0
Let v(k) be the second derivative of 0*k**2 + 4/9*k**3 + 1/45*k**6 - 1/10*k**5 - 3*k + 0 + 0*k**4. Factor v(z).
2*z*(z - 2)**2*(z + 1)/3
Suppose -3*h - 2*b - 1 = -b, -h - b - 1 = 0. Let s = -7 + 23/3. Factor 1/3*x**2 + h + s*x.
x*(x + 2)/3
Let g(z) be the first derivative of -7/12*z**3 - 3/16*z**4 - 1/4*z - 2 - 5/8*z**2. Factor g(n).
-(n + 1)**2*(3*n + 1)/4
Factor 103*j**3 + 3*j**2 - 3*j**5 + 102*j**3 - 202*j**3 - 3*j**4.
-3*j**2*(j - 1)*(j + 1)**2
Let m = -11 + 13. Suppose -m*q = -6*q. Find s such that -2/7*s**4 + q*s - 2/7*s**2 + 0 - 4/7*s**3 = 0.
-1, 0
Factor -2/5 + 9/5*z**3 + 1/5*z + 12/5*z**2.
(z + 1)*(3*z - 1)*(3*z + 2)/5
Let a = 97 + -97. Let i(k) be the first derivative of 0*k**5 + a*k**2 - 1 + 0*k**3 + 0*k - 1/24*k**6 + 0*k**4. Factor i(m).
-m**5/4
Factor -2*j**2 + 4 - 21*j + 20*j - 4.
-j*(2*j + 1)
Let w = 8 - 4. What is f in -4*f**w - f**4 + 3*f**4 + 2*f**3 = 0?
0, 1
Suppose -15 = 5*p - m, -2*p - 5*m = 2*p - 17. Let g(t) = -t**2. Let z(f) = -f + 3 - 3. Let i(r) = p*z(r) + 2*g(r). Suppose i(u) = 0. What is u?
0, 1
Let w(f) = -f**3 - 2*f**2 + 4*f + 3. Let h be w(-3). Let y = 4 - h. Factor 4*v + v**3 - v - y*v.
v*(v - 1)*(v + 1)
Let o = -25 - -30. Let m = 7 - o. Let h + 2/3 + 0*h**m - 1/3*h**3 = 0. Calculate h.
-1, 2
Let a(v) = -7*v**3 - 10*v**2 + 11*v + 18. Let f(h) = 15*h**3 + 21*h**2 - 21*h - 36. Let x(n) = 9*a(n) + 4*f(n). Determine s so that x(s) = 0.
-3, -1, 2
Let a be 2/4 - (-2)/(-4). Suppose -5*j + 0*j = a. Factor -1/2*g**5 - g**2 + 0 + j*g**3 + 1/2*g + g**4.
-g*(g - 1)**3*(g + 1)/2
Let p(z) = z**2 - 9*z + 11. Let c be p(8). Let w(j) = -j**2 + 5*j - 2. Let r be w(4). Solve 5*s + 0*s**r - 1 - 6*s + s**c + s**2 = 0.
-1, 1
Let z be -3*(1/3 + -1). Suppose -i = 5*o - 15, -i = -2*o - 3*o + 5. Suppose -2*s**o - s**z + s**2 = 0. Calculate s.
0
Let r(a) = 3*a**2 + 3*a + 2. Let c be r(-2). Let u be c*((-66)/(-21) + -3). Solve 0 - u*n - 162/7*n**3 + 72/7*n**2 = 0.
0, 2/9
Let y(k) be the second derivative of -k**7/63 + k**6/15 + k**5/15 - 2*k**4/3 + 8*k**3/9 - 44*k. Solve y(x) = 0 for x.
-2, 0, 1, 2
Suppose -3*j = -8*f + 4*f - 29, 26 = 2*j - 4*f. Factor 4/5*y**2 - 2/5*y**j - 2/5*y + 0.
-2*y*(y - 1)**2/5
Factor -2/5*d - 7/5*d**2 + 0 - d**3.
-d*(d + 1)*(5*d + 2)/5
Factor s + 3*s**3 - 3*s**3 - s**3 + s**2 - 5*s**4 + 4*s**4.
-s*(s - 1)*(s + 1)**2
Let f(z) be the second derivative of -11*z**4/4 - 10*z**3 + 6*z**2 - 15*z. Factor f(n).
-3*(n + 2)*(11*n - 2)
Let u(s) = s**2 + 5*s - 13. Let f be u(-7). Factor -2*l - f + 37*l**2 - 36*l**2 + 2.
(l - 1)**2
Let y be (2/(-3) + 1)*3. Let g(s) = s**2 - 50*s + 50*s + y. Let o(j) = 12*j**2 + 6. Let c(t) = -9*g(t) + o(t). What is f in c(f) = 0?
-1, 1
Let p(n) be the first derivative of n**5/20 + n**4/6 + n**3/6 - 3*n + 3. Let k(a) be the first derivative of p(a). Factor k(j).
j*(j + 1)**2
Factor 4*j - 22*j - 16*j**2 + 6*j - 20*j - 2*j**3.
-2*j*(j + 4)**2
Let o = -10/99 + 6/11. Let 0 - 2/3*v**2 - o*v - 2/9*v**3 = 0. Calculate v.
-2, -1, 0
Let h(a) be the second derivative of -3*a + 1/4*a**4 + 0 + 9/20*a**5 - 5/6*a**3 + 1/2*a**2. Suppose h(t) = 0. Calculate t.
-1, 1/3
Factor -75*h**4 - 6*h - 23*h**3 - 12*h**2 - 37*h**3 + 6*h.
-3*h**2*(5*h + 2)**2
Let u be -1*0/(-2) - (5 - 7). Suppose 6/5*b - 6/5*b**3 - 21/5*b**u + 21/5*b**4 + 0 = 0. What is b?
-1, 0, 2/7, 1
Let g(f) be the first derivative of -f**6/75 - 2*f**5/25 - f**4/6 - 2*f**3/15 + 3*f - 3. Let b(j) be the first derivative of g(j). Suppose b(n) = 0. What is n?
-2, -1, 0
Let w(l) = -l**2 - l + 1. Let z(b) = -4*b**2 + 1. Let x(y) = 3*w(y) - z(y). Suppose x(k) = 0. What is k?
1, 2
Let z(g) be the first derivative of -2*g**5/15 + g**4/6 + 4*g**3/9 + 6. Factor z(m).
-2*m**2*(m - 2)*(m + 1)/3
Let j be 6 - (-2)/(2 - 4). Let u = 7 - j. Determine g so that -2/3*g**u - 4/3*g - 2/3 = 0.
-1
Let i(l) be the third derivative of 7*l**6/180 - l**5/45 + l**2. Solve i(u) = 0 for u.
0, 2/7
Find x, given that 2 - 3/4*x**4 + 7/2*x - 5/4*x**2 - 7/2*x**3 = 0.
-4, -1, -2/3, 1
Suppose 0 = -58*j + 41*j + 34. Determine r so that 3/4*r + 1 - 7/4*r**j = 0.
-4/7, 1
Find s, given that 3*s - 3/7*s**3 - 12/7*s**2 + 30/7 = 0.
-5, -1, 2
Suppose -3/2 - 17/4*b - 15/4*b**2 + 1/4*b**4 - 3/4*b**3 = 0. Calculate b.
-1, 6
Suppose 0 = 3*w + w - 8. Let t(a) be the second derivative of a + 7/6*a**4 + 2*a**w + 0 - 3*a**3. Factor t(c).
2*(c - 1)*(7*c - 2)
Let j(u) be the third derivative of u**6/50 + u**5/75 - 4*u**4/15 + 8*u**3/15 + 14*u**2. Solve j(f) = 0 for f.
-2, 2/3, 1
Let s(x) be the first derivative of -72*x**6 + 72*x**5 + 285*x**4/4 - 125*x**3 + 60*x**2 - 12*x + 7. Let s(b) = 0. Calculate b.
-1, 1/4, 2/3
Suppose 2*j + 65 = 7*j. Suppose -c + i = 1, 2*c + 3*i + 0 = j. Factor -6/5*r**c + 4/5 + 2/5*r.
-2*(r - 1)*(3*r + 2)/5
Factor 4/3*p**3 + 32/3 + 16*p + 8*p**2.
4*(p + 2)**3/3
Let g(p) be the first derivative of -p**6/120 + p**5/80 - 5*p + 1. Let x(l) be the first derivative of g(l). Factor x(y).
-y**3*(y - 1)/4
Let q(w) = 10*w**5 - 4*w**4 - 8*w**3 + 9*w**2 + 7*w. Let s(z) = -9*z**5 + 4*z**4 + 7*z**3 - 8*z**2 - 6*z. Let i(u) = -6*q(u) - 7*s(u). Factor i(b).
b**2*(b - 1)**2*(3*b + 2)
Let x(i) be the second derivative of i**9/68040 - i**7/3780 + i**6/1620 + 2*i**4/3 - 3*i. Let t(a) be the third derivative of x(a). Factor t(v).
2*v*(v - 1)**2*(v + 2)/9
Suppose -3*q = -2*q - 2. Factor -t**4 - 2*t**4 - 12*t**3 + 0*t**3 - 14*t**2 + q*t**2.
-3*t**2*(t + 2)**2
Let p(t) be the first derivative of t**6/2 - 3*t**4/2 + 3*t**2/2 + 9. Suppose p(v) = 0. Calculate v.
-1, 0, 1
Let n be (0 - -1)*(-12 - -15). Find m, given that 12/7*m**n + 8/7*m**2 + 8/7*m**4 + 0 + 2/7*m + 2/7*m**5 = 0.
-1, 0
Let w be -1 + (6 - (-1)/(-1)). Suppose 3*v - 2*v - 2*v**2 + w - 2*v - v = 0. Calculate v.
-2, 1
Let a = -382/45 + 80/9. Suppose -6/5*q**2 - 2/5*q**3 - 6/5*q - a = 0. What is q?
-1
Let k(r) be the third derivative of -1/20*r**5 + 5*r**2 + 1/60*r**6 + 0*r + 0*r**3 - 1/12*r**4 + 0. What is f in k(f) = 0?
-1/2, 0, 2
Let j = -363 + 363. Factor 2/7*w - 18/7*w**3 - 8/7*w**5 - 2/7*w**2 - 22/7*w**4 + j.
-2*w*(w + 1)**3*(4*w - 1)/7
Let w(r) be the third derivative of -r**8/1176 + r**6/210 - r**4/84 + 6*r**2. Let w(v) = 0. What is v?
-1, 0, 1
Let s(i) be the first derivative of i**7/105 - i**6/75 - i**5/50 + i**4/30 + 2*i - 2. Let n(w) be the first derivative of s(w). Factor n(x).
2*x**2*(x - 1)**2*(x + 1)/5
Let f(z) be the second derivative of z**7/525 + z**6/900 - z**5/75 - z**4/60 + z**3 - 4*z. Let o(i) be the second derivative of f(i). Factor o(u).
2*(u - 1)*(u + 1)*(4*u + 1)/5
Let i(o) be the second derivative of -1/72*o**4 + 3*o + 1/45*o**5 + 0 + 0*o**3 + 3/2*o**2. Let m(t) be the first derivative of i(t). Find q such that m(q) = 0.
0, 1/4
Let 2*v + 28*v**3 + 2*v + 15*v**4 + 20*v**2 - 3*v**4 = 0. What is v?
-1, -1/3, 0
Let k be (-5)/(-3 + 4 - 2). Suppose -7*p**2 + 3*p - k*p**2 - p + 9*p**3 + p = 0. What is p?
0, 1/3, 1
Suppose -r + d - 3 = 4*d, -2*d - 16 = -4*r. Factor 0 - 5/3*j**4 + 0*j - 2/3*j**2 + 7/3*j**r.
-j**2*(j - 1)*(5*j - 2)/3
Let p be (5/(-10)*-4)/((-5)/(-5)). Factor 7/3*q**p + 3*q + 2/3.
(q + 1)*(7*q + 2)/3
Let d(q) be the second derivative of -3*q**5/40 + q**4/8 + q**3 - 3*q**2 - 5*q. Factor d(i).
-3*(i - 2)*(i - 1)*(i + 2)/2
Let i be (-68)/(-18) + (-2)/(-9). Determine t, given that 2*t**4 + 4*t**2 - t**i + 4*t + 0*t - 5*t**4 - 4*t**3 = 0.
-1, 0, 1
Suppose -11 + 51 = 8*c. Let -4/5*z + 0 - 5*z**4 + c*z**3 + 4/5*z**2 = 0. What is z?
-2/5, 0, 2/5, 1
Let d be ((-4)/(-5))/(4/10). Suppose -12 = -d*w - 0*w. Factor q**2 - w*q**2 + 4 + 2*q**2 + 3*q + q.
-(q - 2)*(3*q + 2)
Let s(j) be the third derivative of -j**6/120 - j**5/30 + j**4/24 + j**3/3 - 30*j**2. Factor s(g).
-(g - 1)*(g + 1)*(g + 2)
Let f(r) = -3*r**2 + 6*r - 2. Let n(q) = -7*q**2 + 13*q - 3. Let w(c) = -5*f(c) + 2*n(c). Suppose w(y) = 0. Calculate y.
2
Suppose 0 = 4*r + r - 10. Factor -c**3 - 3*c**3 + 4*c - 4*c**2 - 2*c**3 + r*c + 4.
-2*(c - 1)*(c + 1)*(3*c + 2)
Factor 15*y**2 - 5*y**2 - 15*y**4 + 5*y**3 - 2*y**3 + 2*y**3.
-5*y**2*(y - 1)*(3*y + 2)
Let w be 1*(6/(-3) - 0). Let p be (1/w)/(3/(-27)). Factor -p*t**4 + 4*t**2 - 16*t - 8 + 12*t**3.
-(t - 2)**2*(3*t + 2)**2/2
Let p(m) be the first derivative of m**4 - 16*m**3/3 + 10*m**2 - 8*m - 9. Suppose p(c) = 0. Calculate c.
1, 2
Let g be (-2)/1080*(-42)/4. Let f(b) be the third derivative of 4/9*b**3 - g*b**6 + 