- 6*p - 104. Suppose r(o) = 0. Calculate o.
-2, -1
Let n(m) be the first derivative of -2*m**3/3 + 12*m**2 + 26*m + 43. Factor n(r).
-2*(r - 13)*(r + 1)
Solve 15*g - 9 - 9*g**2 + 6*g + 116*g**5 - g**2 - 115*g**5 - 6*g**3 + 3*g**4 = 0 for g.
-3, 1
Let j be -5 - ((-8)/(-15))/((-4)/40). Find f such that -f**4 + f - 2/3*f**3 + 1/3 + 2/3*f**2 - j*f**5 = 0.
-1, 1
Suppose 15*f = 13*f - 114. Let j = f + 60. Factor 6/5*w**2 + 0 - 8/5*w**j + 2/5*w.
-2*w*(w - 1)*(4*w + 1)/5
Let v(q) be the first derivative of -q**5/20 - q**4/8 - 4*q**2 - 4. Let d(k) be the second derivative of v(k). Factor d(l).
-3*l*(l + 1)
Factor 672*p**3 - 116 - 262*p**3 + 120*p**2 - 298*p**3 + 2*p**4 - 6*p**4 - 112*p.
-4*(p - 29)*(p - 1)*(p + 1)**2
Let p(o) be the first derivative of -o**4/24 + 5*o**3/18 + o**2/2 + 84. Factor p(b).
-b*(b - 6)*(b + 1)/6
Suppose 0 = -0*r + 4*r - 24. Let k be r*(1 + (-2)/3). Factor 4*x**2 - 5*x**2 + x**4 + k*x**3 + 3 - 2*x - 3.
x*(x - 1)*(x + 1)*(x + 2)
Let z(k) = 25*k**2 + 10 + 14 + 28 - 2. Let g(y) = -y**2 - 1. Let j(v) = 30*g(v) + z(v). Find c, given that j(c) = 0.
-2, 2
Factor 0 + 14*u**4 + 0*u + 30*u**3 + 46/3*u**2 - 2/3*u**5.
-2*u**2*(u - 23)*(u + 1)**2/3
Let k(q) = q**3 - 18*q**2 - 7*q - 23. Let o be k(19). Suppose -3 - 2*i**2 + o*i + 3*i**2 - 203*i = 0. Calculate i.
-3, 1
Let c = 925 + -921. Let y(x) be the first derivative of 0*x + 1 - 3*x**2 - 3/4*x**c - 3*x**3. Factor y(v).
-3*v*(v + 1)*(v + 2)
Let m = -56/43 - -323/215. Factor 0*h + 0 - m*h**2.
-h**2/5
Let q = -36 - -39. Suppose -j = -2*o - 10, -17 = 5*o + 3. Suppose 1/3*i**q + 8/3 + j*i**2 + 4*i = 0. What is i?
-2
Let z be ((-16)/4*5/24)/(35/(-28)). Factor 2*y**2 + 10/3*y**4 + 0*y + 0 - 14/3*y**3 - z*y**5.
-2*y**2*(y - 3)*(y - 1)**2/3
Let w(x) = 2*x**4 - x**3 + x**2 - 1. Let l(t) = 3*t**4 - 7*t**3 + 5*t**2 + 24*t - 33. Let p(g) = l(g) - w(g). Factor p(v).
(v - 4)*(v - 2)**2*(v + 2)
Let u(v) be the second derivative of -v**7/560 - 11*v**6/1440 - v**5/120 - v**4/6 - 19*v. Let t(j) be the third derivative of u(j). Factor t(b).
-(b + 1)*(9*b + 2)/2
Let s be (-27 - -21)*(-1)/3. Factor -u**2 + 5*u**s - 110*u**3 - 4*u**4 + 106*u**3 + 4*u**5.
4*u**2*(u - 1)**2*(u + 1)
Let v(f) be the second derivative of 0*f**2 + 2/3*f**3 + f**4 + 0 - 6*f + 2/5*f**5. Factor v(s).
4*s*(s + 1)*(2*s + 1)
Let p = 37 + -181/5. Let m be (-2)/(6 - (-33)/(-3)). Factor 0 - m*y**2 - p*y.
-2*y*(y + 2)/5
Determine r so that 3232*r**4 - 6*r**2 - 3*r**5 + 32*r**3 - 3206*r**4 - 9*r**5 = 0.
-1, 0, 1/6, 3
Let y(l) be the first derivative of 9*l**4 + 12 + 3*l**3 + 21/5*l**5 - 3*l**2 + 0*l. Factor y(i).
3*i*(i + 1)**2*(7*i - 2)
Find l such that -2*l**2 - 10/3*l - 14/9 - 2/9*l**3 = 0.
-7, -1
Let r(b) = b**4 - b**3 + b. Let h(i) = 5*i. Let p be ((-16)/24)/(4/30). Let n(x) = p*r(x) + h(x). Let n(m) = 0. What is m?
0, 1
Let j(w) = 145*w**2 - 135*w - 7. Let u(o) = -100*o**2 + 90*o + 5. Let i(d) = 5*j(d) + 7*u(d). Factor i(m).
5*m*(5*m - 9)
Let i = -252419/420 + 601. Let s(v) be the third derivative of 1/80*v**6 + i*v**7 + 0*v + 1/60*v**5 - 8*v**2 + 0 + 0*v**3 + 0*v**4. Factor s(c).
c**2*(c + 1)*(c + 2)/2
Suppose 4*p - 3*u = -u + 20, 0 = -p - 3*u - 2. Solve 8*a - p*a**2 - 2 - 20*a + 3*a**2 + 9*a = 0.
-2, -1
Suppose 91*y - 660 = -41*y. Let 0*r + 1/3*r**2 + 1/3*r**3 + 0 - 1/3*r**4 - 1/3*r**y = 0. What is r?
-1, 0, 1
Let r(g) be the second derivative of 6*g - 1/2*g**2 + 1/3*g**3 - 1/12*g**4 + 0. Solve r(d) = 0 for d.
1
Let b(m) = -4*m**2 + 4*m. Let x(t) = t**2 - t. Let i be ((-20)/6 + 4)/(1/(-21)). Let n(h) = i*x(h) - 4*b(h). Factor n(q).
2*q*(q - 1)
Let l be (115/138)/((-30)/(-2)). Let h(b) be the second derivative of l*b**4 + 2/9*b**3 - 5*b + 0 + 1/3*b**2. Find d, given that h(d) = 0.
-1
Suppose -4*c = 5*s - 17, 4*s - 5 + 9 = -c. Let t(q) be the first derivative of 28*q**2 + 32/5*q**5 + 3 + c*q + 22*q**3 - 28*q**4. Find k, given that t(k) = 0.
-1/4, 2
Let z(h) = -25*h - 21. Let p be z(-1). Let q(l) be the second derivative of 1/12*l**3 + 0*l**2 + 1/48*l**p + 5*l + 0. Suppose q(a) = 0. What is a?
-2, 0
Let z(r) be the first derivative of -r**7/105 + 2*r**6/75 - 4*r - 11. Let y(s) be the first derivative of z(s). Determine p, given that y(p) = 0.
0, 2
Let j(c) = 2*c**2 - 15*c + 20. Let d be j(6). Let l be (-497)/(-315) - d/(-9). Factor -6/5 + 6/5*u**2 - l*u.
3*(u - 2)*(2*u + 1)/5
Let 652*z**2 - 4/9*z**5 - 1440*z + 1200 - 1228/9*z**3 + 116/9*z**4 = 0. What is z?
3, 10
Let p(y) = 23*y - 405. Let m be p(18). Let i(k) be the first derivative of -4*k - 2*k**2 + m - 1/3*k**3. Let i(r) = 0. Calculate r.
-2
Let b(c) be the third derivative of -7/30*c**4 + 0 - 1/3*c**3 + 0*c + 1/50*c**5 - 22*c**2. Suppose b(w) = 0. What is w?
-1/3, 5
Suppose -2*k = -27 + 19. Factor -2*v**k + 3*v**5 + v**5 - 6*v**4 + v - 5*v + 8*v**2.
4*v*(v - 1)**3*(v + 1)
Let w be (264/440)/((-18)/(-80)). Factor 2/3*s**3 + 0 - w*s**2 + 2*s.
2*s*(s - 3)*(s - 1)/3
Solve -16*t**4 + 4*t**2 + 16*t - 40*t - 18 + 8*t**3 + 14*t**4 = 0.
-1, 3
Let m = 441 + -438. Let c(f) be the first derivative of 2 + 1/9*f**2 + 1/9*f**4 + 0*f - 2/9*f**m. Factor c(t).
2*t*(t - 1)*(2*t - 1)/9
Let t(s) = 6*s**4 - 11*s**3 + 17*s**2 - 10*s + 3. Let j = 50 + -51. Let y(u) = u**4 - u**3 + u**2. Let n(k) = j*t(k) + 5*y(k). Factor n(m).
-(m - 3)*(m - 1)**3
Let b(q) be the first derivative of q**4/5 - 16*q**3/5 + 96*q**2/5 - 256*q/5 - 235. Factor b(t).
4*(t - 4)**3/5
Let r(w) be the third derivative of 0 - 11*w**2 - 16/15*w**3 + 1/300*w**6 - 1/5*w**4 + 2*w + 0*w**5. Factor r(z).
2*(z - 4)*(z + 2)**2/5
Let r(z) be the first derivative of 4*z**6/9 - 206*z**5/15 + 467*z**4/3 - 6688*z**3/9 + 3200*z**2/3 + 2048*z/3 - 129. What is x in r(x) = 0?
-1/4, 2, 8
Let b(s) be the second derivative of s**6/10 - 6*s**5/5 + 15*s**4/4 + 2*s - 24. Factor b(d).
3*d**2*(d - 5)*(d - 3)
Let h be ((-12)/8)/(6/(-8)). Suppose 0 = -3*m - 2*x + 9, 0 = -11*x + 6*x. Let 0 + 1/3*f**m - f**h + 2/3*f = 0. Calculate f.
0, 1, 2
Let m(s) be the first derivative of 3*s**4/14 - 29*s**3/7 + 111*s**2/14 + 78*s/7 + 101. Determine p, given that m(p) = 0.
-1/2, 2, 13
Solve -40/11 - 18/11*s**2 - 2/11*s**3 - 48/11*s = 0.
-5, -2
Let y be ((-55)/44)/((-15)/(-45) + (-12)/21). Suppose 4*o = 0, 6 = -2*k + 5*k + 3*o. Suppose -5/2*v**k + y*v**3 + 1/2 - 3/4*v - 5/2*v**4 = 0. Calculate v.
-2/5, 1/2, 1
Let o(z) = 3*z**3 + 3*z + 6. Let g be o(-2). Let i be (-10)/g + (-10)/60. Factor -i - 1/4*c + 1/4*c**2 + 1/4*c**3.
(c - 1)*(c + 1)**2/4
Let k = 24 - 27. Let u be 0/((-6)/9*k). Factor 0 - 12/5*q**3 + u*q**2 - 6/5*q**5 + 16/5*q**4 + 2/5*q.
-2*q*(q - 1)**3*(3*q + 1)/5
Let j = -217 + 222. Let g(x) be the third derivative of 1/12*x**4 + 0 + 0*x - 1/60*x**6 + 1/30*x**j + 0*x**3 + 3*x**2 - 1/105*x**7. Let g(r) = 0. What is r?
-1, 0, 1
Let m(t) be the third derivative of -t**6/270 - 7*t**5/135 + 7*t**4/18 + 2*t**3 + 6*t**2 + 14. Factor m(s).
-4*(s - 3)*(s + 1)*(s + 9)/9
Let j = 63/82 + -11/41. Determine q, given that -j*q**5 + 0*q + 1/2*q**4 + q**3 + 0 + 0*q**2 = 0.
-1, 0, 2
Let q(v) be the first derivative of v**3/27 + 41*v**2/18 - 14*v/3 - 73. Let q(s) = 0. Calculate s.
-42, 1
Solve 140/3*n**2 - 5/3*n**5 - 75*n + 230/3*n**3 - 60 + 40/3*n**4 = 0 for n.
-3, -1, 1, 12
Let m(s) be the third derivative of -s**6/40 - 13*s**5/20 - 5*s**4/4 + 12*s**3 - s**2 - 9. Determine r, given that m(r) = 0.
-12, -2, 1
Let x(u) be the first derivative of u**6/6 - 33*u**5/5 + 287*u**4/4 - 223*u**3/3 - 144*u**2 + 256*u - 24. Determine i so that x(i) = 0.
-1, 1, 16
Let l = -17549 - -193041/11. Suppose 4/11 + l*q**2 + 6/11*q = 0. What is q?
-2, -1
Let d = 5 - 3. Let r(q) be the first derivative of 1/2*q**4 + 0*q + 0*q**d + 6 + 2/3*q**3. Factor r(i).
2*i**2*(i + 1)
Let p(a) = -3*a - 3. Let n(u) = u**3 + u**2 - u. Let i be n(-2). Let r be p(i). Factor -6*h - 3*h**2 - 3*h**r - h**3 + 7*h**3.
3*h*(h - 2)*(h + 1)
Let u(q) = -q**3 + 11*q**2 + q. Let s(b) = -2*b**2. Let c = 19 - 30. Let r(p) = c*s(p) - 2*u(p). Factor r(v).
2*v*(v - 1)*(v + 1)
Let j(p) be the second derivative of p**8/5376 + p**7/672 + p**6/288 - 11*p**4/12 - 2*p. Let v(x) be the third derivative of j(x). Solve v(r) = 0 for r.
-2, -1, 0
Let v(o) be the third derivative of o**6/24 + 5*o**5/12 - 2*o**2 + 36*o. Factor v(b).
5*b**2*(b + 5)
Let q = 3173/99 + -119/33. Factor 32/3*a**2 - 16/9*a**3 + 256/9 + 1/9*a**4 - q*a.
(a - 4)**4/9
Let f(u) be