.
-3*(p + 2)*(p + 3)
Let t(p) = 3*p**4 - 24*p**3 + 68*p**2 - 72*p + 27. Let o(j) = j**2. Let a(b) = 2*o(b) - t(b). Find m, given that a(m) = 0.
1, 3
Let n = 3 + 33. Suppose -164*i**2 + 78*i**2 + n*i + 82*i**2 = 0. What is i?
0, 9
Let b(t) = t**3 + 3*t**2 + t - 5. Let f(y) = 3*y**3 + 6*y**2 + 2*y - 11. Let p be (-93)/(-15) - (-2)/(-10). Let r(n) = p*f(n) - 15*b(n). Factor r(c).
3*(c - 3)*(c - 1)*(c + 1)
Let y be -2 + (-2 - (-12 - 1)). Let d = 28 - 25. Factor -11*v + 23*v - y*v - 3*v**2 - 1 + v**d.
(v - 1)**3
Let d(h) be the second derivative of -h**9/6804 + h**8/1512 - h**7/945 + h**6/1620 + h**3/2 - 7*h. Let o(t) be the second derivative of d(t). Factor o(l).
-2*l**2*(l - 1)**2*(2*l - 1)/9
Let r be 1632/20400 - 1/(50/(-146)). Factor 4/15*f - 4/15*f**r + 2/15*f**4 - 2/15*f**2 + 0.
2*f*(f - 2)*(f - 1)*(f + 1)/15
Let o(x) be the third derivative of 11*x**5/240 - x**4/24 - 5*x**2 + 3. Factor o(y).
y*(11*y - 4)/4
Let q(y) be the second derivative of y**6/6 - y**5 - 35*y**4/12 + 25*y**3/3 - 32*y - 5. Factor q(b).
5*b*(b - 5)*(b - 1)*(b + 2)
Let o = -24 - -26. Let i(n) = -n**3 + 2*n**2 + 3*n - 5. Let t be i(o). Solve 1 + 27*v**3 + t + v**5 + v**5 - 6*v - 23*v**3 + 4*v**2 - 6*v**4 = 0 for v.
-1, 1
Suppose -1232*i = -1215*i. Let j(u) be the third derivative of 0*u**5 + 0*u**3 + 1/112*u**8 + 8*u**2 + 9/40*u**6 - 3/35*u**7 + 0*u**4 + 0*u + i. Factor j(y).
3*y**3*(y - 3)**2
Let n(z) be the first derivative of -6*z**5/55 - 117*z**4/22 - 290*z**3/11 - 531*z**2/11 - 420*z/11 + 366. What is m in n(m) = 0?
-35, -2, -1
Let n be 2/(-15) + (-2 - 207/(-90)). Solve 1/6*j**3 - 1/6*j**4 + n*j**2 + 0*j + 0 - 1/6*j**5 = 0 for j.
-1, 0, 1
Suppose -10*w + 15*w = -12*w + 34. Let f = 1471/615 + 1/123. Let 48/5*d - 48/5 + 3/5*d**4 - f*d**3 + 0*d**w = 0. What is d?
-2, 2
Let a(v) be the first derivative of 5*v**3/3 - 10*v**2 - 25*v - 32. What is s in a(s) = 0?
-1, 5
Factor -4*i**2 + 8/3 - 4/3*i**3 + 4/3*i + 4/3*i**4.
4*(i - 2)*(i - 1)*(i + 1)**2/3
Let g(w) be the second derivative of -w**8/53760 - w**7/20160 + w**6/2880 - 5*w**4/12 + w. Let x(v) be the third derivative of g(v). Solve x(n) = 0.
-2, 0, 1
Let l(a) be the second derivative of -a**4/28 + 2*a**3/7 - 146*a. Factor l(r).
-3*r*(r - 4)/7
Let d be -1 - (-7 - (-2 - 0)). Let f be (-3)/10*75/270*-4. What is s in -f*s**d - 2/3*s + 2/3*s**3 + 0*s**2 + 1/3 = 0?
-1, 1
Let q(p) be the first derivative of 18/5*p**2 - 1/5*p**3 - 12/25*p**5 - 12/5*p - 9/5*p**4 - 4. Factor q(l).
-3*(l + 2)**2*(2*l - 1)**2/5
Let s(v) be the third derivative of v**5/300 - 11*v**4/120 + v**3/3 - 47*v**2. Determine w, given that s(w) = 0.
1, 10
Let o(q) be the second derivative of -q**5/20 + q**4/4 + q**3 - 4*q**2 + q - 175. Let o(g) = 0. Calculate g.
-2, 1, 4
Determine w so that 18*w**3 + 39*w**4 - 51*w**4 + 12*w**2 - 3*w**5 - 15*w**3 = 0.
-4, -1, 0, 1
Let n(g) be the second derivative of 0 - g + 3/8*g**2 + 5/16*g**3 + 1/32*g**4 - 3/80*g**5. Factor n(f).
-3*(f - 2)*(f + 1)*(2*f + 1)/8
Determine c, given that 3*c**3 + 27*c**4 + 18*c**4 + c**3 - 41*c**4 - 16*c - 16*c**2 = 0.
-2, -1, 0, 2
Let w(r) be the second derivative of r**8/4480 - r**6/480 + r**4/64 + r**3/2 + 8*r. Let p(k) be the second derivative of w(k). Factor p(g).
3*(g - 1)**2*(g + 1)**2/8
Let j be (-560)/(-2100)*(-5)/(-4). Suppose 4/3*o**2 + j*o**3 + 0 + 4/3*o = 0. Calculate o.
-2, 0
Let u(g) be the second derivative of g**7/420 + g**6/300 - g**5/100 + 11*g - 3. Solve u(y) = 0 for y.
-2, 0, 1
Let m(q) = -q**4 + q**2 + q + 2. Let d(c) = 30*c**5 + 25*c**4 - 25*c**3 - 25*c**2 + 5*c + 20. Let p(z) = d(z) - 10*m(z). Suppose p(a) = 0. Calculate a.
-1, -1/6, 0, 1
Let w(u) be the first derivative of 1/3*u**2 - 5/24*u**4 - 1/3*u**3 + 4/3*u - 1/30*u**5 + 1. Solve w(h) = 0.
-2, 1
Let m(y) be the third derivative of y**8/201600 - y**7/50400 + 2*y**5/15 - y**2. Let o(h) be the third derivative of m(h). Let o(x) = 0. What is x?
0, 1
Let n = -10 - 0. Let t = n + 12. Solve 3*y**2 + 3*y + 3*y - 10*y - y**t + 2*y**3 = 0.
-2, 0, 1
Let u(n) be the second derivative of 10*n - 2/3*n**2 - 3/20*n**5 + 0 - 29/36*n**4 - 4/3*n**3. Factor u(h).
-(h + 1)*(h + 2)*(9*h + 2)/3
Let w(u) = 31*u**2 - u + 1. Suppose -2*d + 1 = -d. Let q be w(d). Factor 12 - q*l**4 + 48*l**2 + 4*l**4 - 31*l**2 - 72*l + 106*l**2 + 21*l**5 - 57*l**3.
3*(l - 1)**3*(l + 2)*(7*l - 2)
Suppose 0*v - 2*v - 4 = 0. Let q be v + 6 - (-48)/(-14). Solve -2/7*n**4 + 0*n + q*n**3 + 0 - 2/7*n**2 = 0.
0, 1
Factor 8*i**2 - 33*i**2 - 2592 + 144*i + 12*i**2 + 11*i**2.
-2*(i - 36)**2
Determine p, given that 90*p - 98*p**2 + 58*p**3 + 11*p**2 - 76*p**3 - 42 + 177*p = 0.
-7, 1/6, 2
Let p(s) be the second derivative of -s**3/3 + 31*s. Let g(h) = 7*h**2 - 6*h**2 - h + 2 - 1 + 0*h. Let b(o) = 4*g(o) - 6*p(o). Factor b(f).
4*(f + 1)**2
Let z(a) be the first derivative of 9*a**6/14 - 603*a**5/35 + 1725*a**4/14 - 254*a**3/7 - 1749*a**2/14 - 363*a/7 + 164. Let z(f) = 0. What is f?
-1/3, 1, 11
Let t(j) be the first derivative of -j**3/3 + j**2/2 + 51. Find v such that t(v) = 0.
0, 1
Suppose 0 = -6*r - 23 + 107. Let y(o) be the first derivative of -49/15*o**6 - 8*o**2 - 5 - 47/2*o**4 - r*o**5 - 58/3*o**3 - 8/5*o. Factor y(l).
-2*(l + 1)**3*(7*l + 2)**2/5
Let l(x) be the first derivative of -3*x**5/25 + 6*x**4/5 - 17*x**3/5 + 3*x**2 - 5. Find f such that l(f) = 0.
0, 1, 2, 5
Suppose 3*o - 3 = 12. Factor 5*t + 4 + t - 4*t**2 - 10*t**5 - 8*t**3 + 12*t**o.
2*(t - 2)*(t - 1)*(t + 1)**3
Let w(u) be the first derivative of 18/5*u**2 + 3/20*u**4 - 6/5*u**3 + 6 - 24/5*u. Factor w(k).
3*(k - 2)**3/5
Let m be 6*(-2)/6 - 4*-1. Let i = 41/5 + -8. Factor -1/5*w + 2/5 - i*w**m.
-(w - 1)*(w + 2)/5
Let g = -13 - -15. Let t be (1 - 6)*(-2)/g. Factor -2 + 0*u**t + 4*u**5 - 4*u**3 - 2*u**4 - 2*u**5 + 4*u**2 + 2*u.
2*(u - 1)**3*(u + 1)**2
Let c(m) be the first derivative of -2*m**5/65 + 5*m**4/13 - 10*m**3/13 - 10*m**2/13 + 32*m/13 + 850. Determine v, given that c(v) = 0.
-1, 1, 2, 8
Factor 1/6*l**3 + 17/6*l**2 + 31/6*l + 5/2.
(l + 1)**2*(l + 15)/6
Suppose b + 4*b - 15 = 0. Factor 8*t**2 + t**b - 6*t**2 + 0*t**3.
t**2*(t + 2)
Let f(d) be the first derivative of 2*d**5 + 145*d**4/4 + 65*d**3/3 - 35*d**2 - 116. Solve f(u) = 0.
-14, -1, 0, 1/2
Let m be 0 + (0 - 1) + -3 + 6. Let o(v) be the first derivative of 7 + 0*v**m + 8/9*v - 1/18*v**4 - 2/9*v**3. Determine r so that o(r) = 0.
-2, 1
Let p(r) be the first derivative of -1/3*r**6 + 20/3*r**3 - 5*r**2 - 5*r**4 + 2*r**5 + 2*r - 24. Factor p(j).
-2*(j - 1)**5
Let g(u) = -7*u**4 + 4*u**3 - 36*u**2 + 260. Let o(x) = -16*x**4 + 9*x**3 - 73*x**2 + 521. Let n(d) = -9*g(d) + 4*o(d). Factor n(r).
-(r - 4)**2*(r + 4)**2
Let w be -331*3/(-645) + -1. Let q = -6/43 + w. Suppose 0 + q*x**2 - 2/5*x = 0. What is x?
0, 1
Let q(i) = 2*i**2 - 4*i + 6. Let m(v) = 2*v**2 - 4*v + 8. Let l(s) = 3*m(s) - 4*q(s). What is a in l(a) = 0?
0, 2
Suppose 0*g + 4*g = 20. Let o = -4 - -6. Find s such that g*s**4 - 3*s**3 + s + 7*s**5 - 5*s**o + 0*s + s - 6*s**3 = 0.
-1, 0, 2/7, 1
Let l = 29/22 + -1129/990. Let x(n) be the third derivative of 1/9*n**4 + 1/36*n**6 + 1/45*n**7 + 0*n**3 + n**2 + 0 - l*n**5 + 0*n. Let x(y) = 0. What is y?
-2, 0, 2/7, 1
Let -6*s + 45 + 1/5*s**2 = 0. What is s?
15
Let f(h) be the third derivative of h**7/735 + h**6/140 - h**5/210 - h**4/28 + 111*h**2. Factor f(v).
2*v*(v - 1)*(v + 1)*(v + 3)/7
Let s(m) = -2*m**3 + 7*m**2 - 2*m - 1. Let h be (-9)/5*(-5)/3. Let v be s(h). Factor u - 1/2 - 1/2*u**v.
-(u - 1)**2/2
Let r(p) be the first derivative of -p**6/360 + p**5/180 + 3*p**2/2 + 4. Let v(y) be the second derivative of r(y). Factor v(z).
-z**2*(z - 1)/3
Let d(i) be the second derivative of i**7/42 + i**6/8 - i**5/6 - 5*i**4/2 - 20*i**3/3 - 26*i**2 - 57*i. Let r(h) be the first derivative of d(h). Factor r(a).
5*(a - 2)*(a + 1)*(a + 2)**2
Let y(d) = 3*d**2 + 24. Suppose 4 = -2*k + 6. Suppose c = t + 14, c - 11 - 15 = 2*t. Let x(z) = z + 1. Let p(o) = k*y(o) + t*x(o). Factor p(m).
3*(m - 2)**2
Let j(t) = -t**3 + 27*t**2 - 29*t + 80. Let i be j(26). What is g in 1/3*g**i + 0*g + 0 - 1/3*g**3 = 0?
0, 1
Determine o, given that -19*o + 3*o**4 - 13*o**3 + 26*o**2 - 5*o + o**3 + 8 - o**4 = 0.
1, 2
Let m be 3456/11900 + (-12)/42 + 0. Let g = 856/1275 - m. Factor -10/3*v**2 - 8/3 + 16/3*v + g*v**3.
2*(v - 2)**2*(v - 1)/3
Factor -13*o - 78 - 597 - 4*o**2 + 103