 -12*v**3 - 16*v**2 - 12*v - 4. Let o(p) = -4*g(p) - 5*t(p). Factor o(y).
4*y*(y + 1)*(3*y + 2)
Let x(r) = -10*r**4 - 85*r**3 + 260*r**2 - 270*r + 90. Let u(m) = m**4 + 2*m**3 - m**2 + m. Let t(j) = 5*u(j) + x(j). Determine n so that t(n) = 0.
-18, 1
Suppose 0 = 3*d + 3, 3*d = -5*y + d + 18. Suppose -y*x + 5*x**2 + 2*x**3 - 7*x**3 - 5*x**4 + 9*x = 0. Calculate x.
-1, 0, 1
Let v = -9/10 - -23/20. Let u(a) be the first derivative of 0*a - v*a**2 + 3 - 1/12*a**3 + 1/16*a**4. Determine k, given that u(k) = 0.
-1, 0, 2
Let o(d) be the first derivative of -49*d**6/16 - 651*d**5/20 - 2043*d**4/32 + 155*d**3 - 75*d**2 + 300. What is y in o(y) = 0?
-5, 0, 4/7
Let c be (-40)/240 - (3 + (-1492)/456). Factor c*q**2 + 0 - 8/19*q.
2*q*(q - 4)/19
Let k(j) = 12 + 0*j**2 - 504*j - 4*j**2 + 526*j. Let u(t) = -3*t**2 + 21*t + 12. Let h(v) = -6*k(v) + 7*u(v). Find c, given that h(c) = 0.
-4, -1
Let i(f) be the first derivative of -5*f**4/2 - 155*f**3/3 + 220*f**2 - 180*f - 196. Let i(o) = 0. What is o?
-18, 1/2, 2
Factor 3*t**3 - 18*t + 12*t**2 + 46 - 38 - 5*t**3.
-2*(t - 4)*(t - 1)**2
Let x(g) be the second derivative of -g**7/147 - 2*g**6/105 + g**5/35 + 2*g**4/21 - g**3/21 - 2*g**2/7 - 134*g. Determine b, given that x(b) = 0.
-2, -1, 1
Let h = 542249/40 - 13555. Let t(j) be the second derivative of 0 + j**2 - 4*j - h*j**5 + 77/24*j**4 - 8/3*j**3. Factor t(y).
-(y - 1)*(7*y - 2)**2/2
Let n(h) be the first derivative of 2/3*h**6 - 6*h**2 + 8/3*h**3 + 4*h + 2*h**4 + 6 - 12/5*h**5. Find d, given that n(d) = 0.
-1, 1
Let w be 2*((-629)/102)/(-37). Factor -2/3*i + w*i**2 + 0 + 1/3*i**3.
i*(i - 1)*(i + 2)/3
Let m = 349/2022 - 2/337. Factor 1/2*g + 1/2*g**2 + 1/6*g**3 + m.
(g + 1)**3/6
Let m(c) be the third derivative of -c**7/630 + c**5/60 + c**4/36 + 3*c**2 - 10. Find l such that m(l) = 0.
-1, 0, 2
Suppose -3*z + 24 = 6. Suppose -z*k = -3*k - 6. Factor 1/2*j - 1/2*j**3 + 1/3*j**k - 1/3.
-(j - 1)*(j + 1)*(3*j - 2)/6
Let o(k) be the third derivative of k**8/336 + k**7/70 - k**6/120 - k**5/20 + k**2 + 18. Suppose o(t) = 0. What is t?
-3, -1, 0, 1
Let q(u) be the second derivative of -4/3*u**4 + 2*u**2 + 1/3*u**3 + 0 + 1/2*u**5 + 9*u. Find a such that q(a) = 0.
-2/5, 1
Let y be ((-165)/40 - -4)*-1290. Let n = 162 - y. Factor n*z**2 + 0*z - 3/4*z**3 + 0.
-3*z**2*(z - 1)/4
Let s(p) = p**2 + 1. Let x be s(1). Let u be -6*((-4)/3 - -1). Factor 5*k**3 - 4*k**3 - 9*k**2 - 4*k**3 + k**u - x - 7*k.
-(k + 1)**2*(3*k + 2)
Let f be ((-32)/28)/((-4)/14). Factor -2*x**2 + x**5 + x**4 - x - 2*x + f*x**3 - 2 - 2*x + 3*x**4.
(x - 1)*(x + 1)**3*(x + 2)
Let p(w) be the third derivative of w**8/840 + 2*w**7/525 - w**6/100 - 2*w**5/75 + w**4/15 + 62*w**2. What is f in p(f) = 0?
-2, 0, 1
Let j(f) be the second derivative of -f**5/30 + f**4/2 - 8*f**3/3 + 20*f**2/3 + 9*f. Solve j(d) = 0 for d.
2, 5
Let h(l) = l**2. Let m(f) = -3*f**2 - 10*f - 25. Let j be -7*((-16)/14)/(-4). Let w(x) = j*h(x) - m(x). Factor w(u).
(u + 5)**2
Let i(h) be the second derivative of -2*h**2 - 18*h + h**3 - 3/10*h**5 + 1/15*h**6 + 1/6*h**4 + 0. Factor i(m).
2*(m - 2)*(m - 1)**2*(m + 1)
Let g(o) = -o**4 + 7*o**3 - 9*o**2 + 5*o. Let c(r) = -6*r**4 + r**4 + 81*r + 111*r**3 - 2*r**4 - 8*r**4 - 144*r**2. Let q(j) = -2*c(j) + 33*g(j). Factor q(t).
-3*t*(t - 1)**3
Let w(y) be the first derivative of 1/5*y**3 + 0*y + 26 - 1/10*y**6 - 9/20*y**4 + 0*y**2 + 9/25*y**5. Let w(n) = 0. Calculate n.
0, 1
Let x(r) be the second derivative of -5*r**4/72 - 5*r**3/18 + 5*r**2/4 - 22*r. Factor x(c).
-5*(c - 1)*(c + 3)/6
Suppose 0 = 2*o - 2*l - 18, -30*l - 9 = 3*o - 29*l. Solve o*c - 4/5*c**2 + 0 + 6/5*c**3 - 2/5*c**4 = 0.
0, 1, 2
Let g(b) be the third derivative of -b**8/840 - b**7/210 + 19*b**3/3 + 19*b**2. Let z(t) be the first derivative of g(t). Factor z(m).
-2*m**3*(m + 2)
Let p(y) be the third derivative of 0*y - 35*y**2 + 0 + 1/276*y**4 + 1/230*y**5 - 1/23*y**3 - 1/1380*y**6. Factor p(z).
-2*(z - 3)*(z - 1)*(z + 1)/23
Let l(q) be the first derivative of 0*q**2 - 2/21*q**3 + 0*q - 10 - 1/14*q**4. Find o, given that l(o) = 0.
-1, 0
Suppose 0 = -5*x + x - 8. Let w be (-23 + 20)/(x/2). Determine g, given that 1 + w*g - 2*g**2 + 5*g - 1 - 8 = 0.
2
Let m(h) = h**2 - 3*h - 4. Let p be m(4). Let q = p - 0. Factor 0*f**3 - 2/3*f**4 + 0*f**2 + 2/3*f**5 + 0 + q*f.
2*f**4*(f - 1)/3
Let r(s) = -s**4 - 34*s**3 + 173*s**2 - 261*s + 123. Let v(i) = 2*i**4 + 32*i**3 - 174*i**2 + 262*i - 122. Let l(k) = 6*r(k) + 5*v(k). Solve l(o) = 0.
1, 2, 4
Solve 35*s + 1/4*s**3 - 34 - 19/2*s**2 = 0 for s.
2, 34
Let d(g) = g**2 + 4*g - 3. Let t be d(-6). Suppose 0 = -u - 3*u - f + t, -3 = -3*u - 2*f. Determine q, given that -q**3 + 3*q**u - q**2 - q**3 - 2*q**3 = 0.
-1, 0
Factor 0 + 3/5*x**3 + 0*x + 114/5*x**2.
3*x**2*(x + 38)/5
Suppose 6 = 4*l + 2, -5*b + 4*l + 21 = 0. Let m(n) be the first derivative of 4/7*n - 2/21*n**3 - b + 1/7*n**2. Suppose m(p) = 0. What is p?
-1, 2
Let w(f) be the first derivative of f**5/5 - 21*f**4/4 + 49*f**3 - 343*f**2/2 + 117. Factor w(l).
l*(l - 7)**3
Let l(z) = -3*z**3 - 2*z**2 + 9*z + 10. Let k(m) = -11*m**3 - 9*m**2 + 33*m + 40. Let r(a) = 2*k(a) - 9*l(a). Solve r(j) = 0 for j.
-1, 2
Suppose 4*m = -2*r + 2, 2*r + 3*m + 2 = -2*m. Factor -r + 11 - 3*x**2 + 1.
-3*(x - 1)*(x + 1)
Suppose 0 = -g - 3*q - 9, -11 = -2*g + 3*q + 16. Let s(j) = -j. Let b(p) = -4*p**2 + 14*p. Let y(a) = g*s(a) + b(a). Factor y(m).
-4*m*(m - 2)
Let g(l) be the first derivative of -2*l**3/27 - 3*l**2 - 138. Determine b, given that g(b) = 0.
-27, 0
Let h(l) be the second derivative of 9/28*l**4 + 3/35*l**5 - 5/7*l**3 - 9/14*l**2 - 8*l + 0. Factor h(f).
3*(f - 1)*(f + 3)*(4*f + 1)/7
Let z(x) = -x**2 - 11*x + 10. Let v(y) = -4*y**2 - 34*y + 31. Let k(f) = -2*v(f) + 7*z(f). Find w, given that k(w) = 0.
1, 8
Let q be 5 + -4 + -1 + 3. Let b(x) = x**3 + 7*x**2 - 5*x + 26. Let z be b(-8). Factor 0 - 3/4*f**q - 1/4*f**z - 1/2*f**4 + 0*f.
-f**2*(f + 1)*(2*f + 1)/4
Let p(f) be the first derivative of -f**5/45 + 5*f**4/36 + f**3/9 - 13*f**2/18 - 10*f/9 + 15. Find j, given that p(j) = 0.
-1, 2, 5
Let d(f) be the first derivative of f**5/5 - 5*f**4/4 - 8*f**3/3 + 6*f**2 + 160. Factor d(a).
a*(a - 6)*(a - 1)*(a + 2)
Let l(q) be the third derivative of q**7/42 + 11*q**6/60 - 17*q**5/60 - 5*q**4/12 - 113*q**2. Suppose l(p) = 0. Calculate p.
-5, -2/5, 0, 1
Factor 1/3*c**5 + 0 + 2*c + 5/3*c**4 - 7/3*c**3 - 5/3*c**2.
c*(c - 1)**2*(c + 1)*(c + 6)/3
Suppose 80*r**2 + 4*r**3 - 40 - 5*r - 5*r**4 + 6*r**3 - 5*r**5 - 19*r**4 - 16*r**4 = 0. What is r?
-8, -1, 1
Suppose -d - 2*z = -9, 8*d - z - 89 = 3*d. Let i be (-4)/(-11)*d/34. Factor -i*f**2 - 6/11*f - 4/11.
-2*(f + 1)*(f + 2)/11
Solve -7*m + 4*m**2 + 65*m + 110 - 951 - 5*m**2 = 0.
29
What is b in 0 + 2/9*b**2 - 2/9*b**3 + 4/9*b = 0?
-1, 0, 2
Let l(j) = 2*j - 17. Let t be l(12). Let h be (-14)/t*(-2 - -1). Determine d, given that -17 + d - h*d**2 + 7*d + 11 = 0.
1, 3
Let f be (-4)/(-18) - 20/9. Let h be -1 - (0 - 3) - f. Suppose -13*c**2 + 36*c - 90*c**3 - 20*c**2 + 49*c**4 - 13*c**4 + 12 + 39*c**h = 0. What is c?
-2/5, 1
Let l = 4837/2 + -2418. Determine u so that 7/4*u - 5/4*u**3 - 1/2*u**5 + l - 7/4*u**4 + 5/4*u**2 = 0.
-2, -1, -1/2, 1
Factor 1/10*a**2 + 16/5*a + 128/5.
(a + 16)**2/10
Let v(s) be the first derivative of 8/5*s**2 + 4/5*s + 27 - 3/5*s**3. Factor v(i).
-(i - 2)*(9*i + 2)/5
Factor 82*o**4 + 3 + 87*o**4 - 2*o**2 - 4*o**3 - 170*o**4 + 4*o.
-(o - 1)*(o + 1)**2*(o + 3)
Let a(o) be the third derivative of -o**7/1680 + o**6/96 - 13*o**5/480 - 5*o**4/16 - 3*o**3/4 + 2*o**2 + o. Factor a(c).
-(c - 6)**2*(c + 1)**2/8
Determine l, given that 29/2*l**3 - 6*l**4 - 9*l**2 + 0*l + 1/2*l**5 + 0 = 0.
0, 1, 2, 9
Let v be 0*1/((1 - 12/14)*7). Solve 9/8*k**3 + v - 3/4*k + 3/8*k**2 = 0 for k.
-1, 0, 2/3
Factor -70/11*s**2 - 2/11*s**4 - 34/11*s - 38/11*s**3 + 0.
-2*s*(s + 1)**2*(s + 17)/11
Let p(x) be the first derivative of -x**4/2 - 16*x**3/3 - 13*x**2 - 12*x - 97. Find q such that p(q) = 0.
-6, -1
Let u be 0 + (0 - 4)/2. Let m = u - -5. Let 9*j**5 - j**5 - m*j**5 - 5*j**4 = 0. What is j?
0, 1
Let j be 83/166*((-4)/6 - 56/(-12)). Factor 12/5 + 147/5*n**j + 84/5*n.
3*(7*n + 2)**2/5
Let o be (5/(-8))/(-1*(-7)/(-56)). Let m(q) be the first derivative of 0*q - 2/5*q**o + 4 - 2/3*q**3 + q**4 + 0*q**2. Suppose m(a) = 0. What is a?
0, 