
-1, -5/6, 1
Let k(t) be the first derivative of -1/7*t**2 + 3 + 2/7*t**3 - 4/7*t. Factor k(p).
2*(p - 1)*(3*p + 2)/7
Factor -k**4 + 3*k**4 + 18*k**2 + 4 - 8*k**3 + 16*k - 2*k + 18*k**3.
2*(k + 1)**3*(k + 2)
Let g(z) be the third derivative of z**7/210 + z**6/30 - z**5/60 - 2*z**4/3 - 2*z**3 + 19*z**2. Determine w so that g(w) = 0.
-3, -2, -1, 2
Let t(y) be the second derivative of y**4/6 + 4*y**3 + 11*y**2 - 14*y + 1. Factor t(v).
2*(v + 1)*(v + 11)
Suppose -3*t = -4*v - 5 - 8, -v - 10 = -3*t. Suppose t*c - 2*l = -3*l + 5, -l + 5 = 0. Solve c*p + 0 - 2/7*p**2 = 0 for p.
0
Let k = -3