et c be s(9). Suppose 3*t - c = -0. Solve -t + 2*k + 5 + 6 - 3*k**2 + k**2 = 0 for k.
-1, 2
Suppose 79*t = -582 + 740. Factor o + 0 + 1/4*o**t.
o*(o + 4)/4
Let a be (1 - 2)*(-12)/60. Let s be 4/2*136/85. Factor -8/5*k - s - a*k**2.
-(k + 4)**2/5
Let y be 4 + -10 - -16 - (-141)/(-15). Factor -y*j**2 - 12/5*j + 3.
-3*(j - 1)*(j + 5)/5
Let x(a) be the first derivative of -a**5/210 + a**4/84 + 2*a**3/21 + 7*a**2 + 14. Let j(n) be the second derivative of x(n). Factor j(p).
-2*(p - 2)*(p + 1)/7
Let p be ((-1)/2)/(4/(-48)). Let k = p - 1. Let 20*x**2 + 17*x**5 - 9*x**k + 8*x**5 + 97*x**3 + 4*x + 72*x**4 + 16*x**2 = 0. What is x?
-2, -1/4, 0
Let o(f) be the third derivative of -13*f**2 + 1/210*f**5 + 0*f + 0*f**4 + 0 - 1/21*f**3. Determine i so that o(i) = 0.
-1, 1
Let i(m) = -7*m - 33. Let s be i(-5). Let w(q) be the second derivative of -8*q - 3/2*q**s + 0 + 3/20*q**5 - 1/2*q**3 + 1/4*q**4. Factor w(d).
3*(d - 1)*(d + 1)**2
Let f(l) be the third derivative of l**5/120 + 7*l**4/48 + 5*l**3/6 - 14*l**2 + 2*l. Let f(y) = 0. What is y?
-5, -2
Let s(c) = c**3 - 7*c**2 - 11*c + 7. Let t(l) = -l**3 + 6*l**2 + 11*l - 8. Let q(g) = 4*s(g) + 5*t(g). Factor q(z).
-(z - 4)*(z - 1)*(z + 3)
Let n be (2 - -9) + (-2 - 6). Let i(c) be the second derivative of 1/10*c**5 - 1/3*c**4 + 0*c**2 + 0 + 0*c**n + 1/15*c**6 + 4*c. Factor i(w).
2*w**2*(w - 1)*(w + 2)
Let g(j) be the third derivative of j**7/90 - 3*j**6/40 + 17*j**5/180 + j**4/24 - 194*j**2. Determine c, given that g(c) = 0.
-1/7, 0, 1, 3
Let y be 11/(66/18) - -2. Let h(n) be the third derivative of 0*n**4 - 1/105*n**5 + y*n**2 + 1/420*n**6 + 0*n**3 + 0*n + 0. Factor h(w).
2*w**2*(w - 2)/7
Suppose -3*t + 3*y = t - 1, 2*t + 4*y = -16. Let z be ((1/1)/t)/(27/(-144)). Solve 4/3*j**4 - z - 6*j**3 + 22/3*j**2 + 0*j = 0 for j.
-1/2, 1, 2
Let i(x) = 41*x**4 + 97*x**3 + 81*x**2 + 17*x + 10. Let g(m) = 20*m**4 + 48*m**3 + 40*m**2 + 8*m + 4. Let n(d) = 9*g(d) - 4*i(d). Factor n(h).
4*(h + 1)**3*(4*h - 1)
Let n = 61193/17 - 3599. Factor 8/17 - n*p + 2/17*p**2.
2*(p - 4)*(p - 1)/17
Let h(k) be the third derivative of k**9/10080 + k**8/3360 - k**7/1008 - k**6/720 + k**4/12 + 4*k**2. Let r(n) be the second derivative of h(n). Factor r(y).
y*(y - 1)*(y + 2)*(3*y + 1)/2
Suppose 588 = 3*a - 10*a. Let c = 254/3 + a. Factor -c*i**3 + 2/3*i + 0 + 0*i**2.
-2*i*(i - 1)*(i + 1)/3
Let d(n) be the first derivative of n**4/18 - 40*n**3/27 + 100*n**2/9 - 891. Find m, given that d(m) = 0.
0, 10
Find w, given that -246*w**2 - 4962312 + 1/3*w**3 + 60516*w = 0.
246
Let n(l) be the third derivative of -l**5/20 - 7*l**4 + 57*l**3/2 - 264*l**2. Find r, given that n(r) = 0.
-57, 1
Let u be 0*-8*1/(-8). Let 0*p + u*p**3 + 3/4*p**4 + 0*p**2 + 0 = 0. What is p?
0
Let o(v) = 7*v**4 + 35*v**3 - 15*v**2 - 273*v + 254. Let x(p) = 8*p**4 + 35*p**3 - 15*p**2 - 272*p + 256. Let u(i) = -3*o(i) + 2*x(i). Factor u(k).
-5*(k - 2)*(k - 1)*(k + 5)**2
Let p = -25 + 10. Let m(a) = 3*a**2 - 10*a + 7. Let d(f) = 12*f**2 - 39*f + 27. Let v(y) = p*m(y) + 4*d(y). Solve v(z) = 0 for z.
1
Let q(c) = c**2 + 40*c + 18. Let x(f) = f**2 + 20*f + 10. Let r(s) = 3*q(s) - 7*x(s). Factor r(i).
-4*(i + 1)*(i + 4)
Let k(i) be the second derivative of -i**4/72 + 2*i**3/3 - 12*i**2 - 44*i. Factor k(o).
-(o - 12)**2/6
Let p(o) = -3*o**2 + 18*o + 2. Let w(q) = 11*q**2 - 55*q - 7. Let j(d) = 21*p(d) + 6*w(d). Let j(s) = 0. What is s?
-16, 0
Let w(p) be the second derivative of -3*p**5/100 - 21*p**4/20 - 39*p**3/10 - 57*p**2/10 - 34*p. Find m such that w(m) = 0.
-19, -1
Let g = -186 + 281. Let n be 4/(-25)*g/(-152). Factor 1/10*x**4 - 1/10*x**3 + n*x + 1/5 - 3/10*x**2.
(x - 2)*(x - 1)*(x + 1)**2/10
Let d(y) be the second derivative of -y**4/28 + 6*y**3/7 - 30*y**2/7 + 29*y - 3. Determine a, given that d(a) = 0.
2, 10
Let i be 4 - ((-4)/4 - (3 - 1)). Let q(d) = -d**2 + 3*d + 30. Let p be q(i). Factor -2/3*s + 1/3*s**p + 1/3.
(s - 1)**2/3
Let n = 7355/4 + -1838. Factor -2*m**3 + 0 - 1/2*m - n*m**4 - 7/4*m**2.
-m*(m + 1)**2*(3*m + 2)/4
Determine c, given that 0 + 1/6*c**3 + 1/6*c**2 - 1/3*c = 0.
-2, 0, 1
Suppose -3*q + 4*q = 5. Suppose -q*b - s = -12, -2*s + 0 + 4 = 0. Find n, given that 1 + 7*n**b - 10*n**2 + 2*n**2 = 0.
-1, 1
Let v be ((-3)/9)/(6/(-54)). Let s(o) be the first derivative of 0*o**v + 4*o**2 - 1/2*o**4 + 0*o - 12. Factor s(p).
-2*p*(p - 2)*(p + 2)
Let b(u) be the first derivative of -u**6/2340 - u**5/130 + 11*u**3/3 - 1. Let y(v) be the third derivative of b(v). Find c such that y(c) = 0.
-6, 0
What is y in 25*y**3 + y**3 - 10*y**4 - 6*y**2 - 4*y - 2*y**2 - 4*y = 0?
-2/5, 0, 1, 2
Let p be -2 + ((-40)/(-125))/(8/80). Factor 3/5*f**3 - 6/5 + p*f**2 - 3/5*f.
3*(f - 1)*(f + 1)*(f + 2)/5
Let j(n) be the first derivative of 2*n**5/45 - 31*n**4/18 + 202*n**3/9 - 949*n**2/9 + 1352*n/9 - 85. Suppose j(m) = 0. What is m?
1, 4, 13
Factor -2*u**4 + 0 - 1/6*u**5 + 0*u**2 - 6*u**3 + 0*u.
-u**3*(u + 6)**2/6
Let u(m) be the second derivative of 1/18*m**3 - 1/90*m**6 - 1/12*m**4 + 2*m + 0*m**2 + 0 + 1/20*m**5. Let u(v) = 0. Calculate v.
0, 1
Suppose 0 = 6*z - 17 - 7. Suppose -3*t + 12 = 0, 3*t - z = 4*w - 0. Let -w*o - 13*o**4 + o + 0*o**2 + o**2 + 12*o**4 + o**3 = 0. Calculate o.
-1, 0, 1
Let l(j) be the third derivative of j**9/60480 - j**8/4032 - j**7/840 + j**5/30 - 18*j**2. Let d(a) be the third derivative of l(a). Factor d(x).
x*(x - 6)*(x + 1)
Let j = -3 - -2. Let c(r) = 13*r**2 + r + 1. Let x be c(j). Find m such that -3*m - 3*m**2 + 2*m - 2*m - x + 19 = 0.
-2, 1
Solve 260*o + 261*o + 254*o - 10*o**3 - 767*o - 16*o**2 = 0 for o.
-2, 0, 2/5
Let h(a) be the third derivative of a**5/40 - 3*a**4/16 + 22*a**2 - a. Factor h(l).
3*l*(l - 3)/2
Suppose -3*f - 3*i = -0*i - 54, -5*f - 3*i + 96 = 0. Let o = 25 - f. Solve j**4 - 5*j**3 + 4*j**3 - j**2 + j + 0*j**o = 0.
-1, 0, 1
Let n be (-80)/28 - (-2)/(-14) - -5. Let z(y) be the second derivative of -1/12*y**4 + 5/12*y**3 + 4*y - 3/4*y**n + 0. Find a such that z(a) = 0.
1, 3/2
Let i(p) be the first derivative of p**6/300 - p**5/50 - 8*p**2 + 2. Let m(n) be the second derivative of i(n). Determine b, given that m(b) = 0.
0, 3
Let z be (21/6)/((-1)/(-2)). Let v be (-7)/2*(-4)/z. Factor -l - 4*l**3 + 5*l**3 - v*l**2 + l + l.
l*(l - 1)**2
Let m = 4 - -2. Let f = m - 6. Solve f*v + 3*v - 5*v**2 - 4 + 3*v**2 + 3*v = 0.
1, 2
Let i(o) be the first derivative of -16*o**3/3 - 44*o**2 - 121*o - 144. Factor i(a).
-(4*a + 11)**2
Let q(i) be the third derivative of -i**8/36 - 38*i**7/315 - 4*i**6/45 + 4*i**5/45 + 47*i**2. Solve q(u) = 0 for u.
-2, -1, 0, 2/7
Let c(n) be the third derivative of -n**7/42 - 5*n**6/6 - 17*n**5/12 + 95*n**4/12 - n**2 + 12*n. Factor c(m).
-5*m*(m - 1)*(m + 2)*(m + 19)
Let i(t) be the first derivative of 2/9*t**2 + 0*t + 8 + 1/18*t**4 + 2/9*t**3. Suppose i(v) = 0. Calculate v.
-2, -1, 0
Let g(a) be the third derivative of 0 + 0*a - 10/3*a**3 - 5/6*a**4 + 18*a**2 - 1/12*a**5. Factor g(q).
-5*(q + 2)**2
Let r(s) be the third derivative of -1/84*s**8 - 1/6*s**4 + 0*s**3 - 11*s**2 + 8/105*s**7 + 0*s - 1/5*s**6 + 0 + 4/15*s**5. Factor r(o).
-4*o*(o - 1)**4
Let z(a) = 2*a**3 + 3 - 12*a + 12 + 0*a**3 - 4 + 9*a**2. Let t(o) = -3*o**3 - 10*o**2 + 12*o - 12. Let h(r) = -3*t(r) - 4*z(r). Factor h(j).
(j - 2)**3
Let s(n) be the first derivative of 5*n**4/4 + 20*n**3/3 - 25*n**2/2 - 68. Factor s(t).
5*t*(t - 1)*(t + 5)
Let t(g) be the third derivative of 1/30*g**5 + 0 + 33*g**2 + 2/3*g**3 - 1/4*g**4 + 0*g. Let t(h) = 0. Calculate h.
1, 2
Let c(u) be the third derivative of -37*u**5/570 + 109*u**4/228 + 2*u**3/19 + 339*u**2. Determine d so that c(d) = 0.
-2/37, 3
Factor 288/5 + 64/5*a**2 - 56*a + 2/5*a**3.
2*(a - 2)**2*(a + 36)/5
Suppose 0*b - 1 = b. Let x(z) = 25*z**2 + 2*z + 1. Let l be x(b). Solve 15*t**2 - l*t + t**3 + 4 + 8 + t**3 - 5*t**3 = 0 for t.
1, 2
Let a(h) = 16*h**2 - 40*h + 44. Let j(m) = 5*m**2 - 13*m + 14. Let l(z) = -3*a(z) + 10*j(z). Factor l(p).
2*(p - 4)*(p - 1)
Let a(i) be the first derivative of i**3/4 - 9*i**2/4 + 311. Factor a(n).
3*n*(n - 6)/4
Let m(o) be the first derivative of 1/2*o**2 + 0*o - 1/10*o**5 - 11 + 1/6*o**3 - 3/8*o**4 + 1/12*o**6. Determine f so that m(f) = 0.
-1, 0, 1, 2
Factor -648/11 + 72/11*t - 2/11*t**2.
-2*(t - 18)**2/11
Let n(r) = 31*r**2 - 11*r - 2. Let f(g) = 1. Let t(p) = 5*f(p) + n(p). Let 