Question 7

Which of the following is the value of m for which the polynomial $$x^{4}+10x^{3}+25x^{2}+15x+m $$ is exactly divisible by $$x+7$$?

Solution

$$f(x)=x^{4}+10x^{3}+25x^{2}+15x+m $$ is exactly divisible by $$x+7$$. Thus, $$x+7$$ is a factor of $$f(x)$$

Therefore, using the remainder theorem, $$f(-7)=0$$

$$(-7)^{4}+10(-7)^{3}+25(-7)^{2}+15(-7)+m=0$$

$$2401-3430+1225-105+m=0$$

$$-1134+1225+m=0$$

$$m=-91$$

View More Questions From Algebra

MAT Quant Questions | MAT Quantitative Ability

MAT Functions, Graphs and Statistics Questions MAT Venn Diagrams Questions MAT Remainders Questions MAT Inequalities Questions MAT Logarithms Questions MAT Time Speed Distance Questions MAT Linear Equations Questions MAT Number Systems Questions MAT Time, Speed and Distance Questions MAT Algebra Questions MAT Averages Mixtures Alligations Questions MAT Progressions and Series Questions MAT Geometry Questions MAT Averages, Ratio and Proportion Questions MAT Number Series Questions MAT Averages Questions MAT Mensuration Questions MAT Arithmetic Questions MAT Data Sufficiency Questions MAT Probability, Combinatorics Questions MAT Profit And Loss Questions MAT Quadratic Equations Questions MAT Time And Work Questions MAT Percentages Questions MAT Coordinate Geometry Questions MAT Simple Interest Compound Interest Questions MAT Profit and Loss Questions MAT Logarithms, Surds and Indices Questions

MAT DILR Questions | LRDI Questions For MAT

MAT DI Miscellaneous Questions MAT Maxima-Minima Questions MAT 2D & 3D LR Questions MAT Coins and Weights Questions MAT Quant Based DI Questions MAT Venn Diagrams Questions MAT Table based DI Sets Questions MAT Puzzles Questions MAT Quant Based LR Questions MAT Special Charts Questions MAT Data change over a period Questions MAT Data Interpretation Questions MAT Routes And Networks Questions MAT Arrangement Questions MAT Charts Questions MAT Scheduling Questions MAT Selection With Condition Questions MAT Truth Lie Concept Questions MAT Data Interpretation Basics Questions MAT Miscellaneous LR Questions MAT Games and Tournamnents Questions MAT DI with connected data sets Questions

MAT Verbal Ability Questions | VARC Questions For MAT

MAT Para Jumbles Questions MAT Reading Comprehension Questions MAT Grammar and Sentence Correction Questions MAT Para Summary Questions MAT Miscellaneous Questions MAT Critical Reasoning Questions MAT Vocabulary Questions MAT Odd One Out Questions MAT Verbal Ability Questions

Free MAT Topicwise Questions

MAT Mensuration

MAT Routes And Networks

MAT Simple Interest Compound Interest

MAT Reading Comprehension

MAT Percentages

MAT Number Systems

MAT Table based DI Sets

MAT Quant Based DI

MAT Inequalities

MAT Para Summary

MAT Averages Mixtures Alligations

MAT DI Miscellaneous

MAT Data change over a period

MAT Arrangement

MAT Time Speed Distance

MAT Averages, Ratio and Proportion

MAT Coordinate Geometry

MAT Truth Lie Concept

MAT Progressions and Series

MAT Coins and Weights

MAT Probability, Combinatorics

MAT Grammar and Sentence Correction

MAT Functions, Graphs and Statistics

MAT Quant Based LR

MAT Data Interpretation Basics

MAT DI with connected data sets

MAT Special Charts

MAT Miscellaneous LR

MAT Time And Work

MAT Verbal Ability

MAT Venn Diagrams

MAT Data Interpretation

MAT Time, Speed and Distance

MAT Profit And Loss

MAT Logarithms, Surds and Indices

MAT Games and Tournamnents

MAT Quadratic Equations

MAT Profit and Loss

MAT Selection With Condition

MAT Odd One Out

MAT Para Jumbles

MAT Data Sufficiency

MAT Ssc Reasoning

MAT Miscellaneous

MAT Critical Reasoning

MAT Number Series

MAT Linear Equations

MAT Venn Diagrams

MAT Maxima-Minima