r - 1)*(r + 1)**3
Let o(d) be the second derivative of -d**5/90 + d**4/9 + d**3/27 - 2*d**2/3 + 46*d - 2. Factor o(q).
-2*(q - 6)*(q - 1)*(q + 1)/9
Let u(f) be the third derivative of 0*f + f**2 + 1/360*f**5 - 1/1080*f**6 + 0 - 1/6*f**3 + 0*f**4. Let h(r) be the first derivative of u(r). Factor h(i).
-i*(i - 1)/3
Let j(s) = -3*s**2 + 12*s + 20. Let u be j(5). Factor -2*y**4 + 0 + 3*y**3 + 1/2*y - 2*y**2 + 1/2*y**u.
y*(y - 1)**4/2
Let u be (-10)/(-6) - 26/18. Solve 2/3*d - u*d**2 - 4/9 = 0.
1, 2
Suppose 0 = 11*h + 2*h. Let 0*w**2 + 1/2*w + 1/2*w**5 - w**3 + 0*w**4 + h = 0. Calculate w.
-1, 0, 1
Let k be (-1 + 3)*10/(-4). Let y = 5 + k. Find l, given that l**4 - 2*l**3 + y*l**4 + l**5 - l**2 + l**3 = 0.
-1, 0, 1
Suppose -y = 6*y + 21. Let a(c) be the first derivative of -3*c**4/4 - 1. Let d(z) = -2*z**3. Let i(v) = y*a(v) + 4*d(v). Let i(t) = 0. What is t?
0
Let x(h) = 2*h**4 + 2*h**3 + 20*h**2. Let t(l) = l**4 + l**3 + 13*l**2. Let q = -17 + 12. Let y(m) = q*x(m) + 8*t(m). Factor y(f).
-2*f**2*(f - 1)*(f + 2)
Let t(o) = -15*o**3 + 8*o**2 + 3. Let s(b) = 16*b**3 - 8*b**2 - 4. Let i(d) = -3*s(d) - 4*t(d). Factor i(g).
4*g**2*(3*g - 2)
Let k(u) = -u**2 + 8*u + 2. Let d be k(8). Find n such that 3*n**d - 3*n**3 + 6*n**3 - 3*n**2 + 5*n**4 - n - n**2 + 2*n**5 = 0.
-1, 0, 1/2
Let a(c) be the first derivative of c**4/16 + 7*c**3/12 - c**2/8 - 7*c/4 - 69. Solve a(f) = 0.
-7, -1, 1
Let r = -2/259 - -524/777. Let k be 1/(9/(-12)) - -2. What is a in -r*a**2 + 0*a + k = 0?
-1, 1
Let v(j) be the first derivative of -j**8/224 + j**7/84 - j**6/120 + 3*j**2 + 3. Let f(n) be the second derivative of v(n). Let f(m) = 0. What is m?
0, 2/3, 1
Let h(o) be the third derivative of -o**9/1512 - o**8/480 - o**7/630 + o**4/24 + o**2. Let a(g) be the second derivative of h(g). Suppose a(s) = 0. Calculate s.
-1, -2/5, 0
Factor -10*t**2 + 20/3*t**3 - 5/3*t**4 + 20/3*t - 5/3.
-5*(t - 1)**4/3
Factor 0*x**3 + 0*x + 4/5*x**2 - 2/5 - 2/5*x**4.
-2*(x - 1)**2*(x + 1)**2/5
Factor -2/7*k**4 + 8/7*k**3 - 10/7*k**2 + 0 + 4/7*k.
-2*k*(k - 2)*(k - 1)**2/7
Let y(p) be the first derivative of -2/11*p**2 - 3 + 0*p + 10/33*p**3 - 2/11*p**4 + 2/55*p**5. Suppose y(o) = 0. Calculate o.
0, 1, 2
Suppose f + 12 = 3*f. Let p be (0 + -2)*(-1)/f. Suppose 1/3 - p*h**2 + 1/3*h - 1/3*h**3 = 0. Calculate h.
-1, 1
Let b = -13/7 - -46/21. Let v(y) be the first derivative of 3 - 1/3*y**2 + b*y + 1/9*y**3. Determine c, given that v(c) = 0.
1
Let 32/7*s**3 + 18/7*s + 0 + 48/7*s**2 = 0. What is s?
-3/4, 0
Determine t so that 0*t - 6/17*t**2 - 2/17*t**3 + 8/17 = 0.
-2, 1
Let o(j) = 2*j**3 - 4*j**2 - j. Let l(n) = -n**3 - n. Let c be -3*2/(-6)*-1. Let u(m) = c*o(m) - 3*l(m). Factor u(z).
z*(z + 2)**2
Let x(i) be the first derivative of -i**7/420 + i**5/20 + i**4/6 - 7*i**3/3 - 6. Let l(s) be the third derivative of x(s). Solve l(f) = 0.
-1, 2
Let w(h) be the third derivative of h**6/216 - h**5/45 + h**4/54 + 21*h**2. Find k such that w(k) = 0.
0, 2/5, 2
Let h(r) be the second derivative of -r**7/33 + 2*r**6/165 + 21*r**5/110 - 10*r**4/33 + 4*r**3/33 - 4*r. Determine i so that h(i) = 0.
-2, 0, 2/7, 1
Let y(n) be the first derivative of n**4/6 - 5*n**3/6 + n**2 - n - 7. Let a(b) be the first derivative of y(b). Factor a(m).
(m - 2)*(2*m - 1)
Let v be ((-12)/5)/((-20)/50). Suppose -v*a + 9 = -3*a. Find r such that -8/7*r**2 + 4/7 + 6/7*r**a - 2/7*r = 0.
-2/3, 1
Let z = 15 + -5. Let f be 15/(-4)*(-4)/z. Find x such that f*x**3 + 0*x - 3/2*x**4 + 0 + 0*x**2 = 0.
0, 1
Let d(a) = a - 7. Let z be d(8). Let p be (-3)/(z/(-4)*6). Factor 0 - 2/5*k**p - 2/5*k.
-2*k*(k + 1)/5
Let p(z) be the second derivative of z**9/7560 + z**8/2100 + z**7/2100 - 2*z**3/3 + 5*z. Let v(r) be the second derivative of p(r). Factor v(h).
2*h**3*(h + 1)**2/5
Factor 0 + 0*y - 6/7*y**3 + 2/7*y**4 - 8/7*y**2.
2*y**2*(y - 4)*(y + 1)/7
Let p(w) = -w**5 + w**4. Let l = -3 + 7. Let i(a) = -2*a**5 + 4*a**2 - 2*a. Let q(j) = l*p(j) - i(j). Find y such that q(y) = 0.
-1, 0, 1
Solve 4/3*v**2 + 1/3*v - 2 + 1/3*v**3 = 0.
-3, -2, 1
Suppose 16/7*x + 2/7*x**3 + 8/7 + 10/7*x**2 = 0. Calculate x.
-2, -1
Factor -j**3 + 7*j**4 - 16*j**2 - 2*j**2 - 9*j**3 + 27*j + 27 - j**5.
-(j - 3)**3*(j + 1)**2
Determine t so that 2/5*t**2 - 2/5*t**5 - 4/5*t + 6/5*t**3 + 0 - 2/5*t**4 = 0.
-2, -1, 0, 1
Suppose 3*r = 4*r - 18. Let z be (r/60)/((-2)/(-10)). Solve -3/2 + 0*b**3 + 0*b + 3*b**2 - z*b**4 = 0 for b.
-1, 1
Let b(s) be the third derivative of -s**9/17640 + s**8/5880 + s**7/8820 - s**6/1260 + s**4/8 - 3*s**2. Let v(h) be the second derivative of b(h). Factor v(k).
-2*k*(k - 1)**2*(3*k + 2)/7
Suppose 0 = 5*i + 16 + 9. Let s be 5/(50/(-4))*i. Find h such that 16/7*h**3 - 2/7 - 24/7*h**s + 12/7*h = 0.
1/2
Suppose j = g - 18, -3*g = 3*j - 0*j - 60. Suppose -3*z + 1 = 4*w, w - 3*z - g = -0. Factor -4/7*y**2 - 2/7*y + 2*y**3 + 0 - 8/7*y**w.
-2*y*(y - 1)**2*(4*y + 1)/7
Let d = -481 - -481. Determine r so that 1/2*r**2 + 0*r + d = 0.
0
Factor b**5 - 3*b**4 + 3*b**3 - 2*b - b**2 - 2*b**5 + 4*b**4 + 0*b**5.
-b*(b - 2)*(b - 1)*(b + 1)**2
Let p(b) be the second derivative of b**4/12 + 2*b**3/3 + 3*b**2/2 - 3*b. What is i in p(i) = 0?
-3, -1
Let a(q) be the first derivative of 5*q**4/4 - 5*q**3 + 5*q**2 - 15. Factor a(m).
5*m*(m - 2)*(m - 1)
Let j be -3 + (153/15)/3. Let u(w) be the second derivative of 1/6*w**4 + 1/5*w**3 - j*w**2 + 0 + w. Factor u(s).
2*(s + 1)*(5*s - 2)/5
Let c(g) be the second derivative of -g**9/30240 + g**7/2520 - g**5/240 - g**4/6 - 5*g. Let w(m) be the third derivative of c(m). Factor w(t).
-(t - 1)**2*(t + 1)**2/2
Let n(r) be the second derivative of -r**7/2520 - r**4/12 + 2*r. Let y(j) be the third derivative of n(j). Suppose y(i) = 0. What is i?
0
Let j(y) be the third derivative of y**6/150 - y**5/25 - y**4/30 + 2*y**3/5 + 7*y**2. Factor j(b).
4*(b - 3)*(b - 1)*(b + 1)/5
Factor -2/7 + 8/7*p + 4/7*p**3 - 10/7*p**2.
2*(p - 1)**2*(2*p - 1)/7
Determine j so that 1/9*j**2 - 7/9*j + 10/9 = 0.
2, 5
Factor 171*n + 5*n**2 - 176*n - 4 + 4.
5*n*(n - 1)
Let 3/5*y + y**4 - 2/5*y**3 - 14/5*y**2 + 9/5 - 1/5*y**5 = 0. Calculate y.
-1, 1, 3
Let y(l) be the first derivative of -4/3*l**3 - 2 + 1/2*l**4 + 0*l + l**2. Factor y(p).
2*p*(p - 1)**2
Let h(a) be the first derivative of -3*a**5/5 - 15*a**4/4 - 9*a**3 - 21*a**2/2 - 6*a - 7. Factor h(x).
-3*(x + 1)**3*(x + 2)
Determine n, given that -22/5*n + 8/5*n**2 + 12/5 = 0.
3/4, 2
Let z(d) = -d**2 - 26*d + 29. Let f be z(-27). Let 2 + 1/2*j**f - 2*j = 0. What is j?
2
Let m(w) = w**3 - 2*w**2 - w + 1. Let y be m(3). What is a in -a**2 - y*a - a**3 + 7*a = 0?
-1, 0
Let f(v) = v**3 + 7*v**2 + 6*v + 8. Let p be f(-6). Suppose 5*k - 7 = p. Factor 0 + 2/3*y + 2*y**2 + 2/3*y**4 + 2*y**k.
2*y*(y + 1)**3/3
Solve -9/2*w - 7/4*w**2 - 2 = 0 for w.
-2, -4/7
Let c(v) be the third derivative of 0 + 0*v + 1/210*v**7 + 0*v**3 - 1/60*v**5 - 1/24*v**4 + 1/120*v**6 - 2*v**2. Factor c(u).
u*(u - 1)*(u + 1)**2
Let a = -4 + 10. Let v(u) = 2*u**2 + u**2 + 4*u**2 - a*u. Let z(s) = -15*s**2 + 13*s. Let h(x) = 13*v(x) + 6*z(x). Factor h(n).
n**2
Let h(r) be the first derivative of r**2 + 2/3*r**3 - 1/2*r**4 - 2/5*r**5 + 4 + 0*r. Factor h(n).
-2*n*(n - 1)*(n + 1)**2
Let p be (-7 - -3 - -7) + (-11)/4. Solve -1/4*b**4 - 1/4*b + p*b**3 + 1/4*b**2 + 0 = 0.
-1, 0, 1
Let x(l) = -l**3 - l + 2. Let o be x(0). Let d(q) be the third derivative of -1/210*q**5 + 0*q**3 + 0 + 0*q - 1/84*q**4 - 2*q**o. Factor d(n).
-2*n*(n + 1)/7
Let k(a) be the second derivative of -3*a**5/70 - a**4/21 + a**3/7 + 2*a**2/7 - 8*a. What is c in k(c) = 0?
-1, -2/3, 1
Let o = 5 + -7. Let m be 5 + (1 - (o + 6)). Factor -2*k**2 - 4*k**2 + 2*k + 3*k**3 + 3*k**3 - m*k**4.
-2*k*(k - 1)**3
Let g = -12 - 1. Let t be (-17)/(-30) + g/78. Factor 0 + t*f**2 + 2/5*f**3 - 4/5*f.
2*f*(f - 1)*(f + 2)/5
Let z = 23 + -24. Let m be ((-10 - -4) + 1)*z. Factor 160*n**3 + m*n + 256*n**5 + 1/4 + 320*n**4 + 40*n**2.
(4*n + 1)**5/4
Suppose -3*d + 81 = 5*k, 2*k = -2*d - d + 36. Let g be (-156)/(-80) - 3/k. Determine v so that -1/2*v**2 - 7/4*v**3 + g*v + 1/2 = 0.
-1, -2/7, 1
Let b(i) = 21*i**2 + 36*i + 1. Let j(s) = -10*s**2 - 18*s. Let q(t) = 4*b(t) + 7*j(t). Factor q(a).
2*(a + 1)*(7*a + 2)
Let u(d) be the first derivative of -1 + 3/5*d + 9/10*d**2 + 3/5*d**3 + 3/20*d**4. Let u(j) = 0. Calculate j.
-1
Let -4/